# LaTeX2HTML 2021 (Released January 1, 2021)
# Associate images original text with physical files.


$key = q//;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5153.png"
 ALT="$\displaystyle = -\frac{h}{\mu} \frac{1}{e}\left[\cos\theta F_r-\left(\frac{2+...
...theta F_\theta \right] -\frac{\cos I \sin(\omega+\theta) r F_z}{h \sin I},$">|; 

$key = q/';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.67ex; vertical-align: 0.76ex; " SRC="|."$dir".q|img965.png"
 ALT="$'$">|; 

$key = q/(1+pislash2)sqrt{Rslashg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img532.png"
 ALT="$(1+\pi/2)\sqrt{R/g}$">|; 

$key = q/(1slash2),cos(alpha_n-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1764.png"
 ALT="$(1/2) \cos(\alpha_n-\phi)$">|; 

$key = q/(3slash2),(J_2+zeta)=0.0626;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1207.png"
 ALT="$(3/2) (J_2+\zeta)= 0.0626$">|; 

$key = q/(3slash2),(J_2+zeta)=3.35times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1198.png"
 ALT="$(3/2) (J_2+\zeta)= 3.35\times 10^{-3}$">|; 

$key = q/(8slash15),(6slashmu)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img298.png"
 ALT="$(8/15) (6/\mu)^{1/2}$">|; 

$key = q/(Eslashc),{bfe}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2811.png"
 ALT="$(E/c) {\bf e}_r$">|; 

$key = q/(Tslashpi),(e,sinhphi-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img928.png"
 ALT="$(T/\pi) (e \sinh \phi-\phi)$">|; 

$key = q/(aslashR),[mslash(m+M)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2926.png"
 ALT="$(a/R) [m/(m+M)]$">|; 

$key = q/(aslashR)tmspace+thinmuskip{.1667em}[mslash(m+M)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img79.png"
 ALT="$(a/R)\tmspace +\thinmuskip {.1667em}[m/(m+M)]$">|; 

$key = q/(g_1-g_5)-(f_1-f_2)simeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2638.png"
 ALT="$(g_1-g_5)-(f_1-f_2)\simeq 0 $">|; 

$key = q/(g_4-g_3)-(f_4-f_3)simeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2637.png"
 ALT="$(g_4-g_3)-(f_4-f_3)\simeq 0$">|; 

$key = q/(m,l^{,2},omegaslash12),sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2080.png"
 ALT="$(m l^{ 2} \omega/12) \sin\alpha$">|; 

$key = q/(m,l^{,2}omega^{,2}slash12),sinalpha,cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2081.png"
 ALT="$(m l^{ 2}\omega^{ 2}/12) \sin\alpha \cos\alpha$">|; 

$key = q/(muslasha^{,3})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2782.png"
 ALT="$(\mu/a^{ 3})^{1/2}$">|; 

$key = q/(x',,y',,z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3953.png"
 ALT="$(x',  y',  z')$">|; 

$key = q/(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2315.png"
 ALT="$(x, y, z)$">|; 

$key = q/(x_0,,y_0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2249.png"
 ALT="$(x_0, y_0, 0)$">|; 

$key = q/(xi,,eta,,zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2314.png"
 ALT="$(\xi, \eta, \zeta)$">|; 

$key = q/({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4263.png"
 ALT="$({\bf r})$">|; 

$key = q/+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img840.png"
 ALT="$+\infty$">|; 

$key = q/+lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1335.png"
 ALT="$+\lambda$">|; 

$key = q/+pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img684.png"
 ALT="$+\pi$">|; 

$key = q/+pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img242.png"
 ALT="$+\pi/4$">|; 

$key = q/+z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1238.png"
 ALT="$+z$">|; 

$key = q/-1leqxleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img430.png"
 ALT="$-1\leq x\leq 1$">|; 

$key = q/-1leq{calE}leq2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img36.png"
 ALT="$-1\leq {\cal E}\leq 2$">|; 

$key = q/-2,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1120.png"
 ALT="$-2 m $">|; 

$key = q/-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.17ex; vertical-align: 0.43ex; " SRC="|."$dir".q|img1098.png"
 ALT="$-$">|; 

$key = q/-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.89ex; vertical-align: 0.04ex; " SRC="|."$dir".q|img839.png"
 ALT="$-\infty$">|; 

$key = q/-lleqmleql;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img4108.png"
 ALT="$-l\leq m\leq l$">|; 

$key = q/-m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1118.png"
 ALT="$-m $">|; 

$key = q/-partialdot{X}slashpartialc_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4678.png"
 ALT="$-\partial \dot{X}/\partial c_j$">|; 

$key = q/-partialdot{Y}slashpartialc_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4679.png"
 ALT="$-\partial \dot{Y}/\partial c_j$">|; 

$key = q/-partialdot{Z}slashpartialc_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4680.png"
 ALT="$-\partial \dot{Z}/\partial c_j$">|; 

$key = q/-pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img683.png"
 ALT="$-\pi$">|; 

$key = q/-pislash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img243.png"
 ALT="$-\pi/4$">|; 

$key = q/-tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1284.png"
 ALT="$-\tau$">|; 

$key = q/-theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3957.png"
 ALT="$-\theta$">|; 

$key = q/-x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3987.png"
 ALT="$-x$">|; 

$key = q/-y(-t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2360.png"
 ALT="$-y(-t)$">|; 

$key = q/-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1239.png"
 ALT="$-z$">|; 

$key = q/-{bff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img370.png"
 ALT="$-{\bf f}$">|; 

$key = q/-{mitOmega}_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1735.png"
 ALT="$-{\mit\Omega}_\phi$">|; 

$key = q/0.07480;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3664.png"
 ALT="$0.07480$">|; 

$key = q/0.083;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img936.png"
 ALT="$0.083$">|; 

$key = q/0.19,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1274.png"
 ALT="$0.19 {\rm m}$">|; 

$key = q/0.2'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1657.png"
 ALT="$0.2''$">|; 

$key = q/0.238;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img881.png"
 ALT="$0.238$">|; 

$key = q/0.252;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img878.png"
 ALT="$0.252$">|; 

$key = q/0.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1650.png"
 ALT="$0.2$">|; 

$key = q/0.36;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1015.png"
 ALT="$0.36$">|; 

$key = q/0.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1114.png"
 ALT="$0.3$">|; 

$key = q/0.41,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1273.png"
 ALT="$0.41 {\rm m}$">|; 

$key = q/0.41;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1029.png"
 ALT="$0.41$">|; 

$key = q/0.43'',{rmyr}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2892.png"
 ALT="$0.43'' {\rm yr}^{-1}$">|; 

$key = q/0.43;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1030.png"
 ALT="$0.43$">|; 

$key = q/0.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4607.png"
 ALT="$0.4$">|; 

$key = q/0.50'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3770.png"
 ALT="$0.50''$">|; 

$key = q/0.67;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1016.png"
 ALT="$0.67$">|; 

$key = q/0.967;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img882.png"
 ALT="$0.967$">|; 

$key = q/0.98560912^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3701.png"
 ALT="$0.98560912^\circ$">|; 

$key = q/0<beta<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4376.png"
 ALT="$0&lt;\beta&lt; 1$">|; 

$key = q/0<bleqa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img3986.png"
 ALT="$0&lt;b\leq a$">|; 

$key = q/0<e<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img681.png"
 ALT="$0&lt;e &lt; 1$">|; 

$key = q/0<ell1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img786.png"
 ALT="$0&lt;e\ll 1$">|; 

$key = q/0<epsilonll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1060.png"
 ALT="$0&lt;\epsilon\ll 1$">|; 

$key = q/0<j_1,,j_2,,j_3<1000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3729.png"
 ALT="$0&lt; j_1, j_2, j_3&lt; 1000$">|; 

$key = q/0<k,all1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1053.png"
 ALT="$0&lt;k a\ll 1$">|; 

$key = q/0<mu_2leq0.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2295.png"
 ALT="$0&lt;\mu_2\leq 0.5$">|; 

$key = q/0<zeta<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3694.png"
 ALT="$0&lt;\zeta&lt;1$">|; 

$key = q/0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img803.png"
 ALT="$0^\circ$">|; 

$key = q/0leqEleqpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img722.png"
 ALT="$0\leq E\leq \pi/2$">|; 

$key = q/0leqaleqR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img4412.png"
 ALT="$0\leq a\leq R$">|; 

$key = q/0leqalpha<3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img4413.png"
 ALT="$0\leq \alpha &lt; 3$">|; 

$key = q/0leqell1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img699.png"
 ALT="$0\leq e\ll 1$">|; 

$key = q/0leqthetaleqpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img431.png"
 ALT="$0\leq\theta\leq \pi$">|; 

$key = q/0leqthetaleqpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img723.png"
 ALT="$0\leq\theta\leq\pi/2$">|; 

$key = q/0leqzetaleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2364.png"
 ALT="$0\leq \zeta\leq 1$">|; 

$key = q/1+(3slash2),beta+{calO}(beta^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2353.png"
 ALT="$1+(3/2) \beta+{\cal O}(\beta^{ 2})$">|; 

$key = q/1.08times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1197.png"
 ALT="$1.08\times 10^{-3}$">|; 

$key = q/1.1^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1942.png"
 ALT="$1.1^\circ$">|; 

$key = q/1.23times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2928.png"
 ALT="$1.23\times 10^{-2}$">|; 

$key = q/1.2^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1943.png"
 ALT="$1.2^\circ$">|; 

$key = q/1.2times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2940.png"
 ALT="$1.2\times 10^{-3}$">|; 

$key = q/1.47times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1206.png"
 ALT="$1.47\times 10^{-2}$">|; 

$key = q/1.48times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2949.png"
 ALT="$1.48\times 10^{-3}$">|; 

$key = q/1.496times10^{11},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img751.png"
 ALT="$1.496\times 10^{11} {\rm m}$">|; 

$key = q/1.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4392.png"
 ALT="$1.4$">|; 

$key = q/1.4^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1809.png"
 ALT="$1.4^\circ$">|; 

$key = q/1.59^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1915.png"
 ALT="$1.59^\circ$">|; 

$key = q/1.5times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2944.png"
 ALT="$1.5\times 10^{-3}$">|; 

$key = q/1.659times10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img763.png"
 ALT="$1.659\times 10^{-7}$">|; 

$key = q/1.65times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2941.png"
 ALT="$1.65\times 10^{-3}$">|; 

$key = q/1.7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1297.png"
 ALT="$1.7$">|; 

$key = q/1.87'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1938.png"
 ALT="$1.87''$">|; 

$key = q/106;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3528.png"
 ALT="$106$">|; 

$key = q/10^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img573.png"
 ALT="$10^3$">|; 

$key = q/10^5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img73.png"
 ALT="$10^5$">|; 

$key = q/10^{,4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2924.png"
 ALT="$10^{ 4}$">|; 

$key = q/10^{-4},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2854.png"
 ALT="$10^{-4} {\rm m}$">|; 

$key = q/11.1,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img503.png"
 ALT="$11.1 {\rm km}$">|; 

$key = q/11.1tmspace+thinmuskip{.1667em}{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1.png"
 ALT="$11.1\tmspace +\thinmuskip {.1667em}{\rm km}$">|; 

$key = q/11.45;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1005.png"
 ALT="$11.45$">|; 

$key = q/12.07;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1004.png"
 ALT="$12.07$">|; 

$key = q/12.79;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1006.png"
 ALT="$12.79$">|; 

$key = q/125;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3529.png"
 ALT="$125$">|; 

$key = q/13.176359^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3700.png"
 ALT="$13.176359^\circ$">|; 

$key = q/13.1764^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2045.png"
 ALT="$13.1764^\circ$">|; 

$key = q/13.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img877.png"
 ALT="$13.4$">|; 

$key = q/135^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3466.png"
 ALT="$135^\circ$">|; 

$key = q/14.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2951.png"
 ALT="$14.4$">|; 

$key = q/14.76;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1346.png"
 ALT="$14.76$">|; 

$key = q/148;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2394.png"
 ALT="$148$">|; 

$key = q/15.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img879.png"
 ALT="$15.3$">|; 

$key = q/15.7'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1935.png"
 ALT="$15.7''$">|; 

$key = q/16';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img875.png"
 ALT="$16'$">|; 

$key = q/16.28;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1007.png"
 ALT="$16.28$">|; 

$key = q/16.8'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1936.png"
 ALT="$16.8''$">|; 

$key = q/16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1264.png"
 ALT="$16$">|; 

$key = q/17.2'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1818.png"
 ALT="$17.2''$">|; 

$key = q/17.75;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1008.png"
 ALT="$17.75$">|; 

$key = q/17.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3660.png"
 ALT="$17.8$">|; 

$key = q/18.59;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1012.png"
 ALT="$18.59$">|; 

$key = q/18.615;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3704.png"
 ALT="$18.615$">|; 

$key = q/18.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1754.png"
 ALT="$18.6$">|; 

$key = q/18.7:1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2396.png"
 ALT="$18.7:1$">|; 

$key = q/180^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img805.png"
 ALT="$180^\circ$">|; 

$key = q/19.50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1011.png"
 ALT="$19.50$">|; 

$key = q/19.63^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3656.png"
 ALT="$19.63^\circ$">|; 

$key = q/1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img39.png"
 ALT="$1$">|; 

$key = q/1>27,mu_2,(1-mu_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2306.png"
 ALT="$1 &gt; 27 \mu_2 (1-\mu_2)$">|; 

$key = q/1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1667.png"
 ALT="$1/2$">|; 

$key = q/1slashalpha'=10.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3652.png"
 ALT="$1/\alpha' = 10.5$">|; 

$key = q/1slashalpha'=8.728;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3666.png"
 ALT="$1/\alpha'= 8.728$">|; 

$key = q/1slashgamma'=18.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3657.png"
 ALT="$1/\gamma'=18.3$">|; 

$key = q/1slashgamma'=18.704;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3672.png"
 ALT="$1/\gamma' = 18.704$">|; 

$key = q/1slashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img927.png"
 ALT="$1/n$">|; 

$key = q/1slashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img947.png"
 ALT="$1/r$">|; 

$key = q/2';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1913.png"
 ALT="$2'$">|; 

$key = q/2,091;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3472.png"
 ALT="$2,091$">|; 

$key = q/2,370;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3473.png"
 ALT="$2,370$">|; 

$key = q/2,alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1907.png"
 ALT="$2 \alpha$">|; 

$key = q/2,e,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img888.png"
 ALT="$2 e a$">|; 

$key = q/2,e,sin{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img3591.png"
 ALT="$2 e \sin {\cal M}$">|; 

$key = q/2,e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1925.png"
 ALT="$2 e$">|; 

$key = q/2,g,a^{,2}slashvarv^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1480.png"
 ALT="$2 g a^{ 2}/\varv^{ 2}$">|; 

$key = q/2.03times10^6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img935.png"
 ALT="$2.03\times 10^6$">|; 

$key = q/2.05;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1003.png"
 ALT="$2.05$">|; 

$key = q/2.10times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2950.png"
 ALT="$2.10\times 10^{-3}$">|; 

$key = q/2.2,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1135.png"
 ALT="$2.2 {\rm cm}$">|; 

$key = q/2.37times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2946.png"
 ALT="$2.37\times 10^{-4}$">|; 

$key = q/2.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1296.png"
 ALT="$2.3$">|; 

$key = q/2.447times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img764.png"
 ALT="$2.447\times 10^{-6}$">|; 

$key = q/2.4times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2937.png"
 ALT="$2.4\times 10^{-4}$">|; 

$key = q/2.53times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2935.png"
 ALT="$2.53\times 10^{-5}$">|; 

$key = q/2.75;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1014.png"
 ALT="$2.75$">|; 

$key = q/2.857times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img768.png"
 ALT="$2.857\times 10^{-4}$">|; 

$key = q/2.86;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1932.png"
 ALT="$2.86$">|; 

$key = q/2.87;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1937.png"
 ALT="$2.87$">|; 

$key = q/2.8times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2933.png"
 ALT="$2.8\times 10^{-4}$">|; 

$key = q/20'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1819.png"
 ALT="$20''$">|; 

$key = q/20.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2083.png"
 ALT="$20.4$">|; 

$key = q/21.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2947.png"
 ALT="$21.0$">|; 

$key = q/21.4,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1195.png"
 ALT="$21.4 {\rm km}$">|; 

$key = q/221.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3699.png"
 ALT="$221.3$">|; 

$key = q/223;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3733.png"
 ALT="$223$">|; 

$key = q/225^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3467.png"
 ALT="$225^\circ$">|; 

$key = q/23.44^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1807.png"
 ALT="$23.44^\circ$">|; 

$key = q/230,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img502.png"
 ALT="$230 {\rm km}$">|; 

$key = q/23^{rmh},56^{rmm},04^{rms};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1088.png"
 ALT="$23^{\rm h} 56^{\rm m} 04^{\rm s} $">|; 

$key = q/25,772;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3702.png"
 ALT="$25,772$">|; 

$key = q/25.90;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2597.png"
 ALT="$25.90$">|; 

$key = q/26.9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2943.png"
 ALT="$26.9$">|; 

$key = q/27.2122;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2072.png"
 ALT="$27.2122$">|; 

$key = q/27.2123;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3709.png"
 ALT="$27.2123$">|; 

$key = q/27.2957;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2052.png"
 ALT="$27.2957$">|; 

$key = q/27.32158;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3706.png"
 ALT="$27.32158$">|; 

$key = q/27.32166;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3705.png"
 ALT="$27.32166$">|; 

$key = q/27.322;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1931.png"
 ALT="$27.322$">|; 

$key = q/27.32;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1914.png"
 ALT="$27.32$">|; 

$key = q/27.5546;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3708.png"
 ALT="$27.5546$">|; 

$key = q/27.555;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1933.png"
 ALT="$27.555$">|; 

$key = q/270^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img806.png"
 ALT="$270^\circ$">|; 

$key = q/29.5306;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3707.png"
 ALT="$29.5306$">|; 

$key = q/29.53;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3470.png"
 ALT="$29.53$">|; 

$key = q/2:1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1344.png"
 ALT="$2:1$">|; 

$key = q/2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img40.png"
 ALT="$2$">|; 

$key = q/2pi,a,A,rho(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2771.png"
 ALT="$2\pi a A \rho(a)$">|; 

$key = q/2pi,a,A,rho(a)llm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2770.png"
 ALT="$2\pi a A \rho(a)\ll m$">|; 

$key = q/2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img694.png"
 ALT="$2\pi$">|; 

$key = q/2pislash(n-n')=T_{rmsynodic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img3717.png"
 ALT="$2\pi/(n-n') = T_{\rm synodic}$">|; 

$key = q/2pislash(n-n_n)=T_{rmdraconic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3719.png"
 ALT="$2\pi/(n-n_n)= T_{\rm draconic}$">|; 

$key = q/2pislash(n-n_p)=T_{rmanomalistic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3718.png"
 ALT="$2\pi/(n-n_p)=T_{\rm anomalistic}$">|; 

$key = q/2pislashomega=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1655.png"
 ALT="$2\pi/\omega = 1$">|; 

$key = q/2pislash{mitOmega}_n=18.6,{rmyears};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1756.png"
 ALT="$2\pi/{\mit\Omega}_n=18.6 {\rm years}$">|; 

$key = q/2slash3pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img926.png"
 ALT="$2/3\pi$">|; 

$key = q/2times10^{-10},{rmm}^2,{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img120.png"
 ALT="$2\times 10^{-10} {\rm m}^2 {\rm s}^{-1}$">|; 

$key = q/3,690;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2395.png"
 ALT="$3,690$">|; 

$key = q/3.039times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img765.png"
 ALT="$3.039\times 10^{-6}$">|; 

$key = q/3.0times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2952.png"
 ALT="$3.0\times 10^{-2}$">|; 

$key = q/3.226times10^{-7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img766.png"
 ALT="$3.226\times 10^{-7}$">|; 

$key = q/3.34;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1013.png"
 ALT="$3.34$">|; 

$key = q/3.8,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1304.png"
 ALT="$3.8 {\rm cm}$">|; 

$key = q/3.85times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2945.png"
 ALT="$3.85\times 10^{-3}$">|; 

$key = q/30^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2372.png"
 ALT="$30^\circ$">|; 

$key = q/31.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3594.png"
 ALT="$31.8$">|; 

$key = q/315^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3468.png"
 ALT="$315^\circ$">|; 

$key = q/31;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1256.png"
 ALT="$31$">|; 

$key = q/34.36^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3651.png"
 ALT="$34.36^\circ$">|; 

$key = q/35;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1257.png"
 ALT="$35$">|; 

$key = q/360,alpha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3649.png"
 ALT="$360 \alpha'$">|; 

$key = q/360,gamma';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3655.png"
 ALT="$360 \gamma'$">|; 

$key = q/360^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img807.png"
 ALT="$360^\circ$">|; 

$key = q/365.24219;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2084.png"
 ALT="$365.24219$">|; 

$key = q/365.24;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img829.png"
 ALT="$365.24$">|; 

$key = q/365.25636;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2082.png"
 ALT="$365.25636$">|; 

$key = q/3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img41.png"
 ALT="$3$">|; 

$key = q/3times10^{-2},{rmm}^2,{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img118.png"
 ALT="$3\times 10^{-2} {\rm m}^2 {\rm s}^{-1}$">|; 

$key = q/3times3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1540.png"
 ALT="$3\times 3$">|; 

$key = q/4,216;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3595.png"
 ALT="$4,216$">|; 

$key = q/4,586;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3596.png"
 ALT="$4,586$">|; 

$key = q/4,g,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1479.png"
 ALT="$4 g a$">|; 

$key = q/4,{mitOmega},varv_0^{,3},sinlambda,sin^2beta,cosbetaslashg^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img1336.png"
 ALT="$4 {\mit\Omega} \varv_0^{ 3} \sin\lambda \sin^2\beta \cos\beta/g^{ 2}$">|; 

$key = q/4-6,alpha+{calO}(alpha^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2351.png"
 ALT="$4-6 \alpha+ {\cal O}(\alpha^{ 2})$">|; 

$key = q/4.0362times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2046.png"
 ALT="$4.0362\times 10^{-4}$">|; 

$key = q/4.08times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2934.png"
 ALT="$4.08\times 10^{-4}$">|; 

$key = q/4.1'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3771.png"
 ALT="$4.1''$">|; 

$key = q/4.353times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img769.png"
 ALT="$4.353\times 10^{-5}$">|; 

$key = q/4.5times10^9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1299.png"
 ALT="$4.5\times 10^9$">|; 

$key = q/4.65times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2931.png"
 ALT="$4.65\times 10^{-5}$">|; 

$key = q/434;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4522.png"
 ALT="$434$">|; 

$key = q/470,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img509.png"
 ALT="$470 {\rm km}$">|; 

$key = q/470tmspace+thinmuskip{.1667em}{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2.png"
 ALT="$470\tmspace +\thinmuskip {.1667em}{\rm km}$">|; 

$key = q/4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2310.png"
 ALT="$4$">|; 

$key = q/5,{rmcm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1303.png"
 ALT="$5 {\rm cm}$">|; 

$key = q/5.0times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2948.png"
 ALT="$5.0\times 10^{-3}$">|; 

$key = q/5.165times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img770.png"
 ALT="$5.165\times10^{-5}$">|; 

$key = q/5.32+0.43=5.75;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1031.png"
 ALT="$5.32+0.43= 5.75$">|; 

$key = q/5.32;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1019.png"
 ALT="$5.32$">|; 

$key = q/5.54;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1002.png"
 ALT="$5.54$">|; 

$key = q/5.66times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2942.png"
 ALT="$5.66\times 10^{-5}$">|; 

$key = q/5.75;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1001.png"
 ALT="$5.75$">|; 

$key = q/50^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2087.png"
 ALT="$50^\circ$">|; 

$key = q/57';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img876.png"
 ALT="$57'$">|; 

$key = q/58.65;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1911.png"
 ALT="$58.65$">|; 

$key = q/5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3745.png"
 ALT="$5$">|; 

$key = q/5times10^4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2598.png"
 ALT="$5\times 10^4$">|; 

$key = q/5times10^{-7},{rmm}^2,{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img119.png"
 ALT="$5\times 10^{-7} {\rm m}^2 {\rm s}^{-1}$">|; 

$key = q/6,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1651.png"
 ALT="$6 {\rm m}$">|; 

$key = q/6.03;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2932.png"
 ALT="$6.03$">|; 

$key = q/6.3149times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2047.png"
 ALT="$6.3149\times 10^{-4}$">|; 

$key = q/6.55;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1009.png"
 ALT="$6.55$">|; 

$key = q/6.5^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1934.png"
 ALT="$6.5^\circ$">|; 

$key = q/60.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img880.png"
 ALT="$60.3$">|; 

$key = q/60.9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3697.png"
 ALT="$60.9$">|; 

$key = q/60^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2247.png"
 ALT="$60^\circ$">|; 

$key = q/63.4^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2722.png"
 ALT="$63.4^\circ$">|; 

$key = q/666;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3502.png"
 ALT="$666$">|; 

$key = q/7.3times10^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2929.png"
 ALT="$7.3\times 10^{-1}$">|; 

$key = q/7.48times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2930.png"
 ALT="$7.48\times 10^{-2}$">|; 

$key = q/7.51;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1010.png"
 ALT="$7.51$">|; 

$key = q/7.7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3678.png"
 ALT="$7.7$">|; 

$key = q/7.81times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2939.png"
 ALT="$7.81\times 10^{-5}$">|; 

$key = q/70,000;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2855.png"
 ALT="$70,000$">|; 

$key = q/74.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2053.png"
 ALT="$74.1$">|; 

$key = q/773;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3501.png"
 ALT="$773$">|; 

$key = q/8.20times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2938.png"
 ALT="$8.20\times 10^{-4}$">|; 

$key = q/8.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1089.png"
 ALT="$8.4$">|; 

$key = q/8.848;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3703.png"
 ALT="$8.848$">|; 

$key = q/8.85;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2923.png"
 ALT="$8.85$">|; 

$key = q/81.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3698.png"
 ALT="$81.3$">|; 

$key = q/87.97=1.5times58.65;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1912.png"
 ALT="$87.97=1.5\times 58.65$">|; 

$key = q/89.0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img833.png"
 ALT="$89.0$">|; 

$key = q/89.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img832.png"
 ALT="$89.8$">|; 

$key = q/8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2547.png"
 ALT="$8$">|; 

$key = q/9.2'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1817.png"
 ALT="$9.2''$">|; 

$key = q/9.542times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img767.png"
 ALT="$9.542\times 10^{-4}$">|; 

$key = q/9.60;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2936.png"
 ALT="$9.60$">|; 

$key = q/9.76times10^{-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2953.png"
 ALT="$9.76\times 10^{-5}$">|; 

$key = q/90.7'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3772.png"
 ALT="$90.7''$">|; 

$key = q/90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img804.png"
 ALT="$90^\circ$">|; 

$key = q/92.75;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img937.png"
 ALT="$92.75$">|; 

$key = q/92.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img830.png"
 ALT="$92.8$">|; 

$key = q/93.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img831.png"
 ALT="$93.6$">|; 

$key = q/=(0,,0,,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1959.png"
 ALT="$= (0, 0, 1)$">|; 

$key = q/=(0,,0,,omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2125.png"
 ALT="$=(0, 0, \omega)$">|; 

$key = q/=(nu_x,,nu_y,,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2033.png"
 ALT="$=(\nu_x, \nu_y, 1)$">|; 

$key = q/=(omega_{x'},,omega_{y'},,omega_{z'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1558.png"
 ALT="$= (\omega_{x'}, \omega_{y'}, \omega_{z'})$">|; 

$key = q/=(tau_{x'},,tau_{y'},tau_{z'});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1557.png"
 ALT="$= (\tau_{x'}, \tau_{y'},\tau_{z'})$">|; 

$key = q/=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1601.png"
 ALT="$=0$">|; 

$key = q/=41^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1334.png"
 ALT="$=41^\circ$">|; 

$key = q/=sum_{i=1,N}{bfr}_itimes{bfF}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img1490.png"
 ALT="$= \sum_{i=1, N} {\bf r}_i\times{\bf F}_i$">|; 

$key = q/={mitOmega},{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3967.png"
 ALT="$={\mit\Omega} {\bf e}_z$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img7.png"
 ALT="$A$">|; 

$key = q/A=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2298.png"
 ALT="$A=1$">|; 

$key = q/A=mu_1slashrho_1^{,3}+mu_2slashrho_2^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2342.png"
 ALT="$A=\mu_1/\rho_1^{ 3}+\mu_2/\rho_2^{ 3}$">|; 

$key = q/A=pi,a,b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img633.png"
 ALT="$A=\pi a b$">|; 

$key = q/A=pi,b^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2842.png"
 ALT="$A=\pi b^{ 2}$">|; 

$key = q/A>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2341.png"
 ALT="$A&gt;1$">|; 

$key = q/AB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1450.png"
 ALT="$AB$">|; 

$key = q/ACP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img703.png"
 ALT="$ACP$">|; 

$key = q/AE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img22.png"
 ALT="$AE$">|; 

$key = q/AP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img709.png"
 ALT="$AP$">|; 

$key = q/APB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1453.png"
 ALT="$APB$">|; 

$key = q/A_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3766.png"
 ALT="$A_1'$">|; 

$key = q/A_1'=15.7'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3761.png"
 ALT="$A_1'=15.7''$">|; 

$key = q/A_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2040.png"
 ALT="$A_1$">|; 

$key = q/A_1=0.37'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2054.png"
 ALT="$A_1=0.37''$">|; 

$key = q/A_1=22,640'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3746.png"
 ALT="$A_1=22,640''$">|; 

$key = q/A_2';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3773.png"
 ALT="$A_2'$">|; 

$key = q/A_2'=0.07'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3762.png"
 ALT="$A_2'=0.07''$">|; 

$key = q/A_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2041.png"
 ALT="$A_2$">|; 

$key = q/A_2=3.25'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2055.png"
 ALT="$A_2=3.25''$">|; 

$key = q/A_2=418'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3747.png"
 ALT="$A_2=418''$">|; 

$key = q/A_3';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img3767.png"
 ALT="$A_3'$">|; 

$key = q/A_3'=0.48'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img3763.png"
 ALT="$A_3'=0.48''$">|; 

$key = q/A_3=2,370'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3748.png"
 ALT="$A_3=2,370''$">|; 

$key = q/A_4';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3768.png"
 ALT="$A_4'$">|; 

$key = q/A_4'=4.3'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3764.png"
 ALT="$A_4'=4.3''$">|; 

$key = q/A_4=4,586'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3749.png"
 ALT="$A_4=4,586''$">|; 

$key = q/A_5';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img3769.png"
 ALT="$A_5'$">|; 

$key = q/A_5'=94.0'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img3765.png"
 ALT="$A_5'=94.0''$">|; 

$key = q/A_5=666'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3750.png"
 ALT="$A_5=666''$">|; 

$key = q/A_r={bfA}cdot{bfe}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3971.png"
 ALT="$A_r = {\bf A}\cdot {\bf e}_r$">|; 

$key = q/Asimeq4+6,alpha+{calO}(alpha^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2349.png"
 ALT="$A\simeq 4+6 \alpha+{\cal O}(\alpha^{ 2})$">|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img25.png"
 ALT="$B$">|; 

$key = q/B=9slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2299.png"
 ALT="$B=9/4$">|; 

$key = q/B=C=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2286.png"
 ALT="$B=C=0$">|; 

$key = q/BA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1215.png"
 ALT="$BA$">|; 

$key = q/BP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1452.png"
 ALT="$BP$">|; 

$key = q/B_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4728.png"
 ALT="$B_2$">|; 

$key = q/C';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img30.png"
 ALT="$C'$">|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img27.png"
 ALT="$C$">|; 

$key = q/C<C_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2244.png"
 ALT="$C &lt; C_4$">|; 

$key = q/C=C_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img61.png"
 ALT="$C= C_1$">|; 

$key = q/C=C_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img62.png"
 ALT="$C= C_2$">|; 

$key = q/C=C_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img63.png"
 ALT="$C =C_3$">|; 

$key = q/C=pmsqrt{27slash16},(1-2,mu_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2300.png"
 ALT="$C=\pm\sqrt{27/16} (1-2 \mu_2)$">|; 

$key = q/C>C_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img59.png"
 ALT="$C&gt; C_1$">|; 

$key = q/CA=CP=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img704.png"
 ALT="$CA=CP=a$">|; 

$key = q/CQ=CS+SQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img715.png"
 ALT="$CQ=CS+SQ$">|; 

$key = q/CQ=a,cosE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img714.png"
 ALT="$CQ=a \cos E$">|; 

$key = q/CR=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img711.png"
 ALT="$CR=a$">|; 

$key = q/CS=e,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img705.png"
 ALT="$CS=e a$">|; 

$key = q/C_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img912.png"
 ALT="$C_1$">|; 

$key = q/C_1>C_2>C_3>C_4=C_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2238.png"
 ALT="$C_1&gt;C_2&gt;C_3&gt;C_4=C_5$">|; 

$key = q/C_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img913.png"
 ALT="$C_2$">|; 

$key = q/C_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2246.png"
 ALT="$C_3$">|; 

$key = q/C_4<C<C_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img64.png"
 ALT="$C_4&lt; C &lt; C_3$">|; 

$key = q/C_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2730.png"
 ALT="$C_D$">|; 

$key = q/C_Dsimeq2.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2732.png"
 ALT="$C_D\simeq 2.2$">|; 

$key = q/C_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2224.png"
 ALT="$C_i$">|; 

$key = q/Csimeq3+mu_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2337.png"
 ALT="$C\simeq 3+\mu_2$">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img29.png"
 ALT="$D$">|; 

$key = q/D=0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3469.png"
 ALT="$D=0^\circ$">|; 

$key = q/D=180^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3525.png"
 ALT="$D=180^\circ$">|; 

$key = q/D=270^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3524.png"
 ALT="$D=270^\circ$">|; 

$key = q/D=3,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2287.png"
 ALT="$D=3 A$">|; 

$key = q/D=3slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2301.png"
 ALT="$D=3/4$">|; 

$key = q/D=45^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3465.png"
 ALT="$D=45^\circ$">|; 

$key = q/D=90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3523.png"
 ALT="$D=90^\circ$">|; 

$key = q/D_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img891.png"
 ALT="$D_1$">|; 

$key = q/D_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img892.png"
 ALT="$D_2$">|; 

$key = q/Dequivdslashdalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2466.png"
 ALT="$D\equiv d/d\alpha$">|; 

$key = q/Dequivpartialslashpartialalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4963.png"
 ALT="$D\equiv \partial/\partial\alpha$">|; 

$key = q/E';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2784.png"
 ALT="$E'$">|; 

$key = q/E,N,c=Lslash4pi,r^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2813.png"
 ALT="$E N c=L/4\pi r^{ 2}$">|; 

$key = q/E-e,sinE={calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img2773.png"
 ALT="$E-e \sin E = {\cal M}$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img19.png"
 ALT="$E$">|; 

$key = q/E<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img201.png"
 ALT="$E&lt;0$">|; 

$key = q/E=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img685.png"
 ALT="$E=0$">|; 

$key = q/E=pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img686.png"
 ALT="$E=\pi$">|; 

$key = q/E>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img202.png"
 ALT="$E&gt;0$">|; 

$key = q/E_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img198.png"
 ALT="$E_0$">|; 

$key = q/E_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img199.png"
 ALT="$E_1$">|; 

$key = q/E_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img200.png"
 ALT="$E_2$">|; 

$key = q/E_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img697.png"
 ALT="$E_n$">|; 

$key = q/ErightarrowE+2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img734.png"
 ALT="$E\rightarrow E + 2\pi$">|; 

$key = q/EslashM=81.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3527.png"
 ALT="$E/M=81.3$">|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img5.png"
 ALT="$F$">|; 

$key = q/F^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4968.png"
 ALT="$F^{ 3}$">|; 

$key = q/F_0=muslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4703.png"
 ALT="$F_0 = \mu/r$">|; 

$key = q/F_X=f_{x_1}slash(n^{,2},a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3115.png"
 ALT="$F_X=f_{x_1}/(n^{ 2} a)$">|; 

$key = q/F_Y=f_{y_1}slash(n^{,2},a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3116.png"
 ALT="$F_Y=f_{y_1}/(n^{ 2} a)$">|; 

$key = q/F_z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2769.png"
 ALT="$F_z=0$">|; 

$key = q/G,(M+m)=n^{,2},a^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img867.png"
 ALT="$G (M+m)=n^{ 2} a^{ 3}$">|; 

$key = q/G,M,mslashr^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img462.png"
 ALT="$G M m/r^{ 2}$">|; 

$key = q/G,M=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2097.png"
 ALT="$G M=1$">|; 

$key = q/G,m_p=n^{,2},a^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1851.png"
 ALT="$G m_p=n^{ 2} a^{ 3}$">|; 

$key = q/G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img343.png"
 ALT="$G$">|; 

$key = q/G=6.67times10^{-11},{rmm}^{,3},{rmkg}^{-1},{rms}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2846.png"
 ALT="$G= 6.67\times 10^{-11} {\rm m}^{ 3} {\rm kg}^{-1} {\rm s}^{-2}$">|; 

$key = q/GSQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img707.png"
 ALT="$GSQ$">|; 

$key = q/H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img846.png"
 ALT="$H$">|; 

$key = q/H=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img847.png"
 ALT="$H=0$">|; 

$key = q/Hsimeq8.5times10^3,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2736.png"
 ALT="$H\simeq 8.5\times 10^3 {\rm m}$">|; 

$key = q/I';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2134.png"
 ALT="$I'$">|; 

$key = q/I'=I+iota;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2075.png"
 ALT="$I'=I+\iota$">|; 

$key = q/I(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img760.png"
 ALT="$I(^\circ)$">|; 

$key = q/I,e',I'sim{calO}(e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4924.png"
 ALT="$I, e', I'\sim {\cal O}(e)$">|; 

$key = q/I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img14.png"
 ALT="$I$">|; 

$key = q/I=0.09008;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3616.png"
 ALT="$I= 0.09008$">|; 

$key = q/I=0.9008;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3714.png"
 ALT="$I=0.9008$">|; 

$key = q/I=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2142.png"
 ALT="$I=0$">|; 

$key = q/I=5.16^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1955.png"
 ALT="$I=5.16^\circ$">|; 

$key = q/I=pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2718.png"
 ALT="$I=\pi/2$">|; 

$key = q/I=sin^{-1}([p^{,2}+q^{,2}]^{1slash2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2678.png"
 ALT="$I=\sin^{-1}([p^{ 2}+q^{ 2}]^{1/2})$">|; 

$key = q/I^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3669.png"
 ALT="$I^{ 2}$">|; 

$key = q/I_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2908.png"
 ALT="$I_0$">|; 

$key = q/I_5=sin^{-1}(2.751times10^{-2})=1.576^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2603.png"
 ALT="$I_5=\sin^{-1}(2.751\times 10^{-2}) = 1.576^\circ$">|; 

$key = q/I_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2550.png"
 ALT="$I_i$">|; 

$key = q/I_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1749.png"
 ALT="$I_m$">|; 

$key = q/I_m=5.16^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1747.png"
 ALT="$I_m=5.16^\circ$">|; 

$key = q/I_s=0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4620.png"
 ALT="$I_s=0^\circ$">|; 

$key = q/I_{ik};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2612.png"
 ALT="$I_{ik}$">|; 

$key = q/I_{il};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img74.png"
 ALT="$I_{il}$">|; 

$key = q/I_{rmfree};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2676.png"
 ALT="$I_{\rm free}$">|; 

$key = q/I_{rmmax}(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2621.png"
 ALT="$I_{\rm max}(^\circ)$">|; 

$key = q/I_{rmmin}(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2620.png"
 ALT="$I_{\rm min}(^\circ)$">|; 

$key = q/Ill1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img776.png"
 ALT="$I\ll 1$">|; 

$key = q/IrightarrowI,[1-(3slash8),m,cos(2,D)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3691.png"
 ALT="$I\rightarrow
I [1-(3/8) m \cos (2  D)]$">|; 

$key = q/J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2138.png"
 ALT="$J$">|; 

$key = q/J_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1196.png"
 ALT="$J_2$">|; 

$key = q/J_2=(2slash5),epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img489.png"
 ALT="$J_2=(2/5) \epsilon$">|; 

$key = q/J_2=({calI}_parallel-{calI}_perp)slash(M,R^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2086.png"
 ALT="$J_2=({\cal I}_\parallel-{\cal I}_\perp)/(M R^{ 2})$">|; 

$key = q/J_2=1.083times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2895.png"
 ALT="$J_2= 1.083\times 10^{-3}$">|; 

$key = q/J_2=1.085times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2088.png"
 ALT="$J_2=1.085\times 10^{-3}$">|; 

$key = q/J_2=1.08times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4430.png"
 ALT="$J_2=1.08\times 10^{-3}$">|; 

$key = q/J_2=1.47times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4438.png"
 ALT="$J_2=1.47\times 10^{-2}$">|; 

$key = q/J_2sim{calO}(epsilon);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img486.png"
 ALT="$J_2\sim{\cal O}(\epsilon)$">|; 

$key = q/J_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2728.png"
 ALT="$J_3$">|; 

$key = q/J_3=-2.112times10^{-6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2896.png"
 ALT="$J_3= -2.112\times 10^{-6}$">|; 

$key = q/J_n(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4022.png"
 ALT="$J_n(x)$">|; 

$key = q/J_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img479.png"
 ALT="$J_n$">|; 

$key = q/K+U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img536.png"
 ALT="$K+U$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img133.png"
 ALT="$K$">|; 

$key = q/K=(1slash2),m,varv^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img196.png"
 ALT="$K=(1/2) m \varv^{ 2}$">|; 

$key = q/K=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img228.png"
 ALT="$K=0$">|; 

$key = q/K_1=0.9991;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2050.png"
 ALT="$K_1=0.9991$">|; 

$key = q/K_1simeq1-3,tauslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2038.png"
 ALT="$K_1\simeq
1-3 \tau/2$">|; 

$key = q/K_2=-2.5017;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2051.png"
 ALT="$K_2=-2.5017$">|; 

$key = q/K_2simeq-2sqrt{tauslashsigma};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2039.png"
 ALT="$K_2\simeq -2\sqrt{\tau/\sigma}$">|; 

$key = q/L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1301.png"
 ALT="$L$">|; 

$key = q/L=(mu,a)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4792.png"
 ALT="$L=(\mu a)^{1/2}$">|; 

$key = q/L=3.846times10^{26},{rmW};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2814.png"
 ALT="$L= 3.846\times 10^{26} {\rm W}$">|; 

$key = q/L=3.85times10^{26},{rmW};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2845.png"
 ALT="$L= 3.85\times 10^{26} {\rm W}$">|; 

$key = q/L_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img55.png"
 ALT="$L_1$">|; 

$key = q/L_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img67.png"
 ALT="$L_2$">|; 

$key = q/L_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img68.png"
 ALT="$L_3$">|; 

$key = q/L_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2218.png"
 ALT="$L_4$">|; 

$key = q/L_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img56.png"
 ALT="$L_5$">|; 

$key = q/L_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2225.png"
 ALT="$L_i$">|; 

$key = q/L_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1647.png"
 ALT="$L_z$">|; 

$key = q/L_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1648.png"
 ALT="$L_{z'}$">|; 

$key = q/M+m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img866.png"
 ALT="$M+m$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img75.png"
 ALT="$M$">|; 

$key = q/M=(4pislash3),R^{,3},gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img457.png"
 ALT="$M=(4\pi/3) R^{ 3} \gamma$">|; 

$key = q/M=(4pislash3),gamma,R^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img475.png"
 ALT="$M=(4\pi/3) \gamma R^{ 3}$">|; 

$key = q/M=1.90times10^{27},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1202.png"
 ALT="$M=1.90\times 10^{27} {\rm kg}$">|; 

$key = q/M=1.99times10^{30},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2847.png"
 ALT="$M= 1.99\times 10^{30} {\rm kg}$">|; 

$key = q/M=5.97times10^{24},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1190.png"
 ALT="$M = 5.97\times 10^{24} {\rm kg}$">|; 

$key = q/M=m+m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1210.png"
 ALT="$M=m+m'$">|; 

$key = q/M=m+m'simeqm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1276.png"
 ALT="$M=m+m'\simeq m$">|; 

$key = q/M=m_1+m_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img333.png"
 ALT="$M=m_1+m_2$">|; 

$key = q/M=sum_{i=1,N}m_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img162.png"
 ALT="$M = \sum_{i=1,N} m_i$">|; 

$key = q/MA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2006.png"
 ALT="$MA$">|; 

$key = q/ME;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1953.png"
 ALT="$ME$">|; 

$key = q/MN;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1954.png"
 ALT="$MN$">|; 

$key = q/MP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1951.png"
 ALT="$MP$">|; 

$key = q/MZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1950.png"
 ALT="$MZ$">|; 

$key = q/M_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1058.png"
 ALT="$M_0$">|; 

$key = q/M_0llM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1059.png"
 ALT="$M_0\ll M$">|; 

$key = q/M_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4588.png"
 ALT="$M_E$">|; 

$key = q/M_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1742.png"
 ALT="$M_m$">|; 

$key = q/M_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1705.png"
 ALT="$M_s$">|; 

$key = q/Mggm,m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2871.png"
 ALT="$M\gg m, m'$">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img149.png"
 ALT="$N$">|; 

$key = q/O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1451.png"
 ALT="$O$">|; 

$key = q/OP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1456.png"
 ALT="$OP$">|; 

$key = q/OPequivr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1680.png"
 ALT="$OP\equiv r$">|; 

$key = q/Omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1063.png"
 ALT="$\Omega$">|; 

$key = q/P(7)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img522.png"
 ALT="$P(7)=0$">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4.png"
 ALT="$P$">|; 

$key = q/P=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img841.png"
 ALT="$P=0$">|; 

$key = q/PGA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img702.png"
 ALT="$PGA$">|; 

$key = q/PRA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img708.png"
 ALT="$PRA$">|; 

$key = q/P_0(0)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img515.png"
 ALT="$P_0(0)=1$">|; 

$key = q/P_1(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img516.png"
 ALT="$P_1(0) = 0$">|; 

$key = q/P_2(0)=-1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img517.png"
 ALT="$P_2(0)=-1/2$">|; 

$key = q/P_2(x)=(1slash2),(3,x^{,2}-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1706.png"
 ALT="$P_2(x)=(1/2) (3 x^{ 2}-1)$">|; 

$key = q/P_3(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img518.png"
 ALT="$P_3(0)=0$">|; 

$key = q/P_4(0)=3slash8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img519.png"
 ALT="$P_4(0)=3/8$">|; 

$key = q/P_5(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img520.png"
 ALT="$P_5(0)=0$">|; 

$key = q/P_6(0)=-5slash16;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img521.png"
 ALT="$P_6(0)=-5/16$">|; 

$key = q/P_8(0)=35slash128;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img523.png"
 ALT="$P_8(0)=35/128$">|; 

$key = q/P_l(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4115.png"
 ALT="$P_l(x)$">|; 

$key = q/P_l^{,m}(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img4113.png"
 ALT="$P_l^{ m}(x)$">|; 

$key = q/P_n(costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img432.png"
 ALT="$P_n(\cos\theta)$">|; 

$key = q/P_n(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img416.png"
 ALT="$P_n(x)$">|; 

$key = q/P{mitPi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1848.png"
 ALT="$P{\mit\Pi}$">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img135.png"
 ALT="$Q$">|; 

$key = q/Q_i,q_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1388.png"
 ALT="$Q_i q_i$">|; 

$key = q/Q_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1387.png"
 ALT="$Q_i$">|; 

$key = q/R';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1318.png"
 ALT="$R'$">|; 

$key = q/R'=(X'^{,2}+Y'^{,2}+Z'^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3087.png"
 ALT="$R'=(X'^{ 2}+Y'^{ 2}+Z'^{ 2})^{1/2}$">|; 

$key = q/R'=1.74times10^6,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1312.png"
 ALT="$R'=1.74\times 10^6 {\rm m}$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img76.png"
 ALT="$R$">|; 

$key = q/R=(X^{,2}+Y^{,2}+Z^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3086.png"
 ALT="$R=(X^{ 2}+Y^{ 2}+Z^{ 2})^{1/2}$">|; 

$key = q/R=6.3710times10^6,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1102.png"
 ALT="$R=6.3710\times 10^6 {\rm m}$">|; 

$key = q/R=6.37times10^6,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1186.png"
 ALT="$R=6.37\times 10^6 {\rm m}$">|; 

$key = q/R=6.4times10^6,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2734.png"
 ALT="$R=6.4\times 10^6 {\rm m}$">|; 

$key = q/R=6.92times10^7,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1200.png"
 ALT="$R=6.92\times 10^7 {\rm m}$">|; 

$key = q/RCS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img712.png"
 ALT="$RCS$">|; 

$key = q/RGQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img710.png"
 ALT="$RGQ$">|; 

$key = q/R_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1253.png"
 ALT="$R_+$">|; 

$key = q/R_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.07ex; " SRC="|."$dir".q|img1254.png"
 ALT="$R_-$">|; 

$key = q/R_csimeq169,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1177.png"
 ALT="$R_c\simeq 169 {\rm km}$">|; 

$key = q/R_e=R,(1+epsilonslash3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img466.png"
 ALT="$R_e=R (1+\epsilon/3)$">|; 

$key = q/R_p=R,(1-2,epsilonslash3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img465.png"
 ALT="$R_p=R (1-2 \epsilon/3)$">|; 

$key = q/RggR_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1178.png"
 ALT="$R\gg R_c$">|; 

$key = q/RllR_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img500.png"
 ALT="$R\ll R_c$">|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3.png"
 ALT="$S$">|; 

$key = q/SG;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img706.png"
 ALT="$SG$">|; 

$key = q/SQ=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img713.png"
 ALT="$SQ=r \cos\theta$">|; 

$key = q/SS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img21.png"
 ALT="$SS$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img17.png"
 ALT="$T$">|; 

$key = q/T=2pi,(R^{,3}slashmu)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2920.png"
 ALT="$T =2\pi (R^{ 3}/\mu)^{1/2}$">|; 

$key = q/T=2pi,(a^{,3}slashG,M)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img731.png"
 ALT="$T=2\pi (a^{ 3}/G M)^{1/2}$">|; 

$key = q/T=2pi,(a^{,3}slashGM)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img693.png"
 ALT="$T= 2\pi (a^{ 3}/GM)^{1/2}$">|; 

$key = q/T=2pislashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2709.png"
 ALT="$T=2\pi/n$">|; 

$key = q/T=365.24;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img889.png"
 ALT="$T=365.24$">|; 

$key = q/T=j_1,T_{rmsynodic}=j_2,T_{rmanomalistic}=j_3,T_{rmdraconic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img3724.png"
 ALT="$T=j_1 T_{\rm synodic}=j_2 T_{\rm anomalistic}=
j_3 T_{\rm draconic}$">|; 

$key = q/T=n,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3088.png"
 ALT="$T = n t$">|; 

$key = q/T_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img245.png"
 ALT="$T_0$">|; 

$key = q/T_0=2pislashomega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img239.png"
 ALT="$T_0 = 2\pi/\omega_0$">|; 

$key = q/T_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img997.png"
 ALT="$T_i$">|; 

$key = q/T_m({rmyr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4594.png"
 ALT="$T_m({\rm yr})$">|; 

$key = q/T_m({rmyr})=0.07480;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4597.png"
 ALT="$T_m({\rm yr})=0.07480$">|; 

$key = q/T_m({rmyr})=0.0748;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1814.png"
 ALT="$T_m({\rm yr})=0.0748$">|; 

$key = q/T_m({rmyr})=n_sslashn_m=0.00748;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1803.png"
 ALT="$T_m({\rm yr})= n_s/n_m=0.00748$">|; 

$key = q/T_n({rmyr})=18.61;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4610.png"
 ALT="$T_n({\rm yr})=18.61$">|; 

$key = q/T_n({rmyr})=n_sslash{mitOmega}_n=18.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1813.png"
 ALT="$T_n({\rm yr}) = n_s/{\mit\Omega}_n = 18.6$">|; 

$key = q/T_phi({rmyr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4595.png"
 ALT="$T_\phi({\rm yr})$">|; 

$key = q/T_phi({rmyr})=25,772,{rmyr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4602.png"
 ALT="$T_\phi({\rm yr})=25,772 {\rm yr}$">|; 

$key = q/T_s({rmday});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4593.png"
 ALT="$T_s({\rm day})$">|; 

$key = q/T_s({rmday})=366.26;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1804.png"
 ALT="$T_s({\rm day})=366.26$">|; 

$key = q/T_s({rmday})=omegaslashn_s=366.26;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1737.png"
 ALT="$T_s({\rm day}) = \omega/n_s = 366.26$">|; 

$key = q/T_{rmanomalistic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3721.png"
 ALT="$T_{\rm anomalistic}$">|; 

$key = q/T_{rmdraconic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3722.png"
 ALT="$T_{\rm draconic}$">|; 

$key = q/T_{rmsynodic};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img3720.png"
 ALT="$T_{\rm synodic}$">|; 

$key = q/Tslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img976.png"
 ALT="$T/2$">|; 

$key = q/U(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1416.png"
 ALT="$U(r)$">|; 

$key = q/U(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img194.png"
 ALT="$U(x)$">|; 

$key = q/U(x,y,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2254.png"
 ALT="$U(x,y,0)$">|; 

$key = q/U(x_1,x_2,cdots,x_{calF},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.53ex; " SRC="|."$dir".q|img1390.png"
 ALT="$U(x_1,x_2,\cdots,x_{\cal F},t)$">|; 

$key = q/U({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img143.png"
 ALT="$U({\bf r})$">|; 

$key = q/U({bfr}_1,{bfr}_2,{bfr}_3)equivU({bfr},{bfr}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2965.png"
 ALT="$U({\bf r}_1,{\bf r}_2,{\bf r}_3)\equiv U({\bf r},{\bf r}')$">|; 

$key = q/U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img148.png"
 ALT="$U$">|; 

$key = q/U=(1slash2),k,x^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img220.png"
 ALT="$U=(1/2) k x^{ 2}$">|; 

$key = q/U=E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img227.png"
 ALT="$U=E$">|; 

$key = q/U_0'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img1772.png"
 ALT="$U_0''$">|; 

$key = q/U_0';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img1765.png"
 ALT="$U_0'$">|; 

$key = q/U_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img568.png"
 ALT="$U_0$">|; 

$key = q/U_0=U(x_0,y_0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2256.png"
 ALT="$U_0=U(x_0,y_0,0)$">|; 

$key = q/U_2(a)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4356.png"
 ALT="$U_2(a)=0$">|; 

$key = q/U_x=U_y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2259.png"
 ALT="$U_x=U_y=0$">|; 

$key = q/U_x=partialU(x_0,y_0,0)slashpartialx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2257.png"
 ALT="$U_x=\partial U(x_0,y_0,0)/\partial x$">|; 

$key = q/U_{xx}=-1-2,A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2288.png"
 ALT="$U_{xx}=-1-2 A$">|; 

$key = q/U_{xx}=-3slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2302.png"
 ALT="$U_{xx} = -3/4$">|; 

$key = q/U_{xx}=partial^{,2}U(x_0,y_0,0)slashpartialx^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2258.png"
 ALT="$U_{xx}=\partial^{ 2} U(x_0,y_0,0)/\partial x^{ 2}$">|; 

$key = q/U_{xy}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2290.png"
 ALT="$U_{xy}=0$">|; 

$key = q/U_{xy}=mpsqrt{27slash16},(1-2,mu_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2304.png"
 ALT="$U_{xy} = \mp\sqrt{27/16} (1-2 \mu_2)$">|; 

$key = q/U_{yy}=-9slash4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2303.png"
 ALT="$U_{yy}=-9/4$">|; 

$key = q/U_{yy}=A-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2289.png"
 ALT="$U_{yy} = A-1$">|; 

$key = q/V(Q);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3948.png"
 ALT="$V(Q)$">|; 

$key = q/V(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img948.png"
 ALT="$V(r)$">|; 

$key = q/V({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3946.png"
 ALT="$V({\bf r})$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img322.png"
 ALT="$V$">|; 

$key = q/V<C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2223.png"
 ALT="$V&lt; C$">|; 

$key = q/V=C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img58.png"
 ALT="$V=C$">|; 

$key = q/V=Uslashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1436.png"
 ALT="$V = U/m$">|; 

$key = q/VE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img20.png"
 ALT="$VE$">|; 

$key = q/V^{,2},R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img887.png"
 ALT="$V^{ 2} R$">|; 

$key = q/Vgeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img2222.png"
 ALT="$V\geq 0$">|; 

$key = q/WS;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img23.png"
 ALT="$WS$">|; 

$key = q/X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img69.png"
 ALT="$X$">|; 

$key = q/X_0-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3142.png"
 ALT="$X_0-1$">|; 

$key = q/X_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3137.png"
 ALT="$X_0$">|; 

$key = q/X_1equivX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4686.png"
 ALT="$X_1\equiv X$">|; 

$key = q/X_2equivY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4687.png"
 ALT="$X_2\equiv Y$">|; 

$key = q/X_3equivZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4688.png"
 ALT="$X_3\equiv Z$">|; 

$key = q/X_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4697.png"
 ALT="$X_l$">|; 

$key = q/Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img736.png"
 ALT="$Y$">|; 

$key = q/Y_l^{,m}(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img4107.png"
 ALT="$Y_l^{ m}(\theta,\phi)$">|; 

$key = q/Y_n^{,m}(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4212.png"
 ALT="$Y_n^{ m}(\theta,\phi)$">|; 

$key = q/Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img70.png"
 ALT="$Z$">|; 

$key = q/Z=z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img4744.png"
 ALT="$Z=z'$">|; 

$key = q/[(k_1+k_2)slashm]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img318.png"
 ALT="$[(k_1+k_2)/m]^{1/2}$">|; 

$key = q/[-x(t),,-y(t),,z(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2365.png"
 ALT="$[-x(t), -y(t), z(t)]$">|; 

$key = q/[k_1,k_2slash(k_1+k_2),m]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img319.png"
 ALT="$[k_1 k_2/(k_1+k_2) m]^{1/2}$">|; 

$key = q/[m_1slash(m_1+m_2)],(rslashr)';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2999.png"
 ALT="$[m_1/(m_1+m_2)] (r/r)'$">|; 

$key = q/[m_2slash(m_1+m_2)],(rslashr)';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2998.png"
 ALT="$[m_2/(m_1+m_2)] (r/r)'$">|; 

$key = q/[p,q]''';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4761.png"
 ALT="$[p,q]'''$">|; 

$key = q/[x(-t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2359.png"
 ALT="$[x(-t)$">|; 

$key = q/[x(t),,y(t),,-z(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2358.png"
 ALT="$[x(t), y(t), -z(t)]$">|; 

$key = q/[x(t),,y(t),,z(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2362.png"
 ALT="$[x(t), y(t), z(t)]$">|; 

$key = q/[x(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2355.png"
 ALT="$[x(t)$">|; 

$key = q/^T,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: 0.71ex; " SRC="|."$dir".q|img2322.png"
 ALT="$^T $">|; 

$key = q/^T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: 0.71ex; " SRC="|."$dir".q|img1534.png"
 ALT="$^T$">|; 

$key = q/a';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1225.png"
 ALT="$a'$">|; 

$key = q/a'=149,598,261,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2994.png"
 ALT="$a'=149,598,261 {\rm km}$">|; 

$key = q/a'>a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2857.png"
 ALT="$a'&gt;a$">|; 

$key = q/a'slasha=389.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3526.png"
 ALT="$a'/a=389.2$">|; 

$key = q/a(t)=a^{(0)}[1+epsilon',a^{(1)}(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2428.png"
 ALT="$a(t)=a^{(0)}[1+\epsilon' a^{(1)}(t)]$">|; 

$key = q/a({rmAU});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img758.png"
 ALT="$a({\rm AU})$">|; 

$key = q/a,b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img315.png"
 ALT="$a, b$">|; 

$key = q/a,b>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3992.png"
 ALT="$a, b &gt; 0$">|; 

$key = q/a,cosE=e,a+r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img716.png"
 ALT="$a \cos E = e a+r \cos\theta$">|; 

$key = q/a,deltaR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3185.png"
 ALT="$a \delta R$">|; 

$key = q/a,mu>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img296.png"
 ALT="$a, \mu&gt;0$">|; 

$key = q/a,{rme}^{-u};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1477.png"
 ALT="$a {\rm e}^{-u}$">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img8.png"
 ALT="$a$">|; 

$key = q/a<a_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1326.png"
 ALT="$a&lt; a_c$">|; 

$key = q/a=!sqrt{2,Eslashk};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img224.png"
 ALT="$a = \!\sqrt{2 E/k}$">|; 

$key = q/a=0.841;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2143.png"
 ALT="$a=0.841$">|; 

$key = q/a=0.916;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2140.png"
 ALT="$a=0.916$">|; 

$key = q/a=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4374.png"
 ALT="$a=0$">|; 

$key = q/a=1.50times10^{11},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1259.png"
 ALT="$a=1.50\times 10^{11} {\rm m}$">|; 

$key = q/a=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2096.png"
 ALT="$a=1$">|; 

$key = q/a=3.84times10^8,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1246.png"
 ALT="$a=3.84\times 10^8 {\rm m}$">|; 

$key = q/a=384,399,{rmkm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2993.png"
 ALT="$a=384,399 {\rm km}$">|; 

$key = q/a=R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4363.png"
 ALT="$a=R$">|; 

$key = q/a=r_cslash(1-e^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img631.png"
 ALT="$a=r_c/(1-e^{ 2})$">|; 

$key = q/a=r_pslash(1-e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img690.png"
 ALT="$a = r_p/(1-e)$">|; 

$key = q/a=r_pslash(e-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img848.png"
 ALT="$a=r_p/(e-1)$">|; 

$key = q/a>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img300.png"
 ALT="$a&gt;0$">|; 

$key = q/a>R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4365.png"
 ALT="$a&gt;R$">|; 

$key = q/a^{(0)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2437.png"
 ALT="$a^{(0)}$">|; 

$key = q/a^{(1)'}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2540.png"
 ALT="$a^{(1)'}=0$">|; 

$key = q/a^{(1)}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2522.png"
 ALT="$a^{(1)}=0$">|; 

$key = q/a^{(1)}sim{calO}(1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4908.png"
 ALT="$a^{(1)}\sim {\cal O}(1)$">|; 

$key = q/a_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3369.png"
 ALT="$a_4$">|; 

$key = q/a_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3376.png"
 ALT="$a_6$">|; 

$key = q/a_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1328.png"
 ALT="$a_c$">|; 

$key = q/a_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img989.png"
 ALT="$a_i$">|; 

$key = q/a_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3239.png"
 ALT="$a_j$">|; 

$key = q/a_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1743.png"
 ALT="$a_m$">|; 

$key = q/a_s=1.50times10^{11},{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1700.png"
 ALT="$a_s= 1.50\times 10^{11} {\rm m}$">|; 

$key = q/a_{0i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3238.png"
 ALT="$a_{0i}$">|; 

$key = q/a_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3384.png"
 ALT="$a_{11}$">|; 

$key = q/aggl;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1367.png"
 ALT="$a\gg l$">|; 

$key = q/alpha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3658.png"
 ALT="$\alpha'$">|; 

$key = q/alpha'=0.11458;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3665.png"
 ALT="$\alpha'=0.11458$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1461.png"
 ALT="$\alpha$">|; 

$key = q/alpha<5slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img557.png"
 ALT="$\alpha&lt;5/2$">|; 

$key = q/alpha=(aslasha')^{(0)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4921.png"
 ALT="$\alpha=(a/a')^{(0)}$">|; 

$key = q/alpha=(mu_2slash3,mu_1)^{1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2345.png"
 ALT="$\alpha = (\mu_2/3 \mu_1)^{1/3}$">|; 

$key = q/alpha=0.15;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img33.png"
 ALT="$\alpha =0.15$">|; 

$key = q/alpha=0.623;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img42.png"
 ALT="$\alpha =0.623$">|; 

$key = q/alpha=0.89;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img44.png"
 ALT="$\alpha =0.89$">|; 

$key = q/alpha=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3403.png"
 ALT="$\alpha=0$">|; 

$key = q/alpha=1.02;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4424.png"
 ALT="$\alpha=1.02$">|; 

$key = q/alpha=1.57;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4433.png"
 ALT="$\alpha=1.57$">|; 

$key = q/alpha=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1044.png"
 ALT="$\alpha= 1$">|; 

$key = q/alpha=G,Mslash({calE},b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img932.png"
 ALT="$\alpha=G M/({\cal E} b)$">|; 

$key = q/alpha=a,eslashH;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2751.png"
 ALT="$\alpha = a e/H$">|; 

$key = q/alpha=aslasha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2465.png"
 ALT="$\alpha=a/a'$">|; 

$key = q/alpha^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1928.png"
 ALT="$\alpha^{-1}$">|; 

$key = q/alpha_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3429.png"
 ALT="$\alpha_0$">|; 

$key = q/alpha_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1751.png"
 ALT="$\alpha_n$">|; 

$key = q/alpha_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1800.png"
 ALT="$\alpha_n=0$">|; 

$key = q/alpha_{n,m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.63ex; " SRC="|."$dir".q|img4211.png"
 ALT="$\alpha_{n,m}$">|; 

$key = q/alphagg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2915.png"
 ALT="$\alpha\gg 1$">|; 

$key = q/alphall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1927.png"
 ALT="$\alpha\ll 1$">|; 

$key = q/alphaneq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img1045.png"
 ALT="$\alpha\neq 1$">|; 

$key = q/alpharightarrowalpha-(15slash8),m,sin(2,D);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3689.png"
 ALT="$\alpha\rightarrow \alpha - (15/8) m \sin (2  D)$">|; 

$key = q/arightarrowzeta,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3693.png"
 ALT="$a\rightarrow \zeta a$">|; 

$key = q/aslashR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2925.png"
 ALT="$a/R$">|; 

$key = q/aslasha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3503.png"
 ALT="$a/a'$">|; 

$key = q/asqrt{6,mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img297.png"
 ALT="$a\sqrt{6 \mu}$">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img9.png"
 ALT="$b$">|; 

$key = q/b=(1-e^{,2})^{1slash2},a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img632.png"
 ALT="$b=(1-e^{ 2})^{1/2} a$">|; 

$key = q/b=hslash(2,{calE})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img930.png"
 ALT="$b=h/(2 {\cal E})^{1/2}$">|; 

$key = q/b>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3989.png"
 ALT="$b&gt;0$">|; 

$key = q/b>R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img934.png"
 ALT="$b&gt;R$">|; 

$key = q/b_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3370.png"
 ALT="$b_4$">|; 

$key = q/b_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3377.png"
 ALT="$b_6$">|; 

$key = q/b_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3240.png"
 ALT="$b_j$">|; 

$key = q/b_s^{(j)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2473.png"
 ALT="$b_s^{(j)}$">|; 

$key = q/b_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3385.png"
 ALT="$b_{11}$">|; 

$key = q/b_{3slash2}^{(1)}(alpha)simeq3,alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2878.png"
 ALT="$b_{3/2}^{(1)}(\alpha)\simeq 3 \alpha$">|; 

$key = q/b_{3slash2}^{(2)}(alpha)simeq(15slash4),alpha^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2879.png"
 ALT="$b_{3/2}^{(2)}(\alpha)
\simeq (15/4) \alpha^{ 2}$">|; 

$key = q/bar{rho}(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4371.png"
 ALT="$\bar{\rho}(a)$">|; 

$key = q/beta(theta,theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4202.png"
 ALT="$\beta(\theta,\theta')$">|; 

$key = q/beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img771.png"
 ALT="$\beta$">|; 

$key = q/beta=(7slash12),(mu_2slashmu_1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2346.png"
 ALT="$\beta=(7/12) (\mu_2/\mu_1)$">|; 

$key = q/beta=I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img801.png"
 ALT="$\beta=I$">|; 

$key = q/beta=b_{3slash2}^{(2)}(alpha)slashb_{3slash2}^{(1)}(alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2870.png"
 ALT="$\beta=b_{3/2}^{(2)}(\alpha)/b_{3/2}^{(1)}(\alpha)$">|; 

$key = q/beta_l(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2595.png"
 ALT="$\beta_l(^\circ)$">|; 

$key = q/beta_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2591.png"
 ALT="$\beta_l$">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img564.png"
 ALT="$c$">|; 

$key = q/c=3.00times10^8,{rmm},{rms}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2848.png"
 ALT="$c=3.00\times 10^8 {\rm m} {\rm s}^{-1}$">|; 

$key = q/c>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img293.png"
 ALT="$c&gt;0$">|; 

$key = q/c_1,cdots,c_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4643.png"
 ALT="$c_1,\cdots,c_6$">|; 

$key = q/c_1,dots,c_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4646.png"
 ALT="$c_1,\dots,c_6$">|; 

$key = q/c_1,ldots,c_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4706.png"
 ALT="$c_1,\ldots,c_6$">|; 

$key = q/c_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3241.png"
 ALT="$c_j$">|; 

$key = q/cdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.28ex; vertical-align: 0.37ex; " SRC="|."$dir".q|img2073.png"
 ALT="$\cdot$">|; 

$key = q/chi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1234.png"
 ALT="$\chi'$">|; 

$key = q/chi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1237.png"
 ALT="$\chi$">|; 

$key = q/chi_2(r,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4226.png"
 ALT="$\chi_2(r,\theta,\phi)$">|; 

$key = q/chi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4227.png"
 ALT="$\chi_2$">|; 

$key = q/chisim{calO}(|epsilon|);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4355.png"
 ALT="$\chi \sim {\cal O}(\vert\epsilon\vert)$">|; 

$key = q/cos(2,D)=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3593.png"
 ALT="$\cos (2 D) = +1$">|; 

$key = q/cos(2,D)=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3592.png"
 ALT="$\cos (2 D)=-1$">|; 

$key = q/cos(vartheta-vartheta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5011.png"
 ALT="$\cos(\vartheta-\vartheta')$">|; 

$key = q/cosI<1slash!sqrt{5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2720.png"
 ALT="$\cos I&lt; 1/\!\sqrt{5}$">|; 

$key = q/cosI=1slash!sqrt{5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2721.png"
 ALT="$\cos I=1/\!\sqrt{5}$">|; 

$key = q/cosI>1slash!sqrt{5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2719.png"
 ALT="$\cos I&gt; 1/\!\sqrt{5}$">|; 

$key = q/cosIsimeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img777.png"
 ALT="$\cos I\simeq 1$">|; 

$key = q/cos^2theta+sin^2thetaequiv1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img250.png"
 ALT="$\cos^2\theta+\sin^2\theta \equiv 1$">|; 

$key = q/cospsi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5012.png"
 ALT="$\cos\psi$">|; 

$key = q/costheta=zslashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1698.png"
 ALT="$\cos\theta=z/r$">|; 

$key = q/cslash(n,a)gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2839.png"
 ALT="$c/(n a)\gg 1$">|; 

$key = q/d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2392.png"
 ALT="$d$">|; 

$key = q/d>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3995.png"
 ALT="$d&gt;0$">|; 

$key = q/dAslashdt=hslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img630.png"
 ALT="$dA/dt=h/2$">|; 

$key = q/dYslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4648.png"
 ALT="$dY/dt$">|; 

$key = q/dZslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4649.png"
 ALT="$dZ/dt$">|; 

$key = q/d^{,2}epsilonslashda^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4373.png"
 ALT="$d^{ 2}\epsilon/da^{ 2}$">|; 

$key = q/d^{,3}{bfr}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img362.png"
 ALT="$d^{ 3}{\bf r}'$">|; 

$key = q/d^{,3}{bfr}'=r'^{,2},sintheta',dr',dtheta',dphi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img391.png"
 ALT="$d^{ 3}{\bf r}' = r'^{ 2} \sin\theta' dr' d\theta' d\phi'$">|; 

$key = q/d^{,3}{bfr}'rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img363.png"
 ALT="$d^{ 3}{\bf r}'\rightarrow 0$">|; 

$key = q/d^{,3}{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1519.png"
 ALT="$d^{ 3}{\bf r}$">|; 

$key = q/d^{,3}{bfr}=r,dr,dtheta,dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3972.png"
 ALT="$d^{ 3}{\bf r} = r dr d\theta dz$">|; 

$key = q/d^{,3}{bfr}=r^{,2},sintheta,dr,dtheta,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3981.png"
 ALT="$d^{ 3}{\bf r} = r^{ 2} \sin\theta dr d\theta d\phi$">|; 

$key = q/d_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3375.png"
 ALT="$d_1$">|; 

$key = q/d_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3391.png"
 ALT="$d_4$">|; 

$key = q/ddot{phantom{X}}equivd^{,2}slashdT^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3117.png"
 ALT="$\ddot{\phantom{X}}\equiv
d^{ 2}/dT^{ 2}$">|; 

$key = q/ddot{phantom{x}}equivd^{,2}slashdt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img301.png"
 ALT="$\ddot{\phantom{x}}\equiv d^{ 2}/dt^{ 2}$">|; 

$key = q/ddot{z},'=-g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1128.png"
 ALT="$\ddot{z} '=-g$">|; 

$key = q/delta(r-R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4443.png"
 ALT="$\delta(r-R)$">|; 

$key = q/delta(r-a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4236.png"
 ALT="$\delta(r-a)$">|; 

$key = q/delta(theta,theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4204.png"
 ALT="$\delta(\theta,\theta')$">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1278.png"
 ALT="$\delta$">|; 

$key = q/delta<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1286.png"
 ALT="$\delta&lt;0$">|; 

$key = q/delta=0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1316.png"
 ALT="$\delta=0.01$">|; 

$key = q/deltaR_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1362.png"
 ALT="$\delta R_x$">|; 

$key = q/deltaR_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1363.png"
 ALT="$\delta R_y$">|; 

$key = q/deltaR_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1364.png"
 ALT="$\delta R_z$">|; 

$key = q/deltaX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3143.png"
 ALT="$\delta X$">|; 

$key = q/deltaY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3144.png"
 ALT="$\delta Y$">|; 

$key = q/deltaZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3145.png"
 ALT="$\delta Z$">|; 

$key = q/delta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4229.png"
 ALT="$\delta_2$">|; 

$key = q/delta_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4262.png"
 ALT="$\delta_{ij}$">|; 

$key = q/delta_{nm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img428.png"
 ALT="$\delta_{nm}$">|; 

$key = q/deltabeta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3680.png"
 ALT="$\delta\beta'$">|; 

$key = q/deltabeta'=0.58'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3686.png"
 ALT="$\delta\beta' = 0.58''$">|; 

$key = q/deltabeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3187.png"
 ALT="$\delta \beta$">|; 

$key = q/deltalambda';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3679.png"
 ALT="$\delta \lambda'$">|; 

$key = q/deltalambda'=6.4'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3685.png"
 ALT="$\delta\lambda' = 6.4''$">|; 

$key = q/deltalambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3186.png"
 ALT="$\delta \lambda$">|; 

$key = q/deltaphi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4568.png"
 ALT="$\delta\phi_1$">|; 

$key = q/deltaphi_1=17.2'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4623.png"
 ALT="$\delta\phi_1=17.2''$">|; 

$key = q/deltaphi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4569.png"
 ALT="$\delta\phi_2$">|; 

$key = q/deltaphi_2=0.21'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4624.png"
 ALT="$\delta\phi_2 = 0.21''$">|; 

$key = q/deltasimeq0.05;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1292.png"
 ALT="$\delta\simeq 0.05$">|; 

$key = q/deltasimeq3^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1293.png"
 ALT="$\delta \simeq 3^\circ$">|; 

$key = q/deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img609.png"
 ALT="$\delta\theta$">|; 

$key = q/deltatheta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4566.png"
 ALT="$\delta\theta_1$">|; 

$key = q/deltatheta_1=9.2'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4621.png"
 ALT="$\delta\theta_1=9.2''$">|; 

$key = q/deltatheta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4567.png"
 ALT="$\delta \theta_2$">|; 

$key = q/deltatheta_2=0.090'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4622.png"
 ALT="$\delta\theta_2 = 0.090''$">|; 

$key = q/deltatrightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img306.png"
 ALT="$\delta t\rightarrow 0$">|; 

$key = q/deltax'(t)=deltax_0',exp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2376.png"
 ALT="$\delta x'(t)=\delta x_0' \exp(\gamma t)$">|; 

$key = q/deltax';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2374.png"
 ALT="$\delta x'$">|; 

$key = q/deltax(t)=deltax_0,exp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2265.png"
 ALT="$\delta x(t) = \delta x_0 \exp(\gamma t)$">|; 

$key = q/deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2252.png"
 ALT="$\delta x$">|; 

$key = q/deltax_0';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2378.png"
 ALT="$\delta x_0'$">|; 

$key = q/deltax_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1379.png"
 ALT="$\delta x_j$">|; 

$key = q/deltay'(t)=deltay_0',exp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2377.png"
 ALT="$\delta y'(t)= \delta y_0'  \exp(\gamma t)$">|; 

$key = q/deltay';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2375.png"
 ALT="$\delta y'$">|; 

$key = q/deltay(t)=deltay_0,exp(gamma,t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2266.png"
 ALT="$\delta y(t) = \delta y_0 \exp(\gamma t)$">|; 

$key = q/deltay;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2253.png"
 ALT="$\delta y$">|; 

$key = q/deltay_0';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img2379.png"
 ALT="$\delta y_0'$">|; 

$key = q/depsilonslashda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4378.png"
 ALT="$d\epsilon/da$">|; 

$key = q/depsilonslashda=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4369.png"
 ALT="$d\epsilon/da=0$">|; 

$key = q/df(0)slashdx=-m,omega_0^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img235.png"
 ALT="$df(0)/dx = -m \omega_0^{ 2}$">|; 

$key = q/df(0)slashdx=m,k^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img254.png"
 ALT="$df(0)/dx = m k^{ 2}$">|; 

$key = q/dgammaslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1891.png"
 ALT="$d\gamma/dt$">|; 

$key = q/displaystyle(1+eta)^{1slash2}=frac{5}{bar{rho},a^{,5}}int_0^abar{rho}(a'),a'^{,4},da'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4395.png"
 ALT="$\displaystyle (1+\eta)^{1/2} =\frac{5}{\bar{\rho} a^{ 5}}\int_0^a\bar{\rho}(a') a'^{ 4} da'.$">|; 

$key = q/displaystyle(1+x)^alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3806.png"
 ALT="$\displaystyle (1+x)^\alpha$">|; 

$key = q/displaystyle(1-sigma),(1+gslashn),skew{3}hat{nu}_x+left[sigma-(1+gslashn)^{,2}right]skew{3}hat{nu}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2060.png"
 ALT="$\displaystyle (1-\sigma) (1+g/n) \skew{3}\hat{\nu}_x+\left[\sigma-(1+g/n)^{ 2}\right]\skew{3}\hat{\nu}_y$">|; 

$key = q/displaystyle(2,alpha,D+alpha^{,2},D^{,2}),b_{1slash2}^{(0)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2507.png"
 ALT="$\displaystyle (2 \alpha D+\alpha^{ 2} D^{ 2}) b_{1/2}^{(0)}$">|; 

$key = q/displaystyle(2-2,alpha,D-alpha^{,2},D^{,2}),b_{1slash2}^{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2509.png"
 ALT="$\displaystyle (2-2 \alpha D-\alpha^{ 2} D^{ 2}) b_{1/2}^{(1)}$">|; 

$key = q/displaystyle(lambda_i-lambda_i^{,ast}),{bfx}_i^{ast,T}{bfx}_i=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4085.png"
 ALT="$\displaystyle (\lambda_i - \lambda_i^{ \ast}) {\bf x}_i^{\ast T} {\bf x}_i = 0.$">|; 

$key = q/displaystyle(lambda_i-lambda_j),{bfx}_i^T{bfx}_j=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4099.png"
 ALT="$\displaystyle (\lambda_i-\lambda_j) {\bf x}_i^T{\bf x}_j = 0.$">|; 

$key = q/displaystyle(x+mu_2)^2+y^{,2}=(x-1+mu_2)^2+y^{,2}=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2214.png"
 ALT="$\displaystyle (x+\mu_2)^2 + y^{ 2} = (x-1+\mu_2)^2 + y^{ 2} = 1,$">|; 

$key = q/displaystyle({bfA}-lambda,{bf1}),{bfx}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4075.png"
 ALT="$\displaystyle ({\bf A} - \lambda {\bf 1}) {\bf x} = {\bf0},$">|; 

$key = q/displaystyle({bfa}times{bfb})cdot({bfc}times{bfd});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3934.png"
 ALT="$\displaystyle ({\bf a}\times {\bf b})\cdot({\bf c}\times {\bf d})$">|; 

$key = q/displaystyle({bfa}times{bfb})times({bfc}times{bfd});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3936.png"
 ALT="$\displaystyle ({\bf a}\times {\bf b})\times ({\bf c}\times {\bf d})$">|; 

$key = q/displaystyle({bfa}times{bfb})times{bfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3932.png"
 ALT="$\displaystyle ({\bf a}\times {\bf b})\times {\bf c}$">|; 

$key = q/displaystyle,,{rmyears}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1740.png"
 ALT="$\displaystyle   {\rm years}.$">|; 

$key = q/displaystyle,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.56ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img190.png"
 ALT="$\displaystyle ,$">|; 

$key = q/displaystyle,times,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1074.png"
 ALT="$\displaystyle  \times,$">|; 

$key = q/displaystyle,{rmyears}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1806.png"
 ALT="$\displaystyle  {\rm years}.$">|; 

$key = q/displaystyle-2,A,aleft.p_2right|_{r=a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img4296.png"
 ALT="$\displaystyle -2 A a\left.p_2\right\vert _{r=a}$">|; 

$key = q/displaystyle-2,UgeqC,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2174.png"
 ALT="$\displaystyle -2 U \geq C,$">|; 

$key = q/displaystyle-c,r_c^{,n}-frac{c,n}{3},r_c^{,n}<0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img970.png"
 ALT="$\displaystyle -c r_c^{ n} -\frac{c n}{3} r_c^{ n} &lt; 0,$">|; 

$key = q/displaystyle-frac{G,M}{R}left[1+left(frac{2}{3},epsilon-J_2right)P_2(costheta)right]+frac{G,M}{R},zeta,left[P_2(costheta)-1right]simeqc,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1165.png"
 ALT="$\displaystyle - \frac{G M}{R} \left[1+ \left(\frac{2}{3} \epsilon - J_2\right...
...\theta)\right]
+\frac{G M}{R}  \zeta \left[P_2(\cos\theta)-1\right]\simeq c,$">|; 

$key = q/displaystyle-frac{h^{,2}}{r_c^{,3}}=f(r_c),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img958.png"
 ALT="$\displaystyle -\frac{h^{ 2}}{r_c^{ 3}} = f(r_c),$">|; 

$key = q/displaystyle-muleft[(4,A+B),r^{,2},frac{partialp_2}{partialx_i}+2,frac{partialphi_2}{partialx_i}right]_{r=a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4293.png"
 ALT="$\displaystyle -\mu\left[(4 A+B) r^{ 2} \frac{\partial p_2}{\partial x_i}+2 \frac{\partial \phi_2}{\partial x_i}\right]_{r=a}$">|; 

$key = q/displaystyle-nabla(p+rho,{mitPhi})={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4267.png"
 ALT="$\displaystyle - \nabla(p+\rho {\mit\Phi}) = {\bf0}.$">|; 

$key = q/displaystyle-nablap_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4270.png"
 ALT="$\displaystyle -\nabla p_2$">|; 

$key = q/displaystyle.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.28ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle .
$">|; 

$key = q/displaystyle1+costheta=2,cos^2(thetaslash2)=frac{2,(1-e),cos^2(Eslash2)}{1-e,cosE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img719.png"
 ALT="$\displaystyle 1+\cos\theta = 2 \cos^2(\theta/2) = \frac{2 (1-e) \cos^2( E/2)}{1-e \cos E},$">|; 

$key = q/displaystyle1-costheta=2,sin^2(thetaslash2)=frac{2,(1+e),sin^2(Eslash2)}{1-e,cosE}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img720.png"
 ALT="$\displaystyle 1-\cos\theta = 2 \sin^2(\theta/2) = \frac{2 (1+e) \sin^2 (E/2)}{1-e \cos E}.$">|; 

$key = q/displaystyle10,A,mu+2,B,mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4302.png"
 ALT="$\displaystyle 10 A \mu + 2 B \mu$">|; 

$key = q/displaystyle2,omega_1,x_1+omega_1^{,2},y_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3395.png"
 ALT="$\displaystyle 2 \omega_1 x_1+\omega_1^{ 2} y_1$">|; 

$key = q/displaystyle2,r+(e-1),frac{r^{,2}}{r_p}-(e+1),r_p=frac{r_p}{1-e},e^{,2},(1-cos^2E)=frac{r_p}{1-e},e^{,2},sin^2E.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img688.png"
 ALT="$\displaystyle 2 r + (e-1) \frac{r^{ 2}}{r_p}- (e+1) r_p = \frac{r_p}{1-e} e^{ 2} (1-\cos^2 E)= \frac{r_p}{1-e} e^{ 2} \sin^2E.$">|; 

$key = q/displaystyle2,skew{5}ddot{theta}+cos(theta-phi),skew{5}ddot{phi}+sin(theta-phi),skew{5}dot{phi}^{,2}+frac{2,g}{l},sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1457.png"
 ALT="$\displaystyle 2 \skew{5}\ddot{\theta} + \cos(\theta-\phi) \skew{5}\ddot{\phi} + \sin(\theta-\phi) \skew{5}\dot{\phi}^{ 2} + \frac{2 g}{l} \sin\theta$">|; 

$key = q/displaystyle4,A,mu+5,B,mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4301.png"
 ALT="$\displaystyle 4 A \mu + 5 B \mu$">|; 

$key = q/displaystyle=(-1)^n,J_n(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4029.png"
 ALT="$\displaystyle =(-1)^n J_n(x),$">|; 

$key = q/displaystyle=(-8,sin^3alpha+4,sinalpha),cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3867.png"
 ALT="$\displaystyle = (-8 \sin^3\alpha+4 \sin\alpha) \cos\alpha$">|; 

$key = q/displaystyle=(-sintheta,,costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img592.png"
 ALT="$\displaystyle = (-\sin\theta,  \cos\theta),$">|; 

$key = q/displaystyle=(-sintheta,,costheta,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4156.png"
 ALT="$\displaystyle = (-\sin\theta, \cos\theta, 0),$">|; 

$key = q/displaystyle=(0,,0,,-g),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1111.png"
 ALT="$\displaystyle = (0, 0, -g),$">|; 

$key = q/displaystyle=(0,,0,,1).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4157.png"
 ALT="$\displaystyle = (0, 0, 1).$">|; 

$key = q/displaystyle=(0,,0,,R),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1109.png"
 ALT="$\displaystyle = (0, 0, R),$">|; 

$key = q/displaystyle=(0,,0,,omega_z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1843.png"
 ALT="$\displaystyle =(0,  0,  \omega_z),$">|; 

$key = q/displaystyle=(1-e^{,2})^{1slash2},n,a^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img647.png"
 ALT="$\displaystyle = (1-e^{ 2})^{1/2} n a^{ 2},$">|; 

$key = q/displaystyle=(2,A+B),r^{,2},frac{partialp_2}{partialx_i}+2,(2,A+B),p_2,x_i+2,frac{partialphi_2}{partialx_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4287.png"
 ALT="$\displaystyle = (2 A+B) r^{ 2} \frac{\partial p_2}{\partial x_i} + 2 (2 A+B) p_2 x_i + 2 \frac{\partial\phi_2}{\partial x_i},$">|; 

$key = q/displaystyle=(A_1,C_2-A_2,C_1),cos^2{mitOmega}+(B_1,D_2-B_2,D_1),sin^2{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4730.png"
 ALT="$\displaystyle =
(A_1 C_2-A_2 C_1) \cos^2{\mit\Omega} + (B_1 D_2-B_2 D_1) \sin^2{\mit\Omega}$">|; 

$key = q/displaystyle=(B_1,D_2-B_2,D_1),cos^2{mitOmega}+(A_1,C_2-A_2,C_1),sin^2{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4733.png"
 ALT="$\displaystyle =
(B_1 D_2-B_2 D_1) \cos^2{\mit\Omega} + (A_1 C_2-A_2 C_1) \sin^2{\mit\Omega}$">|; 

$key = q/displaystyle=(a_y,b_z-a_z,b_y),{bfe}_x+(a_z,b_x-a_x,b_z),{bfe}_y+(a_x,b_y-a_y,b_x),{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3929.png"
 ALT="$\displaystyle = (a_y b_z-a_z b_y) {\bf e}_x+(a_z b_x-a_x b_z) {\bf e}_y+(a_x b_y-a_y b_x) {\bf e}_z$">|; 

$key = q/displaystyle=(costheta,,sintheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img590.png"
 ALT="$\displaystyle = (\cos\theta,  \sin\theta),$">|; 

$key = q/displaystyle=(costheta,,sintheta,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4155.png"
 ALT="$\displaystyle = (\cos\theta, \sin\theta, 0),$">|; 

$key = q/displaystyle=(mu,a)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4795.png"
 ALT="$\displaystyle = (\mu a)^{1/2},$">|; 

$key = q/displaystyle=(x+mu_2)^2+y^{,2}+z^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2153.png"
 ALT="$\displaystyle = (x+\mu_2)^2+y^{ 2} + z^{ 2},$">|; 

$key = q/displaystyle=(x-mu_1)^2+y^{,2}+z^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2154.png"
 ALT="$\displaystyle = (x-\mu_1)^2+y^{ 2} + z^{ 2}.$">|; 

$key = q/displaystyle=(xi-xi_1)^2+(eta-eta_1)^2+zeta^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2113.png"
 ALT="$\displaystyle = (\xi-\xi_1)^2+(\eta-\eta_1)^2 + \zeta^{ 2},$">|; 

$key = q/displaystyle=(xi-xi_2)^2+(eta-eta_2)^2+zeta^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2115.png"
 ALT="$\displaystyle = (\xi-\xi_2)^2+(\eta-\eta_2)^2 + \zeta^{ 2}.$">|; 

$key = q/displaystyle=(xi_1,,eta_1,,0)=left(-mu_2,cos(omega,t),,-mu_2,sin(omega,t),,0right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2103.png"
 ALT="$\displaystyle = (\xi_1, \eta_1, 0)=\left(-\mu_2 \cos (\omega  t), -\mu_2 \sin(\omega  t), 0\right),$">|; 

$key = q/displaystyle=(xi_2,,eta_2,,0)=left(mu_1,cos(omega,t),,mu_1,(sinomega,t),,0right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2104.png"
 ALT="$\displaystyle =(\xi_2, \eta_2, 0)= \left(\mu_1 \cos( \omega  t), \mu_1 (\sin\omega  t), 0\right),$">|; 

$key = q/displaystyle=({bfa}cdot{bfc}),({bfb}cdot{bfd})-({bfa}cdot{bfd}),({bfb}cdot{bfc});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3935.png"
 ALT="$\displaystyle =
({\bf a}\cdot{\bf c}) ({\bf b}\cdot{\bf d}) - ({\bf a}\cdot{\bf d}) ({\bf b}\cdot{\bf c})$">|; 

$key = q/displaystyle=({bfa}cdot{bfc}),{bfb}-({bfa}cdot{bfb}),{bfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3931.png"
 ALT="$\displaystyle = ({\bf a}\cdot{\bf c}) {\bf b} - ({\bf a}\cdot{\bf b}) {\bf c}$">|; 

$key = q/displaystyle=({bfa}times{bfb}cdot{bfd}),{bfc}-({bfa}times{bfb}cdot{bfc}),{bfd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3937.png"
 ALT="$\displaystyle = ({\bf a}\times
{\bf b}\cdot{\bf d}) {\bf c} - ({\bf a}\times {\bf b}\cdot{\bf c}) {\bf d}$">|; 

$key = q/displaystyle=({bfc}cdot{bfa}),{bfb}-({bfc}cdot{bfb}),{bfa};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3933.png"
 ALT="$\displaystyle = ({\bf c}\cdot{\bf a}) {\bf b}- ({\bf c}\cdot{\bf b}) {\bf a}$">|; 

$key = q/displaystyle=+cos({mitOmega}-{mitOmega}'),cos(omega+theta),cos(omega'+theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4178.png"
 ALT="$\displaystyle = +\cos({\mit\Omega}-{\mit\Omega}') \cos(\omega+\theta) \cos(\omega'+\theta')$">|; 

$key = q/displaystyle=+cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3827.png"
 ALT="$\displaystyle =+ \cos\alpha$">|; 

$key = q/displaystyle=+coshalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3885.png"
 ALT="$\displaystyle =+ \cosh\alpha$">|; 

$key = q/displaystyle=-1+frac{11}{12},m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3567.png"
 ALT="$\displaystyle = -1 + \frac{11}{12} m^{ 2},$">|; 

$key = q/displaystyle=-1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img481.png"
 ALT="$\displaystyle = - 1,$">|; 

$key = q/displaystyle=-1-frac{19}{6},m-frac{125}{18},m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3448.png"
 ALT="$\displaystyle = -1-\frac{19}{6} m -\frac{125}{18} m^{ 2},$">|; 

$key = q/displaystyle=-2,omega,dot{x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1341.png"
 ALT="$\displaystyle = -2 \omega \dot{x},$">|; 

$key = q/displaystyle=-2,sinleft(frac{alpha+beta}{2}right),sinleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3845.png"
 ALT="$\displaystyle =-2 \sin\left(\frac{\alpha+\beta}{2}\right) \sin\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=-2,{mitOmega},sinlambda,dot{x}'+2,{mitOmega},coslambda,dot{z}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1125.png"
 ALT="$\displaystyle =-2 {\mit\Omega} \sin\lambda \dot{x}'+2 {\mit\Omega} \cos\lambda \dot{z}',$">|; 

$key = q/displaystyle=-3,m,e',sin{calM}'+frac{77}{16},m^{,2},e',sin(2,D-{calM}')-frac{11}{16},m^{,2},e',sin(2,D+{calM}'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3497.png"
 ALT="$\displaystyle =-3 m e' \sin{\cal M}'+\frac{77}{16} m^{ 2} e' \sin(2 D-{\cal M}') -\frac{11}{16} m^{ 2} e' \sin(2 D + {\cal M}'),$">|; 

$key = q/displaystyle=-3,n^{,2},tau,frac{x,z}{a^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1980.png"
 ALT="$\displaystyle =-3 n^{ 2} \tau \frac{x z}{a^{ 2}},$">|; 

$key = q/displaystyle=-3.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3480.png"
 ALT="$\displaystyle =-3.$">|; 

$key = q/displaystyle=-4,sin^3alpha+3,sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3863.png"
 ALT="$\displaystyle =-4 \sin^3\alpha+3 \sin\alpha$">|; 

$key = q/displaystyle=-A,h-sum_{i=1,8}A_i,h_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2646.png"
 ALT="$\displaystyle = -A h -\sum_{i=1,8}A_i h_i,$">|; 

$key = q/displaystyle=-B,p-sum_{i=1,8}B_i,p_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2648.png"
 ALT="$\displaystyle = -B p -\sum_{i=1,8}B_i p_i,$">|; 

$key = q/displaystyle=-C.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2282.png"
 ALT="$\displaystyle = - C.$">|; 

$key = q/displaystyle=-[c_k,c_j].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4693.png"
 ALT="$\displaystyle = -[c_k,c_j].$">|; 

$key = q/displaystyle=-a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4772.png"
 ALT="$\displaystyle = -a,$">|; 

$key = q/displaystyle=-a,n,frac{{calM}}{(1-e)^2}+{calO}({calM}^{,3}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4766.png"
 ALT="$\displaystyle = -a n \frac{{\cal M}}{(1-e)^2}+{\cal O}({\cal M}^{ 3}),$">|; 

$key = q/displaystyle=-cos({mitOmega}-{mitOmega}'),sin(omega+theta),cos(omega'+theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4183.png"
 ALT="$\displaystyle = -\cos({\mit\Omega}-{\mit\Omega}') \sin(\omega+\theta) \cos(\omega'+\theta')$">|; 

$key = q/displaystyle=-cos{mitOmega},sinI,r,F_theta+left[sin{mitOmega},sin(omega+theta)-cos{mitOmega},cos(omega+theta),cosIright]r,F_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5135.png"
 ALT="$\displaystyle =- \cos{\mit\Omega} \sin I r F_\theta +\left[\sin{\mit\Omega} \sin(\omega+\theta)-\cos{\mit\Omega} \cos(\omega+\theta) \cos I\right]r F_z,$">|; 

$key = q/displaystyle=-e,I,sin(F-{calM})+e,I,sin(F+{calM}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3633.png"
 ALT="$\displaystyle =-e I \sin(F-{\cal M}) + e I \sin(F+{\cal M}).$">|; 

$key = q/displaystyle=-frac{11}{16}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3490.png"
 ALT="$\displaystyle =-\frac{11}{16}.$">|; 

$key = q/displaystyle=-frac{15}{8},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3293.png"
 ALT="$\displaystyle =- \frac{15}{8},$">|; 

$key = q/displaystyle=-frac{15}{8}-frac{199}{32},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3569.png"
 ALT="$\displaystyle = -\frac{15}{8} -\frac{199}{32} m,$">|; 

$key = q/displaystyle=-frac{15}{8}-frac{93}{8},m.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3513.png"
 ALT="$\displaystyle =-\frac{15}{8}-\frac{93}{8} m.$">|; 

$key = q/displaystyle=-frac{15}{8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3509.png"
 ALT="$\displaystyle =-\frac{15}{8}.$">|; 

$key = q/displaystyle=-frac{1}{2},frac{C_D,A,rho(a)}{m},frac{mu}{a},{rme}^{,alpha,cosE},frac{(1+e,cosE)^{1slash2}}{(1-e,cosE)^{3slash2}},e,sinE,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2747.png"
 ALT="$\displaystyle = -\frac{1}{2} \frac{C_D A \rho(a)}{m} \frac{\mu}{a} {\rm e}^{ \alpha \cos E} \frac{(1+e \cos E)^{1/2}}{(1-e \cos E)^{3/2}} e \sin E,$">|; 

$key = q/displaystyle=-frac{1}{4},I^{,2},sin(2,F),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3632.png"
 ALT="$\displaystyle =-\frac{1}{4} I^{ 2} \sin(2 F),$">|; 

$key = q/displaystyle=-frac{1}{4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3626.png"
 ALT="$\displaystyle =-\frac{1}{4}.$">|; 

$key = q/displaystyle=-frac{1}{6},m^{,2}+r_{01},m^{,4}+r_{02},e^{,2}+r_{03},I^{,2}+r_1,e,cos{calM}+r_2,e^{,2},cos(2,{calM})+r_3,I^{,2},cos(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3228.png"
 ALT="$\displaystyle = -\frac{1}{6} m^{ 2}+ r_{01} m^{ 4}+ r_{02} e^{ 2}+r_{03}\...
..._1 e \cos{\cal M} +r_2 e^{ 2} \cos(2 {\cal M})
+ r_3 I^{ 2} \cos(2 F)$">|; 

$key = q/displaystyle=-frac{1}{m_2},frac{partialU}{partial{bfr}_2}+frac{1}{m_1},frac{partialU}{partial{bfr}_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2962.png"
 ALT="$\displaystyle =-\frac{1}{m_2} \frac{\partial U}{\partial {\bf r}_2}+\frac{1}{m_1} \frac{\partial U}{\partial{\bf r}_1},$">|; 

$key = q/displaystyle=-frac{1}{sqrt{1-x^{,2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3787.png"
 ALT="$\displaystyle = -\frac{1}{\sqrt{1-x^{ 2}}}$">|; 

$key = q/displaystyle=-frac{21}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3287.png"
 ALT="$\displaystyle =- \frac{21}{4},$">|; 

$key = q/displaystyle=-frac{21}{4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3481.png"
 ALT="$\displaystyle =-\frac{21}{4}.$">|; 

$key = q/displaystyle=-frac{25}{64},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3515.png"
 ALT="$\displaystyle =- \frac{25}{64},$">|; 

$key = q/displaystyle=-frac{2pi,G}{r^{,n+1}}int_0^rint_0^pir'^{,n+2},rho(r',theta'),P_n(costheta'),sintheta',dtheta',dr';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img440.png"
 ALT="$\displaystyle = -\frac{2\pi G}{r^{ n+1}}\int_0^r \int_0^\pi r'^{ n+2} 
\rho(r',\theta') P_n(\cos\theta') \sin\theta' d\theta' dr'$">|; 

$key = q/displaystyle=-frac{2}{3},epsilon,R,P_2(costheta)+skew{3}tilde{delta}(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4446.png"
 ALT="$\displaystyle = - \frac{2}{3} \epsilon R P_2(\cos\theta) + \skew{3}\tilde{\delta}(\theta,\phi)$">|; 

$key = q/displaystyle=-frac{2}{3},epsilon,a,P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4315.png"
 ALT="$\displaystyle = -\frac{2}{3} \epsilon a P_2(\cos\theta),$">|; 

$key = q/displaystyle=-frac{2}{3}sqrt{frac{4pi}{5}},epsilon,R,Y_2^{,0}+skew{3}tilde{delta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4447.png"
 ALT="$\displaystyle = -\frac{2}{3}\sqrt{\frac{4\pi}{5}} \epsilon R Y_2^{ 0}+ \skew{3}\tilde{\delta},$">|; 

$key = q/displaystyle=-frac{3,J_3}{8}left(frac{R}{a}right)^3frac{(5,cos^2I-1)}{(1-e^{,2})^{,2}},sinI,cosomega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2899.png"
 ALT="$\displaystyle =-\frac{3 J_3}{8}\left(\frac{R}{a}\right)^3 \frac{(5 \cos^2 I-1)}{(1-e^{ 2})^{ 2}} \sin I \cos\omega,$">|; 

$key = q/displaystyle=-frac{3}{10}+frac{5}{2},{calC}-frac{15}{8},{calC}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4408.png"
 ALT="$\displaystyle = -\frac{3}{10}+\frac{5}{2} {\cal C} -\frac{15}{8} {\cal C}^{ 2},$">|; 

$key = q/displaystyle=-frac{3}{2}+frac{1}{4},m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3278.png"
 ALT="$\displaystyle = -\frac{3}{2}+\frac{1}{4} m^{ 2},$">|; 

$key = q/displaystyle=-frac{3}{2}+frac{1}{4},m^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3446.png"
 ALT="$\displaystyle = -\frac{3}{2}+\frac{1}{4} m^{ 2}.$">|; 

$key = q/displaystyle=-frac{3}{2},x_1^{,2}+frac{3}{4},y_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3245.png"
 ALT="$\displaystyle = -\frac{3}{2} x_1^{ 2}+\frac{3}{4} y_1^{ 2},$">|; 

$key = q/displaystyle=-frac{3}{2},x_1^{,2}-frac{3}{4},y_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3251.png"
 ALT="$\displaystyle = -\frac{3}{2} x_1^{ 2}-\frac{3}{4} y_1^{ 2},$">|; 

$key = q/displaystyle=-frac{3}{2},x_1^{,2}-frac{3}{4},y_1^{,2}=-frac{9}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3575.png"
 ALT="$\displaystyle = -\frac{3}{2} x_1^{ 2} -\frac{3}{4} y_1^{ 2}=-\frac{9}{2},$">|; 

$key = q/displaystyle=-frac{3}{2},x_4,z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3300.png"
 ALT="$\displaystyle = -\frac{3}{2} x_4 z_1,$">|; 

$key = q/displaystyle=-frac{3}{2},x_4,z_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3295.png"
 ALT="$\displaystyle =-\frac{3}{2} x_4 z_4,$">|; 

$key = q/displaystyle=-frac{3}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3267.png"
 ALT="$\displaystyle = -\frac{3}{4},$">|; 

$key = q/displaystyle=-frac{3}{4},frac{skew{3}tilde{epsilon}}{omega,skew{5}dot{mitOmega},(1-e^{,2})^{,3slash2}},frac{G,m}{a^{,3}},sin(2,I),costheta_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.25ex; " SRC="|."$dir".q|img4559.png"
 ALT="$\displaystyle =-\frac{3}{4} \frac{\skew{3}\tilde{\epsilon}}{\omega \skew{5}\d...
...t\Omega} (1-e^{ 2})^{ 3/2}} \frac{G m}{a^{ 3}} \sin(2 I) \cos\theta_0,$">|; 

$key = q/displaystyle=-frac{3}{4},x_1+frac{3}{4},y_1+frac{3}{2},x_1,y_4-frac{3}{2},y_1,x_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3282.png"
 ALT="$\displaystyle =- \frac{3}{4} x_1+\frac{3}{4} y_1+\frac{3}{2} x_1 y_4-\frac{3}{2} y_1 x_4,$">|; 

$key = q/displaystyle=-frac{3}{4},x_1+frac{3}{4},y_1+frac{3}{2},x_1,y_4-frac{3}{2},y_1,x_4.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3530.png"
 ALT="$\displaystyle =-\frac{3}{4} x_1+\frac{3}{4} y_1+\frac{3}{2} x_1 y_4-\frac{3}{2} y_1 x_4.$">|; 

$key = q/displaystyle=-frac{3}{4},x_1-frac{3}{4},y_1+frac{3}{2},x_1,y_4+frac{3}{2},y_1,x_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3284.png"
 ALT="$\displaystyle = -\frac{3}{4} x_1-\frac{3}{4} y_1+\frac{3}{2} x_1 y_4+\frac{3}{2} y_1 x_4,$">|; 

$key = q/displaystyle=-frac{3}{4},x_1-frac{3}{4},y_1+frac{3}{2},x_1,y_4+frac{3}{2},y_1,x_4.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3535.png"
 ALT="$\displaystyle =-\frac{3}{4} x_1-\frac{3}{4} y_1+\frac{3}{2} x_1 y_4+\frac{3}{2} y_1 x_4.$">|; 

$key = q/displaystyle=-frac{3}{4},x_4-frac{3}{4},y_4+frac{3}{2},x_4,y_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3280.png"
 ALT="$\displaystyle =- \frac{3}{4} x_4-\frac{3}{4} y_4+\frac{3}{2} x_4 y_4,$">|; 

$key = q/displaystyle=-frac{3}{4},x_4-frac{3}{4},y_4+frac{3}{2},x_4,y_4=-frac{75}{32},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3452.png"
 ALT="$\displaystyle =-\frac{3}{4} x_4-\frac{3}{4} y_4+\frac{3}{2} x_4 y_4=-\frac{75}{32},$">|; 

$key = q/displaystyle=-frac{3}{4},x_6+frac{3}{4},y_6-frac{3}{2},x_4,y_6+frac{3}{2},y_4,x_6,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3273.png"
 ALT="$\displaystyle =-\frac{3}{4} x_6+ \frac{3}{4} y_6
-\frac{3}{2} x_4 y_6
+\frac{3}{2} y_4 x_6,$">|; 

$key = q/displaystyle=-frac{3}{4},x_6+frac{3}{4},y_6-frac{3}{2},x_4,y_6+frac{3}{2},y_4,x_6.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3540.png"
 ALT="$\displaystyle = -\frac{3}{4} x_6+\frac{3}{4} y_6-\frac{3}{2} x_4 y_6+\frac{3}{2} y_4 x_6.$">|; 

$key = q/displaystyle=-frac{3}{4},z_1=-frac{3}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3623.png"
 ALT="$\displaystyle =-\frac{3}{4} z_1 = -\frac{3}{4},$">|; 

$key = q/displaystyle=-frac{3}{4},z_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3253.png"
 ALT="$\displaystyle = -\frac{3}{4} z_1^{ 2},$">|; 

$key = q/displaystyle=-frac{3}{8},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3505.png"
 ALT="$\displaystyle =-\frac{3}{8},$">|; 

$key = q/displaystyle=-frac{3}{8},frac{skew{3}tilde{epsilon}}{omega,skew{5}dot{mitOmega},(1-e^{,2})^{,3slash2}},frac{G,m}{a^{,3}}sin^2I,costheta_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.25ex; " SRC="|."$dir".q|img4564.png"
 ALT="$\displaystyle =- \frac{3}{8} \frac{\skew{3}\tilde{\epsilon}}{\omega \skew{5}\dot{\mit\Omega} (1-e^{ 2})^{ 3/2}} \frac{G m}{a^{ 3}}\sin^2 I \cos\theta_0.$">|; 

$key = q/displaystyle=-frac{3}{8},frac{skew{3}tilde{epsilon}}{omega,skew{5}dot{mitOmega},(1-e^{,2})^{,3slash2}},frac{G,m}{a^{,3}}sin^2I,sintheta_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.25ex; " SRC="|."$dir".q|img4561.png"
 ALT="$\displaystyle = -\frac{3}{8} \frac{\skew{3}\tilde{\epsilon}}{\omega \skew{5}\dot{\mit\Omega} (1-e^{ 2})^{ 3/2}} \frac{G m}{a^{ 3}}\sin^2 I \sin\theta_0,$">|; 

$key = q/displaystyle=-frac{3}{8}-frac{3}{4},x_{11},m+frac{3}{4},y_{11},m-frac{3}{2},x_4,y_{11},m+frac{3}{2},y_4,x_{11},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3291.png"
 ALT="$\displaystyle = -\frac{3}{8}-\frac{3}{4} x_{11} m+\frac{3}{4} y_{11} m-\frac{3}{2} x_4 y_{11} m+\frac{3}{2} y_4 x_{11} m,$">|; 

$key = q/displaystyle=-frac{459}{512},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3546.png"
 ALT="$\displaystyle = -\frac{459}{512},$">|; 

$key = q/displaystyle=-frac{4}{42}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4306.png"
 ALT="$\displaystyle = -\frac{4}{42}.$">|; 

$key = q/displaystyle=-frac{5}{4},frac{omega^{,2},R^{,3}}{G,m},frac{1}{1+tilde{mu}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1359.png"
 ALT="$\displaystyle = -\frac{5}{4} \frac{\omega^{ 2} R^{ 3}}{G m} \frac{1}{1+\tilde{\mu}},$">|; 

$key = q/displaystyle=-frac{5}{4},frac{omega^{,2},R^{,3}}{G,m},frac{1}{1+tilde{mu}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1360.png"
 ALT="$\displaystyle = -\frac{5}{4} \frac{\omega^{ 2} R^{ 3}}{G m} \frac{1}{1+\tilde{\mu}}.$">|; 

$key = q/displaystyle=-frac{5}{6},frac{omega^{,2},R^{,3}}{G,m},frac{1}{1+tilde{mu}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1357.png"
 ALT="$\displaystyle = -\frac{5}{6} \frac{\omega^{ 2} R^{ 3}}{G m} \frac{1}{1+\tilde{\mu}},$">|; 

$key = q/displaystyle=-frac{77}{16}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3485.png"
 ALT="$\displaystyle =-\frac{77}{16}.$">|; 

$key = q/displaystyle=-frac{8pi,G}{3}left{frac{epsilon(a)}{a}int_0^arho(a'),a'^{,2},da'-frac{1}{5,a^{,3}}int_0^arho(a'),d[epsilon(a'),a'^{,5}]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4350.png"
 ALT="$\displaystyle =-\frac{8\pi G}{3}\left\{\frac{\epsilon(a)}{a}\int_0^a \rho(a')\...
...2} da'-\frac{1}{5 a^{ 3}}\int_0^a \rho(a') d[\epsilon(a') a'^{ 5}]\right.$">|; 

$key = q/displaystyle=-frac{C_D,A,a,rho(a)}{m},n,(1-e^{,2}),{rme}^{,alpha,cosE},frac{(1+e,cosE)^{1slash2}}{(1-e,cosE)^{3slash2}},cosE,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2767.png"
 ALT="$\displaystyle =-\frac{C_D A a \rho(a)}{m} n (1-e^{ 2}) {\rm e}^{ \alpha \cos E} \frac{(1+e \cos E)^{1/2}}{(1-e  \cos E)^{3/2}} \cos E,$">|; 

$key = q/displaystyle=-frac{C_D,A,a,rho(a)}{m},n,{rme}^{,alpha,cosE},frac{(1+e,cosE)^{3slash2}}{(1-e,cosE)^{3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2765.png"
 ALT="$\displaystyle = -\frac{C_D A a \rho(a)}{m} n {\rm e}^{ \alpha \cos E} \frac{(1+e \cos E)^{3/2}}{(1-e  \cos E)^{3/2}},$">|; 

$key = q/displaystyle=-frac{C_D,A,a,rho(a)}{m},noint{rme}^{,alpha,cosE},frac{(1+e,cosE)^{1slash2}}{(1-e,cosE)^{1slash2}},(1+cosE),frac{dE}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2914.png"
 ALT="$\displaystyle = -\frac{C_D A a \rho(a)}{m} n\oint {\rm e}^{ \alpha \cos E} \frac{(1+e \cos E)^{1/2}}{(1-e  \cos E)^{1/2}} (1+\cos E) \frac{dE}{2\pi},$">|; 

$key = q/displaystyle=-frac{C_D,A,a,rho(a)}{m},noint{rme}^{,alpha,cosE},frac{(1+e,cosE)^{1slash2}}{(1-e,cosE)^{1slash2}},(1-cosE),frac{dE}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2912.png"
 ALT="$\displaystyle = -\frac{C_D A a \rho(a)}{m} n\oint {\rm e}^{ \alpha \cos E} \frac{(1+e \cos E)^{1/2}}{(1-e  \cos E)^{1/2}} (1-\cos E) \frac{dE}{2\pi},$">|; 

$key = q/displaystyle=-frac{C_D,A,a,rho(a)}{m},noint{rme}^{,alpha,cosE},frac{(1+e,cosE)^{3slash2}}{(1-e,cosE)^{1slash2}},frac{dE}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2775.png"
 ALT="$\displaystyle = -\frac{C_D A a \rho(a)}{m} n\oint {\rm e}^{ \alpha \cos E} \frac{(1+e \cos E)^{3/2}}{(1-e  \cos E)^{1/2}} \frac{dE}{2\pi},$">|; 

$key = q/displaystyle=-frac{C_D,A,a,rho(r_p)}{m},nleft(frac{r_a}{r_p}right)^{1slash2}left(frac{2}{pi,alpha}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2916.png"
 ALT="$\displaystyle = -\frac{C_D A a \rho(r_p)}{m} n\left(\frac{r_a}{r_p}\right)^{1/2}\left(\frac{2}{\pi \alpha}\right)^{1/2},$">|; 

$key = q/displaystyle=-frac{L,A}{4pi,a^{,2},m,c^{,2}},frac{2+3,e^{,2}}{(1-e^{,2})^{3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2826.png"
 ALT="$\displaystyle = - \frac{L A}{4\pi a^{ 2} m c^{ 2}} \frac{2+3 e^{ 2}}{(1-e^{ 2})^{3/2}},$">|; 

$key = q/displaystyle=-frac{L,A}{4pi,a^{,2},m,c^{,2}},frac{2,c}{n,a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2827.png"
 ALT="$\displaystyle = -\frac{L A}{4\pi a^{ 2} m c^{ 2}} \frac{2 c}{n a},$">|; 

$key = q/displaystyle=-frac{L,A}{4pi,a^{,2},m,c^{,2}},frac{5,e}{2,(1-e^{,2})^{1slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2828.png"
 ALT="$\displaystyle =-\frac{L A}{4\pi a^{ 2} m c^{ 2}} \frac{5 e}{2 (1-e^{ 2})^{1/2}},$">|; 

$key = q/displaystyle=-frac{L,A}{4pi,r^{,2},m,c},frac{r,skew{5}dot{theta}}{c}=-frac{L,A}{4pi,a^{,2},m,c}left(frac{a}{r}right)^3frac{h}{c,a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2823.png"
 ALT="$\displaystyle =-\frac{L A}{4\pi r^{ 2} m c} \frac{r \skew{5}\dot{\theta}}{c} =-\frac{L A}{4\pi a^{ 2} m c}\left(\frac{a}{r}\right)^3\frac{h}{c a},$">|; 

$key = q/displaystyle=-frac{a,n}{(1-e)^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4776.png"
 ALT="$\displaystyle =- \frac{a n}{(1-e)^2},$">|; 

$key = q/displaystyle=-frac{dV}{dr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1433.png"
 ALT="$\displaystyle = - \frac{d V}{dr},$">|; 

$key = q/displaystyle=-frac{e,r_c}{1-e^{,2}}=-e,a.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4010.png"
 ALT="$\displaystyle =- \frac{e r_c}{1-e^{ 2}}=- e a.$">|; 

$key = q/displaystyle=-frac{e}{2}+left(1-frac{3,e^{,2}}{8}right)cos{calM}+frac{e}{2}left(1-frac{2,e^{,2}}{3}right)cos2{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4054.png"
 ALT="$\displaystyle =-\frac{e}{2} +\left(1-\frac{3 e^{ 2}}{8}\right)\cos {\cal M}+\frac{e}{2}\left(1-\frac{2 e^{ 2}}{3}\right)\cos 2{\cal M}$">|; 

$key = q/displaystyle=-frac{e}{2}+sum_{n=1,infty}left[frac{J_{n-1}(n,e)-J_{-n-1}(-n,e)}{n}right]cos(n,{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img4049.png"
 ALT="$\displaystyle =-\frac{e}{2} + \sum_{n=1,\infty}
\left[\frac{J_{n-1}(n e)-J_{-n-1}(-n e)}{n}\right]\cos (n {\cal M})$">|; 

$key = q/displaystyle=-frac{e}{2}+sum_{n=1,infty}left[frac{J_{n-1}(n,e)-J_{n+1}(n,e)}{n}right]cos(n,{calM}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img4050.png"
 ALT="$\displaystyle = -\frac{e}{2} + \sum_{n=1,\infty}\left[\frac{J_{n-1}(n e)-J_{n+1}(n e)}{n}\right]\cos(n {\cal M}),$">|; 

$key = q/displaystyle=-frac{g,a^{,2}}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4250.png"
 ALT="$\displaystyle = - \frac{g a^{ 2}}{r},$">|; 

$key = q/displaystyle=-frac{g}{2,a},(3,a^{,2}-r^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4248.png"
 ALT="$\displaystyle =-\frac{g}{2 a} (3 a^{ 2}-r^{ 2}),$">|; 

$key = q/displaystyle=-frac{h}{mu}left(frac{e,sintheta}{1+e,costheta}right)F_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5112.png"
 ALT="$\displaystyle = -\frac{h}{\mu}\left(\frac{e \sin\theta}{1+e \cos\theta}\right)F_z,$">|; 

$key = q/displaystyle=-frac{h}{mu}left[costheta,F_r-left(frac{2+e,costheta}{1+e,costheta}right)sintheta,F_thetaright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5110.png"
 ALT="$\displaystyle = -\frac{h}{\mu}\left[\cos\theta  F_r-\left(\frac{2+e \cos\theta}{1+e \cos\theta}\right)\sin\theta F_\theta\right],$">|; 

$key = q/displaystyle=-frac{m_2}{m_1+m_2},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img860.png"
 ALT="$\displaystyle = -\frac{m_2}{m_1+m_2} {\bf r},$">|; 

$key = q/displaystyle=-frac{mu_1,(x+mu_2)}{rho_1^{,3}}-frac{mu_2,(x-mu_1)}{rho_2^{,3}}+omega^{,2},x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2156.png"
 ALT="$\displaystyle = - \frac{\mu_1 (x+\mu_2)}{\rho_1^{ 3}}- \frac{\mu_2 (x-\mu_1)}{\rho_2^{ 3}}
+ \omega^{ 2} x,$">|; 

$key = q/displaystyle=-frac{mu_1,y}{rho_1^{,3}}-frac{mu_2,y}{rho_2^{,3}}+omega^{,2},y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2158.png"
 ALT="$\displaystyle = - \frac{\mu_1 y}{\rho_1^{ 3}}- \frac{\mu_2 y}{\rho_2^{ 3}}
+ \omega^{ 2} y,$">|; 

$key = q/displaystyle=-frac{mu_1,z}{rho_1^{,3}}-frac{mu_2,z}{rho_2^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2160.png"
 ALT="$\displaystyle = - \frac{\mu_1 z}{\rho_1^{ 3}}- \frac{\mu_2 z}{\rho_2^{ 3}},$">|; 

$key = q/displaystyle=-frac{n,a}{2},(1-e^{,2})^{1slash2},(1-cosI),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4817.png"
 ALT="$\displaystyle = - \frac{n a}{2} (1-e^{ 2})^{1/2} (1-\cos I),$">|; 

$key = q/displaystyle=-frac{n,a}{2},[1-(1-e^{,2})^{1slash2}],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4815.png"
 ALT="$\displaystyle = - \frac{n a}{2} [1-(1-e^{ 2})^{1/2}],$">|; 

$key = q/displaystyle=-frac{n_i}{4},epsilon_{ij},alpha_{ij},bar{alpha}_{ij},b^{(2)}_{3slash2}(alpha_{ij}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2574.png"
 ALT="$\displaystyle = -\frac{n_i}{4} \epsilon_{ij} \alpha_{ij} \bar{\alpha}_{ij} b^{(2)}_{3/2}(\alpha_{ij}),$">|; 

$key = q/displaystyle=-frac{n}{2}left(frac{1+e}{1-e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4778.png"
 ALT="$\displaystyle = -\frac{n}{2}\left(\frac{1+e}{1-e}\right)^{1/2},$">|; 

$key = q/displaystyle=-frac{n}{4},epsilon_i,alpha_i,bar{alpha}_i,b_{3slash2}^{(2)}(alpha_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2651.png"
 ALT="$\displaystyle = - \frac{n}{4} \epsilon_i \alpha_i \bar{\alpha}_i b_{3/2}^{(2)}(\alpha_i),$">|; 

$key = q/displaystyle=-frac{partialU}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2161.png"
 ALT="$\displaystyle = -\frac{\partial U}{\partial x},$">|; 

$key = q/displaystyle=-frac{partialU}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2162.png"
 ALT="$\displaystyle = -\frac{\partial U}{\partial y},$">|; 

$key = q/displaystyle=-frac{partialU}{partialz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2163.png"
 ALT="$\displaystyle = -\frac{\partial U}{\partial z},$">|; 

$key = q/displaystyle=-frac{partialU}{partial{bfr}}-left(frac{m_1}{m_1+m_2}right)frac{partialU}{partial{bfr}'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2968.png"
 ALT="$\displaystyle =-\frac{\partial U}{\partial {\bf r}}-\left(\frac{m_1}{m_1+m_2}\right)\frac{\partial U}{\partial{\bf r}'},$">|; 

$key = q/displaystyle=-g-2,{mitOmega},coslambda,dot{y}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1127.png"
 ALT="$\displaystyle = -g - 2 {\mit\Omega} \cos\lambda \dot{y}'.$">|; 

$key = q/displaystyle=-gamma,R^{,4},{rmi},sqrt{frac{2pi}{15}}ointleft(Y_2^{,1}+Y_2^{-1}right)delta,d{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4492.png"
 ALT="$\displaystyle = -\gamma R^{ 4} {\rm i} \sqrt{\frac{2\pi}{15}}\oint\left(Y_2^{ 1}+Y_2^{-1}\right)\delta d{\mit\Omega}.$">|; 

$key = q/displaystyle=-gamma,R^{,4}sqrt{frac{2pi}{15}}ointleft(-Y_2^{,1}+Y_2^{-1}right)delta,d{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4490.png"
 ALT="$\displaystyle =- \gamma R^{ 4}\sqrt{\frac{2\pi}{15}}\oint\left(-Y_2^{ 1}+Y_2^{-1}\right)\delta d{\mit\Omega},$">|; 

$key = q/displaystyle=-h,cos{mitOmega},sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img5125.png"
 ALT="$\displaystyle = -h \cos{\mit\Omega} \sin I,$">|; 

$key = q/displaystyle=-left(e-frac{11}{12},m^{,2},eright),cos{calM}+frac{1}{2},e^{,2}-frac{1}{2},e^{,2},cos(2,{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3586.png"
 ALT="$\displaystyle =-\left(e-\frac{11}{12} m^{ 2} e\right) \cos{\cal M} +\frac{1}{2} e^{ 2}-\frac{1}{2} e^{ 2} \cos(2 {\cal M})$">|; 

$key = q/displaystyle=-left(frac{m_2}{m_1+m_2}right){bfr}-left(frac{m_3}{m_1+m_2+m_3}right){bfr}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2975.png"
 ALT="$\displaystyle =-\left(\frac{m_2}{m_1+m_2}\right){\bf r} -\left(\frac{m_3}{m_1+m_2+m_3}\right){\bf r}',$">|; 

$key = q/displaystyle=-left(frac{r'}{a'}right)left(frac{a}{r}right)^2,cospsi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4950.png"
 ALT="$\displaystyle =-\left(\frac{r'}{a'}\right)\left(\frac{a}{r}\right)^2 \cos\psi.$">|; 

$key = q/displaystyle=-left(frac{r}{a}right)left(frac{a'}{r'}right)^2cospsi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4948.png"
 ALT="$\displaystyle = - \left(\frac{r}{a}\right)\left(\frac{a'}{r'}\right)^2\cos\psi,$">|; 

$key = q/displaystyle=-m^{,3},a_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3394.png"
 ALT="$\displaystyle = -m^{ 3} a_1,$">|; 

$key = q/displaystyle=-m^{,3},b_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3396.png"
 ALT="$\displaystyle = -m^{ 3} b_1,$">|; 

$key = q/displaystyle=-m_p,frac{partial{mitPhi}}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1824.png"
 ALT="$\displaystyle =-m_p \frac{\partial{\mit\Phi}}{\partial x},$">|; 

$key = q/displaystyle=-m_p,frac{partial{mitPhi}}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1826.png"
 ALT="$\displaystyle =-m_p \frac{\partial{\mit\Phi}}{\partial y},$">|; 

$key = q/displaystyle=-m_p,frac{partial{mitPhi}}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img1828.png"
 ALT="$\displaystyle =-m_p \frac{\partial{\mit\Phi}}{\partial z}.$">|; 

$key = q/displaystyle=-mu_1,frac{(eta-eta_1)}{rho_1^{,3}}-mu_2,frac{(eta-eta_2)}{rho_2^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2109.png"
 ALT="$\displaystyle = -\mu_1 \frac{(\eta-\eta_1)}{\rho_1^{ 3}} - \mu_2 \frac{(\eta-\eta_2)}{\rho_2^{ 3}},$">|; 

$key = q/displaystyle=-mu_1,frac{(xi-xi_1)}{rho_1^{,3}}-mu_2,frac{(xi-xi_2)}{rho_2^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2107.png"
 ALT="$\displaystyle = -\mu_1 \frac{(\xi-\xi_1)}{\rho_1^{ 3}} - \mu_2 \frac{(\xi-\xi_2)}{\rho_2^{ 3}},$">|; 

$key = q/displaystyle=-mu_1,frac{zeta}{rho_1^{,3}}-mu_2,frac{zeta}{rho_2^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2111.png"
 ALT="$\displaystyle = -\mu_1 \frac{\zeta}{\rho_1^{ 3}} - \mu_2 \frac{\zeta}{\rho_2^{ 3}},$">|; 

$key = q/displaystyle=-n,a^{,2},(1-e^{,2})^{1slash2},sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4812.png"
 ALT="$\displaystyle = - n a^{ 2} (1-e^{ 2})^{1/2} \sin I,$">|; 

$key = q/displaystyle=-n,a^{,2},(1-e^{,2})^{1slash2},sinI.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4822.png"
 ALT="$\displaystyle = -n a^{ 2} (1-e^{ 2})^{1/2} \sin I.$">|; 

$key = q/displaystyle=-n,a^{,2},e,(1-e^{,2})^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4806.png"
 ALT="$\displaystyle = - n a^{ 2} e (1-e^{ 2})^{-1/2},$">|; 

$key = q/displaystyle=-n,a^{,2},e,(1-e^{,2})^{-1slash2},cosI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4810.png"
 ALT="$\displaystyle = - n a^{ 2} e (1-e^{ 2})^{-1/2} \cos I,$">|; 

$key = q/displaystyle=-r,costheta,F_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5100.png"
 ALT="$\displaystyle = -r \cos\theta F_z,$">|; 

$key = q/displaystyle=-sin(n,t),x'+cos(n,t),y',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3046.png"
 ALT="$\displaystyle = -\sin(n t) x' + \cos(n t) y',$">|; 

$key = q/displaystyle=-sin(n,t),x+cos(n,t),y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3040.png"
 ALT="$\displaystyle =-\sin(n t) x+\cos(n t) y,$">|; 

$key = q/displaystyle=-sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3825.png"
 ALT="$\displaystyle = -\sin\alpha$">|; 

$key = q/displaystyle=-sinhalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3883.png"
 ALT="$\displaystyle = -\sinh\alpha$">|; 

$key = q/displaystyle=-sintheta,,x+costheta,,y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3955.png"
 ALT="$\displaystyle = -\sin\theta  x + \cos\theta  y,$">|; 

$key = q/displaystyle=-sinx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3781.png"
 ALT="$\displaystyle = -\sin x$">|; 

$key = q/displaystyle=-skew{3}dot{h},cos{mitOmega},sinI+h,sin{mitOmega},sinI,skew{5}dot{mitOmega}-h,cos{mitOmega},cosI,dot{I},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img5131.png"
 ALT="$\displaystyle = -\skew{3}\dot{h} \cos{\mit\Omega} \sin I + h \sin{\mit\Omega} \sin I \skew{5}\dot{\mit\Omega} -h \cos{\mit\Omega} \cos I \dot{I},$">|; 

$key = q/displaystyle=-skew{3}dot{x},frac{partialU}{partialx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2166.png"
 ALT="$\displaystyle = -\skew{3}\dot{x} \frac{\partial U}{\partial x},$">|; 

$key = q/displaystyle=-skew{3}dot{y},frac{partialU}{partialy},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2168.png"
 ALT="$\displaystyle = -\skew{3}\dot{y} \frac{\partial U}{\partial y},$">|; 

$key = q/displaystyle=-skew{3}dot{z},frac{partialU}{partialz}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img2170.png"
 ALT="$\displaystyle =-\skew{3}\dot{z} \frac{\partial U}{\partial z}.$">|; 

$key = q/displaystyle=-sqrt{frac{15}{8pi}},sintheta,costheta,,{rme}^{,{rmi},phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img4133.png"
 ALT="$\displaystyle = -\sqrt{\frac{15}{8\pi}} \sin\theta \cos\theta  {\rm e}^{ {\rm i} \phi},$">|; 

$key = q/displaystyle=-sqrt{frac{3}{8pi}},sintheta,,{rme}^{,{rmi},phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4125.png"
 ALT="$\displaystyle =- \sqrt{\frac{3}{8\pi}} \sin\theta  {\rm e}^{ {\rm i} \phi},$">|; 

$key = q/displaystyle=-sum_{i=1,8}frac{n}{4},epsilon_i,alpha_i,bar{alpha}_i,b_{3slash2}^{(1)}(alpha_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2652.png"
 ALT="$\displaystyle =- \sum_{i=1,8} \frac{n}{4} \epsilon_i \alpha_i \bar{\alpha}_i b_{3/2}^{(1)}(\alpha_i),$">|; 

$key = q/displaystyle=-sum_{i=1,N}x_i,y_i,m_i=-intx,y,dm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1506.png"
 ALT="$\displaystyle = - \sum_{i=1,N}x_i y_i  m_i=- \int x y dm,$">|; 

$key = q/displaystyle=-sum_{i=1,N}x_i,z_i,m_i=-intx,z,dm.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1510.png"
 ALT="$\displaystyle = - \sum_{i=1,N}x_i z_i  m_i= -\int x z dm.$">|; 

$key = q/displaystyle=-sum_{i=1,N}y_i,z_i,m_i=-inty,z,dm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1508.png"
 ALT="$\displaystyle = - \sum_{i=1,N}y_i z_i  m_i= -\int y z dm,$">|; 

$key = q/displaystyle=-sum_{j=1,8}A_{ij},h_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2566.png"
 ALT="$\displaystyle =-\sum_{j=1,8} A_{ij} h_j,$">|; 

$key = q/displaystyle=-sum_{j=1,8}B_{ij},p_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2570.png"
 ALT="$\displaystyle =-\sum_{j=1,8} B_{ij} p_j,$">|; 

$key = q/displaystyle=-sum_{jneqi}frac{n_i}{4},epsilon_{ij},alpha_{ij},bar{alpha}_{ij},b^{(1)}_{3slash2}(alpha_{ij}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img2576.png"
 ALT="$\displaystyle =- \sum_{j\neq i} \frac{n_i}{4} \epsilon_{ij} \alpha_{ij} \bar{\alpha}_{ij}  b^{(1)}_{3/2}(\alpha_{ij}),$">|; 

$key = q/displaystyle=-sum_{l=1,8}frac{mu_l}{B-f_l},cos(f_l,t+gamma_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2670.png"
 ALT="$\displaystyle = - \sum_{l=1,8} \frac{\mu_l}{B-f_l} \cos(f_l t+\gamma_l),$">|; 

$key = q/displaystyle=-sum_{l=1,8}frac{mu_l}{B-f_l},sin(f_l,t+gamma_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2668.png"
 ALT="$\displaystyle = - \sum_{l=1,8} \frac{\mu_l}{B-f_l} \sin(f_l t+\gamma_l),$">|; 

$key = q/displaystyle=-sum_{l=1,8}frac{nu_l}{A-g_l},cos(g_l,t+beta_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2666.png"
 ALT="$\displaystyle = - \sum_{l=1,8} \frac{\nu_l}{A-g_l} \cos(g_l t+\beta_l),$">|; 

$key = q/displaystyle=-sum_{l=1,8}frac{nu_l}{A-g_l},sin(g_l,t+beta_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2664.png"
 ALT="$\displaystyle = - \sum_{l=1,8} \frac{\nu_l}{A-g_l} \sin(g_l t+\beta_l),$">|; 

$key = q/displaystyle=-tanalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3829.png"
 ALT="$\displaystyle = -\tan\alpha$">|; 

$key = q/displaystyle=-tanhalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3887.png"
 ALT="$\displaystyle = -\tanh\alpha$">|; 

$key = q/displaystyle=-tau_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1836.png"
 ALT="$\displaystyle =-\tau_x,$">|; 

$key = q/displaystyle=-tau_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1838.png"
 ALT="$\displaystyle =-\tau_y,$">|; 

$key = q/displaystyle=-tau_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1840.png"
 ALT="$\displaystyle =-\tau_z,$">|; 

$key = q/displaystyle=-zeta,a,P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4313.png"
 ALT="$\displaystyle = -\zeta a P_2(\cos\theta),$">|; 

$key = q/displaystyle=-{bff},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle = -{\bf f},$">|; 

$key = q/displaystyle=-{mitOmega}_phi,t+deltaphi_1left(sin{mitOmega}-sin{mitOmega}_0right)-deltaphi_2left[sin(2,{mitOmega})-sin(2,{mitOmega}_0)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4555.png"
 ALT="$\displaystyle = -{\mit\Omega}_\phi t +\delta\phi_1\left(\sin{\mit\Omega}-\sin{...
...ght) - \delta\phi_2
\left[\sin(2 {\mit\Omega})-\sin(2 {\mit\Omega}_0)\right],$">|; 

$key = q/displaystyle=-{mitOmega}_phi,t-deltaphi,sin({mitOmega}_n,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1792.png"
 ALT="$\displaystyle = - {\mit\Omega}_\phi t - \delta\phi \sin({\mit\Omega}_n t),$">|; 

$key = q/displaystyle=-{rmi}sqrt{frac{2pi}{15}},r^{,2}left(Y_2^{,2}-Y_2^{,-2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4473.png"
 ALT="$\displaystyle = - {\rm i}\sqrt{\frac{2\pi}{15}} r^{ 2}\left(Y_2^{ 2}-Y_2^{ -2}\right),$">|; 

$key = q/displaystyle=-|skew{5}dot{mitOmega}_m|,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4584.png"
 ALT="$\displaystyle = -\vert\skew{5}\dot{\mit\Omega}_m\vert,$">|; 

$key = q/displaystyle=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1428.png"
 ALT="$\displaystyle = 0,$">|; 

$key = q/displaystyle=0.28,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4435.png"
 ALT="$\displaystyle =0.28,$">|; 

$key = q/displaystyle=0.332,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4426.png"
 ALT="$\displaystyle =0.332,$">|; 

$key = q/displaystyle=0.67.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4519.png"
 ALT="$\displaystyle = 0.67.$">|; 

$key = q/displaystyle=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1426.png"
 ALT="$\displaystyle = 0.$">|; 

$key = q/displaystyle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3613.png"
 ALT="$\displaystyle =0$">|; 

$key = q/displaystyle=1+3,e,cos{calM}+{calO}(e^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1854.png"
 ALT="$\displaystyle = 1+ 3 e \cos{\cal M} + {\cal O}(e^{ 2}),$">|; 

$key = q/displaystyle=1+alpha,x+frac{alpha,(alpha-1)}{2!},x^{,2}+frac{alpha,(alpha-1),(alpha-2)}{3!},x^{,3}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3807.png"
 ALT="$\displaystyle = 1 + \alpha x + \frac{\alpha (\alpha-1)}{2!} x^{ 2} + \frac{\alpha (\alpha-1) (\alpha-2)}{3!}  x^{ 3}+\cdots$">|; 

$key = q/displaystyle=1+eleft(1-frac{e^{,2}}{8}right)cos{calM}+e^{,2}left(1-frac{e^{,2}}{3}right)cos2{calM}+frac{9,e^{,3}}{8},cos3{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4064.png"
 ALT="$\displaystyle =1+e\left(1-\frac{e^{ 2}}{8}\right)\cos{\cal M} + e^{ 2}\left(1-\frac{e^{ 2}}{3}\right)
\cos 2{\cal M} +\frac{9 e^{ 3}}{8} \cos 3{\cal M}$">|; 

$key = q/displaystyle=1+frac{1}{2},m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3153.png"
 ALT="$\displaystyle = 1+\frac{1}{2} m^{ 2},$">|; 

$key = q/displaystyle=1+frac{x^{,2}}{2!}+frac{x^{,4}}{4!}+frac{x^{,6}}{6!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3821.png"
 ALT="$\displaystyle = 1+\frac{x^{ 2}}{2!} + \frac{x^{ 4}}{4!}+\frac{x^{ 6}}{6!} + \cdots$">|; 

$key = q/displaystyle=1+x+frac{x^{,2}}{2!}+frac{x^{,3}}{3!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3809.png"
 ALT="$\displaystyle = 1 + x + \frac{x^{ 2}}{2!}+ \frac{x^{ 3}}{3!} + \cdots$">|; 

$key = q/displaystyle=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img420.png"
 ALT="$\displaystyle = 1,$">|; 

$key = q/displaystyle=1-e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4770.png"
 ALT="$\displaystyle = 1-e,$">|; 

$key = q/displaystyle=1-e,cos{calM}+frac{e^{,2}}{2},(1-cos2{calM})+frac{3,e^{,3}}{8}left(cos{calM}-cos3{calM}right)+{calO}(e^4).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img790.png"
 ALT="$\displaystyle =1 -e \cos {\cal M} + \frac{e^{ 2}}{2} (1-\cos 2{\cal M}) + \frac{3 e^{ 3}}{8}\left(\cos {\cal M} -\cos 3{\cal M}\right)+ {\cal O}(e^4).$">|; 

$key = q/displaystyle=1-e,cos{calM}-frac{e^{,2}}{2}left(cos2{calM}-1right)-frac{3,e^{,3}}{8}left(cos3{calM}-cos{calM}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4059.png"
 ALT="$\displaystyle =1-e \cos{\cal M} -\frac{e^{ 2}}{2}\left(\cos 2{\cal M}-1\right) - \frac{3 e^{ 3}}{8}\left( \cos 3{\cal M}-
\cos{\cal M}\right)$">|; 

$key = q/displaystyle=1-frac{3}{2},m^{,2}+{calO}(m^{,3}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3565.png"
 ALT="$\displaystyle = 1-\frac{3}{2} m^{ 2}+{\cal O}(m^{ 3}),$">|; 

$key = q/displaystyle=1-frac{x^{,2}}{2!}+frac{x^{,4}}{4!}-frac{x^{,6}}{6!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3815.png"
 ALT="$\displaystyle = 1-\frac{x^{ 2}}{2!} + \frac{x^{ 4}}{4!}-\frac{x^{ 6}}{6!} + \cdots$">|; 

$key = q/displaystyle=1-frac{x^{,2}}{4}+{calO}(x^{,4}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4033.png"
 ALT="$\displaystyle = 1-\frac{x^{ 2}}{4} + {\cal O}(x^{ 4}),$">|; 

$key = q/displaystyle=1.08times10^{-3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4427.png"
 ALT="$\displaystyle = 1.08\times 10^{-3},$">|; 

$key = q/displaystyle=1.15times10^{-3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4422.png"
 ALT="$\displaystyle =1.15\times 10^{-3},$">|; 

$key = q/displaystyle=1.64times10^{-2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4436.png"
 ALT="$\displaystyle = 1.64\times 10^{-2},$">|; 

$key = q/displaystyle=17.9''.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1816.png"
 ALT="$\displaystyle = 17.9''.$">|; 

$key = q/displaystyle=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3831.png"
 ALT="$\displaystyle =1$">|; 

$key = q/displaystyle=2,A,r^{,2},frac{partialp_2}{partialx_i}+2,B,p_2,x_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4289.png"
 ALT="$\displaystyle = 2 A r^{ 2} \frac{\partial p_2}{\partial x_i} + 2 B p_2 x_i,$">|; 

$key = q/displaystyle=2,coshleft(frac{alpha+beta}{2}right),coshleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3900.png"
 ALT="$\displaystyle =2 \cosh\left(\frac{\alpha+\beta}{2}\right) \cosh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,coshleft(frac{alpha+beta}{2}right),sinhleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3898.png"
 ALT="$\displaystyle =2 \cosh\left(\frac{\alpha+\beta}{2}\right) \sinh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,cosleft(frac{alpha+beta}{2}right),cosleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3843.png"
 ALT="$\displaystyle =2 \cos\left(\frac{\alpha+\beta}{2}\right) \cos\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,cosleft(frac{alpha+beta}{2}right),sinleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3841.png"
 ALT="$\displaystyle =2 \cos\left(\frac{\alpha+\beta}{2}\right) \sin\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,e,sin{calM}+frac{5}{4},e^{,2},sin(2,{calM})-frac{1}{4},I^{,2},sin(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3640.png"
 ALT="$\displaystyle =2 e \sin{\cal M} +\frac{5}{4} e^{ 2} \sin(2 {\cal M})-\frac{1}{4} I^{ 2} \sin(2 F)$">|; 

$key = q/displaystyle=2,e,sin{calM}+frac{5}{4},e^{,2},sin(2,{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3588.png"
 ALT="$\displaystyle =2 e \sin{\cal M} +\frac{5}{4} e^{ 2} \sin(2 {\cal M})$">|; 

$key = q/displaystyle=2,n,epsilon'alpha,frac{partial{calS}}{partialskew{5}bar{lambda}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.78ex; " SRC="|."$dir".q|img4887.png"
 ALT="$\displaystyle =2 n \epsilon'\alpha \frac{\partial {\cal S}}{\partial\skew{5}\bar{\lambda}},$">|; 

$key = q/displaystyle=2,omega_1+a_{1,y},m^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3554.png"
 ALT="$\displaystyle = 2 \omega_1+a_{1 y} m^{ 3},$">|; 

$key = q/displaystyle=2,omega_1+b_{1,x},m^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3556.png"
 ALT="$\displaystyle = 2 \omega_1+b_{1 x} m^{ 3},$">|; 

$key = q/displaystyle=2,r_p,P,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img909.png"
 ALT="$\displaystyle =2 r_p P,$">|; 

$key = q/displaystyle=2,sinalpha,cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3859.png"
 ALT="$\displaystyle = 2 \sin\alpha \cos\alpha$">|; 

$key = q/displaystyle=2,sinhalpha,coshalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3916.png"
 ALT="$\displaystyle = 2 \sinh\alpha \cosh\alpha$">|; 

$key = q/displaystyle=2,sinhleft(frac{alpha+beta}{2}right),coshleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3896.png"
 ALT="$\displaystyle =2 \sinh\left(\frac{\alpha+\beta}{2}\right) \cosh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,sinhleft(frac{alpha+beta}{2}right),sinhleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3902.png"
 ALT="$\displaystyle =2 \sinh\left(\frac{\alpha+\beta}{2}\right) \sinh\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,sinleft(frac{alpha+beta}{2}right),cosleft(frac{alpha-beta}{2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3839.png"
 ALT="$\displaystyle =2 \sin\left(\frac{\alpha+\beta}{2}\right) \cos\left(\frac{\alpha-\beta}{2}\right)$">|; 

$key = q/displaystyle=2,skew{5}dot{D}+skew{5}dot{F}=3-2,m+g,m^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3445.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}+\skew{5}\dot{F} = 3-2 m+g m^{ 2}.$">|; 

$key = q/displaystyle=2,skew{5}dot{D}+skew{5}dot{{calM}}'=2-m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3423.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}+\skew{5}\dot{{\cal M}}'=2-m,$">|; 

$key = q/displaystyle=2,skew{5}dot{D}+skew{5}dot{{calM}}=3-2,m-c,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3417.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}+\skew{5}\dot{{\cal M}}=3-2 m-c m^{ 2},$">|; 

$key = q/displaystyle=2,skew{5}dot{D}-skew{5}dot{F}=1-2,m-g,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3443.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}-\skew{5}\dot{F} = 1-2 m-g m^{ 2},$">|; 

$key = q/displaystyle=2,skew{5}dot{D}-skew{5}dot{{calM}}'=2-3,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3421.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}-\skew{5}\dot{{\cal M}}'=2-3 m,$">|; 

$key = q/displaystyle=2,skew{5}dot{D}-skew{5}dot{{calM}}=1-2,m+c,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3415.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}-\skew{5}\dot{{\cal M}}=1-2 m+c m^{ 2},$">|; 

$key = q/displaystyle=2,skew{5}dot{D}=2-2,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3411.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{D}=2-2 m,$">|; 

$key = q/displaystyle=2,skew{5}dot{F}=2+2,g,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3409.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{F}= 2+2 g m^{ 2},$">|; 

$key = q/displaystyle=2,skew{5}dot{{calM}}=2-2,c,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3407.png"
 ALT="$\displaystyle = 2 \skew{5}\dot{{\cal M}}= 2-2 c m^{ 2},$">|; 

$key = q/displaystyle=2,{mitOmega},sinlambda,dot{y}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1123.png"
 ALT="$\displaystyle =2 {\mit\Omega} \sin\lambda \dot{y}',$">|; 

$key = q/displaystyle=2-frac{1}{3},m^{,.2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3568.png"
 ALT="$\displaystyle = 2 - \frac{1}{3} m^{ .2}.$">|; 

$key = q/displaystyle=2-frac{3}{2},m^{,2}+{calO}(m^{,3}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3564.png"
 ALT="$\displaystyle =2-\frac{3}{2} m^{ 2}+{\cal O}(m^{ 3}),$">|; 

$key = q/displaystyle=2.70times10^{-2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4431.png"
 ALT="$\displaystyle =2.70\times 10^{-2},$">|; 

$key = q/displaystyle=2.751times10^{-2},cosgamma_5,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2602.png"
 ALT="$\displaystyle =2.751\times 10^{-2} \cos\gamma_5,$">|; 

$key = q/displaystyle=2.751times10^{-2},singamma_5,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2601.png"
 ALT="$\displaystyle =2.751\times 10^{-2} \sin\gamma_5,$">|; 

$key = q/displaystyle=3,n^{,2},sigma,frac{y,z}{a^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1978.png"
 ALT="$\displaystyle =3 n^{ 2} \sigma \frac{y z}{a^{ 2}},$">|; 

$key = q/displaystyle=3,omega^{,2},x+2,omega,dot{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1339.png"
 ALT="$\displaystyle =3 \omega^{ 2} x + 2 \omega \dot{y},$">|; 

$key = q/displaystyle=3,skew{5}dot{D}=3-3,m.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3427.png"
 ALT="$\displaystyle = 3 \skew{5}\dot{D}=3-3 m.$">|; 

$key = q/displaystyle=3.35times10^{-3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4517.png"
 ALT="$\displaystyle = 3.35\times 10^{-3},$">|; 

$key = q/displaystyle=3.35times10^{-3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4423.png"
 ALT="$\displaystyle = 3.35\times 10^{-3}.$">|; 

$key = q/displaystyle=3left[frac{mu_1,(x+mu_2)^2}{rho_1^{,5}}+frac{mu_2,(x-mu_1)^2}{rho_2^{,5}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.48ex; " SRC="|."$dir".q|img2276.png"
 ALT="$\displaystyle = 3\left[\frac{\mu_1 (x+\mu_2)^2}{\rho_1^{ 5}}+\frac{\mu_2 (x-\mu_1)^2}{\rho_2^{ 5}}\right],$">|; 

$key = q/displaystyle=3left[frac{mu_1,(x+mu_2)}{rho_1^{,5}}+frac{mu_2,(x-mu_1)}{rho_2^{,5}}right]y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.48ex; " SRC="|."$dir".q|img2274.png"
 ALT="$\displaystyle = 3\left[\frac{\mu_1 (x+\mu_2)}{\rho_1^{ 5}}+\frac{\mu_2 (x-\mu_1)}{\rho_2^{ 5}}\right]y,$">|; 

$key = q/displaystyle=3left[frac{mu_1}{rho_1^{,5}}+frac{mu_2}{rho_2^{,5}}right]y^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.48ex; " SRC="|."$dir".q|img2272.png"
 ALT="$\displaystyle = 3\left[ \frac{\mu_1}{\rho_1^{ 5}} + \frac{\mu_2}{\rho_2^{ 5}}\right]y^{ 2},$">|; 

$key = q/displaystyle=4+{calO}(m^{,3}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3563.png"
 ALT="$\displaystyle = 4+{\cal O}(m^{ 3}),$">|; 

$key = q/displaystyle=4,cos^3alpha-3,cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3865.png"
 ALT="$\displaystyle =4 \cos^3\alpha-3 \cos\alpha$">|; 

$key = q/displaystyle=4,skew{5}dot{D}=4-4,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3413.png"
 ALT="$\displaystyle = 4 \skew{5}\dot{D}=4-4 m,$">|; 

$key = q/displaystyle=6.49times10^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img4432.png"
 ALT="$\displaystyle = 6.49\times 10^{-2}.$">|; 

$key = q/displaystyle=8,cos^4alpha-8,cos^2alpha+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3869.png"
 ALT="$\displaystyle =8 \cos^4\alpha-8 \cos^2\alpha+1$">|; 

$key = q/displaystyle=9.6'',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1815.png"
 ALT="$\displaystyle = 9.6'',$">|; 

$key = q/displaystyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.61ex; vertical-align: 0.21ex; " SRC="|."$dir".q|img1632.png"
 ALT="$\displaystyle =$">|; 

$key = q/displaystyle=A,k+sum_{i=1,8}A_i,k_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2645.png"
 ALT="$\displaystyle = A k + \sum_{i=1,8} A_i k_i,$">|; 

$key = q/displaystyle=A-B-1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2280.png"
 ALT="$\displaystyle = A - B - 1,$">|; 

$key = q/displaystyle=A-D-1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2278.png"
 ALT="$\displaystyle = A - D - 1,$">|; 

$key = q/displaystyle=A_0+sum_{n=1,infty}(A_n+A_{-n}),cos(n,{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img4048.png"
 ALT="$\displaystyle = A_0 + \sum_{n=1,\infty}(A_n+A_{-n}) \cos(n {\cal M})$">|; 

$key = q/displaystyle=A_1,cos{mitOmega}-B_1,sin{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4714.png"
 ALT="$\displaystyle = A_1 \cos{\mit\Omega} - B_1 \sin{\mit\Omega},$">|; 

$key = q/displaystyle=B,q+sum_{i=1,8}B_i,q_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2647.png"
 ALT="$\displaystyle = B q + \sum_{i=1,8} B_i q_i,$">|; 

$key = q/displaystyle=B_1,cos{mitOmega}+A_1,sin{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4716.png"
 ALT="$\displaystyle = B_1 \cos{\mit\Omega} +A_1 \sin{\mit\Omega},$">|; 

$key = q/displaystyle=C_1,cos{mitOmega}-D_1,sin{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4718.png"
 ALT="$\displaystyle = C_1 \cos{\mit\Omega} - D_1 \sin{\mit\Omega},$">|; 

$key = q/displaystyle=D_1,cos{mitOmega}+C_1,sin{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4720.png"
 ALT="$\displaystyle = D_1 \cos{\mit\Omega} +C_1 \sin{\mit\Omega},$">|; 

$key = q/displaystyle=F_r,{bfe}_r+F_theta,{bfe}_theta+F_z,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2740.png"
 ALT="$\displaystyle = F_r {\bf e}_r+ F_\theta {\bf e}_\theta+ F_z {\bf e}_z,$">|; 

$key = q/displaystyle=F_{X}+G_{X},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3094.png"
 ALT="$\displaystyle = F_{X}+ G_{X},$">|; 

$key = q/displaystyle=F_{Y}+G_{Y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3096.png"
 ALT="$\displaystyle =F_{Y}+G_{Y},$">|; 

$key = q/displaystyle=F_{Z}+G_{Z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3098.png"
 ALT="$\displaystyle = F_{Z}+G_{Z}.$">|; 

$key = q/displaystyle=G,M,m,frac{bfr}{r^{,3}}+G,M,m',frac{{bfr}'}{r'^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2405.png"
 ALT="$\displaystyle = G M m \frac{\bf r}{r^{ 3}} + G M m' \frac{{\bf r}'}{r'^{ 3}},$">|; 

$key = q/displaystyle=G,m',m,frac{{bfr}-{bfr}'}{|{bfr}-{bfr}'|^{,3}}-G,m',M,frac{{bfr}'}{r'^{,3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img2409.png"
 ALT="$\displaystyle = G m' m \frac{{\bf r}-{\bf r}'}{\vert{\bf r}-{\bf r}'\vert^{ 3}}
- G m' M \frac{{\bf r}'}{r'^{ 3}}.$">|; 

$key = q/displaystyle=G,m'left(frac{{bfr}'-{bfr}}{|{bfr}'-{bfr}|^{,3}}-frac{{bfr}'}{r'^{,3}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2411.png"
 ALT="$\displaystyle =G m'\left(\frac{{\bf r}'-{\bf r}}{\vert{\bf r}'-{\bf r}\vert^{ 3}} - \frac{{\bf r}'}{r'^{ 3}}\right),$">|; 

$key = q/displaystyle=G,m,m',frac{{bfr}'-{bfr}}{|{bfr}'-{bfr}|^{,3}}-G,m,M,frac{{bfr}}{r^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img2407.png"
 ALT="$\displaystyle = G m m' \frac{{\bf r}'-{\bf r}}{\vert{\bf r}'-{\bf r}\vert^{ 3}}
- G m M \frac{{\bf r}}{r^{ 3}},$">|; 

$key = q/displaystyle=G,mleft(frac{{bfr}-{bfr}'}{|{bfr}-{bfr}'|^{,3}}-frac{{bfr}}{r^{,3}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2413.png"
 ALT="$\displaystyle = G m\left(\frac{{\bf r}-{\bf r}'}{\vert{\bf r}-{\bf r}'\vert^{ 3}} - \frac{{\bf r}}{r^{ 3}}\right),$">|; 

$key = q/displaystyle=I,sinF+left(frac{3}{8},m,I+frac{25}{32},m^{,2},Iright)sin(2,D-F)+frac{11}{16},m^{,2},I,sin(2,D+F).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3614.png"
 ALT="$\displaystyle =I \sin F+\left(\frac{3}{8} m I +\frac{25}{32} m^{ 2} I\right)\sin(2 D-F) + \frac{11}{16} m^{ 2} I \sin(2 D+F).$">|; 

$key = q/displaystyle=I,sinF-e,I,sin(F-{calM})+e,I,sin(F+{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3645.png"
 ALT="$\displaystyle =I \sin F-e I \sin(F-{\cal M}) + e I \sin(F+{\cal M})$">|; 

$key = q/displaystyle=I_m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4583.png"
 ALT="$\displaystyle = I_m,$">|; 

$key = q/displaystyle=I_s=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4578.png"
 ALT="$\displaystyle = I_s=0,$">|; 

$key = q/displaystyle=J_n(x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4031.png"
 ALT="$\displaystyle = J_n(x).$">|; 

$key = q/displaystyle=M,dot{bfr}_{cm},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img330.png"
 ALT="$\displaystyle = M \dot{\bf r}_{cm},$">|; 

$key = q/displaystyle=M,{bfr}_{cm}timesdot{bfr}_{cm}+mu,{bfr}timesdot{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img332.png"
 ALT="$\displaystyle = M {\bf r}_{cm}\times \dot{\bf r}_{cm} + \mu {\bf r}\times \dot{\bf r},$">|; 

$key = q/displaystyle=P.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img838.png"
 ALT="$\displaystyle = P.$">|; 

$key = q/displaystyle=R_X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3147.png"
 ALT="$\displaystyle =R_X,$">|; 

$key = q/displaystyle=R_Y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3149.png"
 ALT="$\displaystyle =R_Y,$">|; 

$key = q/displaystyle=R_Z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3151.png"
 ALT="$\displaystyle =R_Z,$">|; 

$key = q/displaystyle=X,P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4317.png"
 ALT="$\displaystyle = X P_2(\cos\theta),$">|; 

$key = q/displaystyle=X_0+deltaX,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3134.png"
 ALT="$\displaystyle =X_0 + \delta X,$">|; 

$key = q/displaystyle=[G,(M+m_i)slasha_i^{,3}]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2561.png"
 ALT="$\displaystyle = [G (M+m_i)/a_i^{ 3}]^{1/2},$">|; 

$key = q/displaystyle=[mu,a,(1-e^{,2})]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4797.png"
 ALT="$\displaystyle = [\mu a (1-e^{ 2})]^{1/2},$">|; 

$key = q/displaystyle=[mu,a,(1-e^{,2})]^{1slash2},cosI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4799.png"
 ALT="$\displaystyle = [\mu a (1-e^{ 2})]^{1/2} \cos I,$">|; 

$key = q/displaystyle=[p,q]'+frac{partial({mitOmega},x',dot{y}'-y',dot{x}')}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4749.png"
 ALT="$\displaystyle = [p,q]' + \frac{\partial({\mit\Omega}, x' \dot{y}'-y' \dot{x}')}{\partial (p,q)}.$">|; 

$key = q/displaystyle=a,(1-e)+{calO}({calM}^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4763.png"
 ALT="$\displaystyle = a (1-e)+ {\cal O}({\cal M}^{ 2}),$">|; 

$key = q/displaystyle=a,(1-e,cosE),,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img728.png"
 ALT="$\displaystyle =a (1-e \cos E)&#8222;$">|; 

$key = q/displaystyle=a,(1-e,cosE),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2741.png"
 ALT="$\displaystyle =a (1-e \cos E),$">|; 

$key = q/displaystyle=a,(1-e^{,2})^{1slash2},sinE,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img907.png"
 ALT="$\displaystyle =a (1-e^{ 2})^{1/2} \sin E,$">|; 

$key = q/displaystyle=a,(cosE-e),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img906.png"
 ALT="$\displaystyle = a (\cos E-e),$">|; 

$key = q/displaystyle=a,(e,coshH-1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img844.png"
 ALT="$\displaystyle = a (e \cosh H - 1),$">|; 

$key = q/displaystyle=a,(e-coshH),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img910.png"
 ALT="$\displaystyle = a (e-\cosh H),$">|; 

$key = q/displaystyle=a,(e^{,2}-1)^{1slash2},sinhH,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img911.png"
 ALT="$\displaystyle =a (e^{ 2}-1)^{1/2} \sinh H,$">|; 

$key = q/displaystyle=a,delta_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4291.png"
 ALT="$\displaystyle = a \delta_2,$">|; 

$key = q/displaystyle=a,n,(1+e)^{-1slash2},(1-e)^{-3slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4780.png"
 ALT="$\displaystyle = a n (1+e)^{-1/2} (1-e)^{-3/2},$">|; 

$key = q/displaystyle=a,nleft(frac{1+e}{1-e}right)^{1slash2}+{calO}({calM}^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4768.png"
 ALT="$\displaystyle = a n\left(\frac{1+e}{1-e}\right)^{1/2}+{\cal O}({\cal M}^{ 2})$">|; 

$key = q/displaystyle=a,{calM}left(frac{1+e}{1-e}right)^{1slash2}+{calO}({calM}^{,3}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4764.png"
 ALT="$\displaystyle = a {\cal M}\left(\frac{1+e}{1-e}\right)^{1/2}+{\cal O}({\cal M}^{ 3}),$">|; 

$key = q/displaystyle=a^{(0)}left[1+epsilon',a^{(1)}(t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4904.png"
 ALT="$\displaystyle = a^{(0)}\left[1+\epsilon' a^{(1)}(t)\right],$">|; 

$key = q/displaystyle=a_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img107.png"
 ALT="$\displaystyle = a_x,$">|; 

$key = q/displaystyle=a_x,b_x+a_y,b_y+a_z,b_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3926.png"
 ALT="$\displaystyle = a_x b_x+a_y b_y+a_z b_z$">|; 

$key = q/displaystyle=a_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle = a_y,$">|; 

$key = q/displaystyle=a_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle =a_z.$">|; 

$key = q/displaystyle=a_{01},m^{,4}+a_{02},e^{,2}+a_{03},I^{,2}+a_1,m^{,3},e,cos{calM}+a_2,e^{,2},cos(2,{calM})+a_3,I^{,2},cos(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3218.png"
 ALT="$\displaystyle = a_{01} m^{ 4}+ a_{02} e^{ 2}+a_{03} I^{ 2} + a_1 m^{ 3} e \cos{\cal M} +a_2 e^{ 2} \cos(2 {\cal M}) + a_3 I^{ 2} \cos(2 F)$">|; 

$key = q/displaystyle=a_{1,x},x_1+a_{1,y},y_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3541.png"
 ALT="$\displaystyle = a_{1 x} x_1+ a_{1 y} y_1,$">|; 

$key = q/displaystyle=aleft(frac{1+e}{1-e}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4774.png"
 ALT="$\displaystyle = a\left(\frac{1+e}{1-e}\right)^{1/2},$">|; 

$key = q/displaystyle=alpha+frac{alpha^{,2}}{3}-frac{alpha^{,3}}{9}-frac{31,alpha^{,4}}{81}+{calO}(alpha^{,5}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img2203.png"
 ALT="$\displaystyle = \alpha + \frac{\alpha^{ 2}}{3} - \frac{\alpha^{ 3}}{9} -\frac{31 \alpha^{ 4}}{81}+{\cal O}(\alpha^{ 5}).$">|; 

$key = q/displaystyle=alpha,cos(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4506.png"
 ALT="$\displaystyle =\alpha \cos(\omega t),$">|; 

$key = q/displaystyle=alpha,sin(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4508.png"
 ALT="$\displaystyle =\alpha \sin(\omega t),$">|; 

$key = q/displaystyle=alpha,{calS}_D+alpha^{-1}{calS}_I,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4945.png"
 ALT="$\displaystyle = \alpha {\cal S}_D +\alpha^{-1}{\cal S}_I,$">|; 

$key = q/displaystyle=b_1,m^{,3},e,sin{calM}+b_2,e^{,2},sin(2,{calM})+b_3,I^{,2},sin(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3222.png"
 ALT="$\displaystyle = b_1 m^{ 3} e \sin{\cal M} +b_2 e^{ 2} \sin(2 {\cal M}) + b_3 I^{ 2} \sin(2 F)$">|; 

$key = q/displaystyle=b_{1,x},x_1+a_{1,y},y_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3542.png"
 ALT="$\displaystyle = b_{1 x} x_1+a_{1 y} y_1,$">|; 

$key = q/displaystyle=beta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3184.png"
 ALT="$\displaystyle = \beta.$">|; 

$key = q/displaystyle=c_1,m^{,3},I,sinF+c_2,e,I,sin(F-{calM})+c_3,e,I,sin(F+{calM})+c_4,m^{,2},I,sin(2,D-F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3226.png"
 ALT="$\displaystyle = c_1 m^{ 3} I \sin F + c_2 e I \sin (F-{\cal M}) + c_3 e I \sin(F+{\cal M}) + c_4 m^{ 2} I \sin(2 D-F)$">|; 

$key = q/displaystyle=cos(n,t),x'+sin(n,t),y',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3044.png"
 ALT="$\displaystyle =\cos(n t) x'+\sin(n t) y',$">|; 

$key = q/displaystyle=cos(n,t),x+sin(n,t),y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3038.png"
 ALT="$\displaystyle =\cos(n t) x+\sin(n t) y,$">|; 

$key = q/displaystyle=cos(tilde{omega}+f),sintheta,sin({mitOmega}-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4535.png"
 ALT="$\displaystyle = \cos(\tilde{\omega}+f) \sin\theta \sin({\mit\Omega}-\phi)$">|; 

$key = q/displaystyle=cos2{calM}+2,e,(cos3{calM}-cos{calM})+{calO}(e^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1857.png"
 ALT="$\displaystyle =\cos 2{\cal M} +2 e (\cos 3{\cal M} - \cos{\cal M})+{\cal O}(e^{ 2}),$">|; 

$key = q/displaystyle=cosI,r,F_theta-sinI,cos(omega+theta),r,F_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5136.png"
 ALT="$\displaystyle = \cos I r F_\theta -\sin I \cos(\omega+\theta) r F_z.$">|; 

$key = q/displaystyle=cos^2alpha-sin^2alpha=2,cos^2alpha-1=1-2,sin^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3861.png"
 ALT="$\displaystyle =\cos^2\alpha-\sin^2\alpha = 2 \cos^2\alpha-1=1-2 \sin^2\alpha$">|; 

$key = q/displaystyle=cosalpha,cosbetampsinalpha,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3835.png"
 ALT="$\displaystyle =\cos\alpha \cos\beta\mp \sin\alpha \sin\beta$">|; 

$key = q/displaystyle=cosh^2alpha+sinh^2alpha=2,cosh^2alpha-1=2,sinh^2alpha+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3918.png"
 ALT="$\displaystyle =\cosh^2\alpha+\sinh^2\alpha = 2 \cosh^2\alpha-1=2 \sinh^2\alpha+1$">|; 

$key = q/displaystyle=coshalpha,coshbetapmsinhalpha,sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3892.png"
 ALT="$\displaystyle =\cosh\alpha \cosh\beta\pm \sinh\alpha \sinh\beta$">|; 

$key = q/displaystyle=coshx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3791.png"
 ALT="$\displaystyle = \cosh x$">|; 

$key = q/displaystyle=cospsi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2010.png"
 ALT="$\displaystyle =\cos\psi,$">|; 

$key = q/displaystyle=cospsi,sintheta,,skew{5}dot{phi}-sinpsi,,skew{5}dot{theta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1637.png"
 ALT="$\displaystyle = \cos\psi \sin\theta  \skew{5}\dot{\phi}-\sin\psi  \skew{5}\dot{\theta},$">|; 

$key = q/displaystyle=cospsi,{bfe}_{x'}-sinpsi,{bfe}_{y'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1630.png"
 ALT="$\displaystyle = \cos\psi {\bf e}_{x'} -\sin\psi {\bf e}_{y'}.$">|; 

$key = q/displaystyle=cospsi-cos(vartheta-vartheta'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4956.png"
 ALT="$\displaystyle =\cos \psi- \cos(\vartheta-\vartheta'),$">|; 

$key = q/displaystyle=costheta,,skew{5}dot{phi}+skew{5}dot{psi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1638.png"
 ALT="$\displaystyle = \cos\theta  \skew{5}\dot{\phi} +\skew{5}\dot{\psi}.$">|; 

$key = q/displaystyle=costheta,,x+sintheta,,y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3954.png"
 ALT="$\displaystyle = \cos\theta   x+ \sin \theta  y,$">|; 

$key = q/displaystyle=costheta,costheta',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img409.png"
 ALT="$\displaystyle =\cos\theta \cos\theta',$">|; 

$key = q/displaystyle=cosx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3779.png"
 ALT="$\displaystyle = \cos x$">|; 

$key = q/displaystyle=cos{mitOmega},x'-sin{mitOmega},y',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4711.png"
 ALT="$\displaystyle = \cos{\mit\Omega} x' - \sin{\mit\Omega} y',$">|; 

$key = q/displaystyle=d_1,I,sinF+d_2,e,I,sin(F-{calM})+d_3,e,I,sin(F+{calM})+d_4,m,I,sin(2,D-F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3236.png"
 ALT="$\displaystyle = d_1 I \sin F + d_2 e I \sin (F-{\cal M}) + d_3 e I \sin(F+{\cal M}) + d_4 m I \sin(2 D-F)$">|; 

$key = q/displaystyle=deltaY,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3135.png"
 ALT="$\displaystyle = \delta Y,$">|; 

$key = q/displaystyle=deltaZ.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3136.png"
 ALT="$\displaystyle = \delta Z.$">|; 

$key = q/displaystyle=delta_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4297.png"
 ALT="$\displaystyle = \delta_2,$">|; 

$key = q/displaystyle=e,cosvarpi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4860.png"
 ALT="$\displaystyle = e \cos\varpi,$">|; 

$key = q/displaystyle=e,sinvarpi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4858.png"
 ALT="$\displaystyle =e \sin\varpi,$">|; 

$key = q/displaystyle=e_m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4582.png"
 ALT="$\displaystyle =e_m,$">|; 

$key = q/displaystyle=e_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4577.png"
 ALT="$\displaystyle =e_s,$">|; 

$key = q/displaystyle=e_{rmfree},cos(A,t+beta_{rmfree})+k_{rmforced}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2658.png"
 ALT="$\displaystyle = e_{\rm free} \cos(A t+\beta_{\rm free})+ k_{\rm forced}(t),$">|; 

$key = q/displaystyle=e_{rmfree},sin(A,t+beta_{rmfree})+h_{rmforced}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2656.png"
 ALT="$\displaystyle = e_{\rm free} \sin(A t+\beta_{\rm free})+ h_{\rm forced}(t),$">|; 

$key = q/displaystyle=epsilon',n^{(0)}left[2,alpha,frac{partial{calS}}{partialskew{5}bar{lambda}^{(0)}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4909.png"
 ALT="$\displaystyle =\epsilon' n^{(0)}\left[2 \alpha \frac{\partial {\cal S}}{\partial\skew{5}\bar{\lambda}^{(0)}}\right],$">|; 

$key = q/displaystyle=epsilon',nleft(-alpha,frac{partial{calS}_{2,s}}{partialh}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2518.png"
 ALT="$\displaystyle =\epsilon' n\left(- \alpha \frac{\partial {\cal S}_{2 s}}{\partial h}\right),$">|; 

$key = q/displaystyle=epsilon',nleft(-alpha,frac{partial{calS}_{2,s}}{partialp}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2520.png"
 ALT="$\displaystyle =\epsilon' n\left(- \alpha \frac{\partial {\cal S}_{2 s}}{\partial p}\right),$">|; 

$key = q/displaystyle=epsilon',nleft(-frac{3}{2},a^{(1)}-2,alpha^{,2},frac{partial{calS}_{0,s}}{partialalpha}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2516.png"
 ALT="$\displaystyle = \epsilon' n\left(- \frac{3}{2} a^{(1)}
- 2 \alpha^{ 2} \frac{\partial {\cal S}_{0 s}}{\partial \alpha} \right),$">|; 

$key = q/displaystyle=epsilon',nleft(alpha,frac{partial{calS}_{2,s}}{partialk}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2517.png"
 ALT="$\displaystyle = \epsilon' n\left(\alpha \frac{\partial {\cal S}_{2 s}}{\partial k}\right),$">|; 

$key = q/displaystyle=epsilon',nleft(alpha,frac{partial{calS}_{2,s}}{partialq}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2519.png"
 ALT="$\displaystyle = \epsilon' n\left(\alpha \frac{\partial {\cal S}_{2 s}}{\partial q}\right),$">|; 

$key = q/displaystyle=epsilon',nleft[-alpha,h,frac{partial{calS}_0}{partialskew{5}bar{lambda}}+alpha,frac{partial({calS}_1+{calS}_2)}{partialk}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2446.png"
 ALT="$\displaystyle = \epsilon' n\left[-\alpha 
h \frac{\partial {\cal S}_0}{\part...
...\lambda}} + \alpha \frac{\partial ({\cal S}_1+{\cal S}_2)}{\partial k}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[-alpha,k,frac{partial{calS}_0}{partialskew{5}bar{lambda}}-alpha,frac{partial({calS}_1+{calS}_2)}{partialh}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2448.png"
 ALT="$\displaystyle = \epsilon' n\left[-\alpha k 
\frac{\partial {\cal S}_0}{\part...
...{\lambda}} -\alpha \frac{\partial ({\cal S}_1+{\cal S}_2)}{\partial h}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[-frac{1}{4},h,alpha^{,2},b^{(1)}_{3slash2}+frac{1}{4},h',alpha^{,2},b_{3slash2}^{(2)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2525.png"
 ALT="$\displaystyle = \epsilon' n\left[ -\frac{1}{4} h \alpha^{ 2} b^{(1)}_{3/2}+\frac{1}{4} h' \alpha^{ 2} b_{3/2}^{(2)}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[-frac{1}{4},q,alpha^{,2},b^{(1)}_{3slash2}+frac{1}{4},q',alpha^{,2},b_{3slash2}^{(1)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2526.png"
 ALT="$\displaystyle = \epsilon' n\left[ -\frac{1}{4} q \alpha^{ 2} b^{(1)}_{3/2}+\frac{1}{4} q' \alpha^{ 2} b_{3/2}^{(1)}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[-frac{alpha}{2},p,frac{partial{calS}_0}{partialskew{5}bar{lambda}}+alpha,frac{partial{calS}_2}{partialq}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2450.png"
 ALT="$\displaystyle =\epsilon' n\left[ - \frac{\alpha}{2} 
p \frac{\partial {\cal ...
...\skew{5}\bar{\lambda}}
+ \alpha \frac{\partial {\cal S}_2}{\partial q}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[-frac{alpha}{2},q,frac{partial{calS}_0}{partialskew{5}bar{lambda}}-alpha,frac{partial{calS}_2}{partialp}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2452.png"
 ALT="$\displaystyle = \epsilon' n\left[- \frac{\alpha}{2} 
q \frac{\partial {\cal ...
...l\skew{5}\bar{\lambda}}- \alpha \frac{\partial {\cal S}_2}{\partial p}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[-frac{alpha}{2},q,frac{partial{calS}_0}{partialskew{5}bar{lambda}}-alpha,frac{partial{calS}_2}{partialp}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4929.png"
 ALT="$\displaystyle = \epsilon' n\left[- \frac{\alpha}{2} 
q \frac{\partial {\cal ...
...l\skew{5}\bar{\lambda}}- \alpha \frac{\partial {\cal S}_2}{\partial p}\right].$">|; 

$key = q/displaystyle=epsilon',nleft[2,alpha,frac{partial({calS}_0+{calS}_1)}{partialskew{5}bar{lambda}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2442.png"
 ALT="$\displaystyle =\epsilon' n\left[2 \alpha \frac{\partial ({\cal S}_0+{\cal S}_1)}{\partial\skew{5}\bar{\lambda}}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[frac{1}{4},k,alpha^{,2},b^{(1)}_{3slash2}-frac{1}{4},k',alpha^{,2},b_{3slash2}^{(2)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2524.png"
 ALT="$\displaystyle = \epsilon' n\left[\frac{1}{4} k \alpha^{ 2} b^{(1)}_{3/2}-\frac{1}{4} k' \alpha^{ 2} b_{3/2}^{(2)}\right],$">|; 

$key = q/displaystyle=epsilon',nleft[frac{1}{4},p,alpha^{,2},b^{(1)}_{3slash2}-frac{1}{4},p',alpha^{,2},b_{3slash2}^{(1)}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2527.png"
 ALT="$\displaystyle = \epsilon' n\left[ \frac{1}{4} p \alpha^{ 2} b^{(1)}_{3/2}-\frac{1}{4} p' \alpha^{ 2} b_{3/2}^{(1)}\right].$">|; 

$key = q/displaystyle=epsilon,n'left(-alpha^{-1},frac{partial{calS}_{2,s}'}{partialh'}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2537.png"
 ALT="$\displaystyle =\epsilon n'\left(- \alpha^{-1} \frac{\partial {\cal S}_{2 s}'}{\partial h'}\right),$">|; 

$key = q/displaystyle=epsilon,n'left(-alpha^{-1},frac{partial{calS}_{2,s}'}{partialp'}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2539.png"
 ALT="$\displaystyle =\epsilon n'\left(- \alpha^{-1} \frac{\partial {\cal S}_{2 s}'}{\partial p'}\right).$">|; 

$key = q/displaystyle=epsilon,n'left(-frac{3}{2},a^{(1)'}+2,frac{partial{calS}_{0,s}'}{partialalpha}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2535.png"
 ALT="$\displaystyle = \epsilon n'\left(- \frac{3}{2} a^{(1)'}
+2 \frac{\partial {\cal S}_{0 s}'}{\partial \alpha}\right),$">|; 

$key = q/displaystyle=epsilon,n'left(alpha^{-1},frac{partial{calS}_{2,s}'}{partialk'}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2536.png"
 ALT="$\displaystyle = \epsilon n'\left(\alpha^{-1} \frac{\partial {\cal S}_{2 s}'}{\partial k'}\right),$">|; 

$key = q/displaystyle=epsilon,n'left(alpha^{-1},frac{partial{calS}_{2,s}'}{partialq'}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2538.png"
 ALT="$\displaystyle =\epsilon n'\left( \alpha^{-1} \frac{\partial {\cal S}_{2 s}'}{\partial q'}\right),$">|; 

$key = q/displaystyle=epsilon,n'left[-frac{1}{4},h',alpha,b^{(1)}_{3slash2}+frac{1}{4},h,alpha,b_{3slash2}^{(2)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2544.png"
 ALT="$\displaystyle = \epsilon n' \left[-\frac{1}{4} h' \alpha b^{(1)}_{3/2}+\frac{1}{4} h \alpha b_{3/2}^{(2)}\right],$">|; 

$key = q/displaystyle=epsilon,n'left[-frac{1}{4},q',alpha,b^{(1)}_{3slash2}+frac{1}{4},q,alpha,b_{3slash2}^{(1)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2545.png"
 ALT="$\displaystyle = \epsilon  n'\left[-\frac{1}{4} q' \alpha b^{(1)}_{3/2}+\frac{1}{4} q \alpha b_{3/2}^{(1)}\right],$">|; 

$key = q/displaystyle=epsilon,n'left[2,alpha^{-1},frac{partial({calS}_0'+{calS}_1')}{partialskew{5}bar{lambda}'}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2475.png"
 ALT="$\displaystyle =\epsilon n'\left[2 \alpha^{-1} \frac{\partial ({\cal S}_0'+{\cal S}_1')}{\partial\skew{5}\bar{\lambda}'}\right],$">|; 

$key = q/displaystyle=epsilon,n'left[frac{1}{4},k',alpha,b^{(1)}_{3slash2}-frac{1}{4},k,alpha,b_{3slash2}^{(2)}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2543.png"
 ALT="$\displaystyle = \epsilon  n'\left[\frac{1}{4} k' \alpha b^{(1)}_{3/2}-\frac{1}{4} k \alpha b_{3/2}^{(2)}\right],$">|; 

$key = q/displaystyle=epsilon,n'left[frac{1}{4},p',alpha,b^{(1)}_{3slash2}-frac{1}{4},p,alpha,b_{3slash2}^{(1)}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2546.png"
 ALT="$\displaystyle = \epsilon n'\left[\frac{1}{4} p' \alpha b^{(1)}_{3/2}-\frac{1}{4} p \alpha b_{3/2}^{(1)}\right].$">|; 

$key = q/displaystyle=f(a)+frac{(x-a)}{1!},f^{(1)}(a)+frac{(x-a)^2}{2!},f^{(2)}(a)+cdotsfrac{(x-a)^n}{n!},f^{(n)}(a)+cdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3805.png"
 ALT="$\displaystyle = f(a) + \frac{(x-a)}{1!} f^{(1)}(a) + \frac{(x-a)^2}{2!} f^{(2)}(a)+\cdots \frac{(x-a)^n}{n!} f^{(n)}(a)+\cdot$">|; 

$key = q/displaystyle=f_1(c_1,c_2,c_3,c_4,c_5,c_6,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4634.png"
 ALT="$\displaystyle =f_1(c_1,c_2,c_3,c_4,c_5,c_6,t),$">|; 

$key = q/displaystyle=f_2(c_1,c_2,c_3,c_4,c_5,c_6,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4635.png"
 ALT="$\displaystyle =f_2(c_1,c_2,c_3,c_4,c_5,c_6,t),$">|; 

$key = q/displaystyle=f_3(c_1,c_2,c_3,c_4,c_5,c_6,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4636.png"
 ALT="$\displaystyle =f_3(c_1,c_2,c_3,c_4,c_5,c_6,t),$">|; 

$key = q/displaystyle=f_{x_1}+g_{x_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3069.png"
 ALT="$\displaystyle =f_{x_1} + g_{x_1}$">|; 

$key = q/displaystyle=f_{x}+g_{x},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3063.png"
 ALT="$\displaystyle = f_{x}+g_{x},$">|; 

$key = q/displaystyle=f_{y_1}=g_{y_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3071.png"
 ALT="$\displaystyle =f_{y_1}=g_{y_1},$">|; 

$key = q/displaystyle=f_{y}+g_{y},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3065.png"
 ALT="$\displaystyle = f_{y}+g_{y},$">|; 

$key = q/displaystyle=f_{z_1}+g_{z_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3073.png"
 ALT="$\displaystyle =f_{z_1}+g_{z_1}.$">|; 

$key = q/displaystyle=f_{z}+g_{z}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3067.png"
 ALT="$\displaystyle = f_{z}+g_{z}.$">|; 

$key = q/displaystyle=frac{(1-e^{,2})^{-1slash2}}{n,a^{,2},sinI},frac{partial{calR}}{partialI}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2704.png"
 ALT="$\displaystyle = \frac{(1-e^{ 2})^{-1/2}}{n a^{ 2} \sin I} \frac{\partial{\cal R}}{\partial I}.$">|; 

$key = q/displaystyle=frac{(1-e^{,2})^{1slash2},sinE}{1-e,cosE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img900.png"
 ALT="$\displaystyle = \frac{(1-e^{ 2})^{1/2} \sin E}{1- e \cos E},$">|; 

$key = q/displaystyle=frac{(1-e^{,2})^{1slash2},sintheta}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img896.png"
 ALT="$\displaystyle = \frac{(1-e^{ 2})^{1/2} \sin\theta}{1+e \cos\theta},$">|; 

$key = q/displaystyle=frac{11}{8}+frac{59}{12},m+frac{1753}{144},m^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3450.png"
 ALT="$\displaystyle = \frac{11}{8}+\frac{59}{12} m +\frac{1753}{144} m^{ 2}.$">|; 

$key = q/displaystyle=frac{12,beta}{7}+frac{144,beta^{,2}}{49}+frac{1567,beta^{,3}}{343}+{calO}(beta^{,4}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img2209.png"
 ALT="$\displaystyle = \frac{12 \beta}{7} + \frac{144 \beta^{ 2}}{49} + \frac{1567 \beta^{ 3}}{343} + {\cal O}(\beta^{ 4}),$">|; 

$key = q/displaystyle=frac{15}{16}+frac{81}{16},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3512.png"
 ALT="$\displaystyle = \frac{15}{16}+\frac{81}{16} m,$">|; 

$key = q/displaystyle=frac{15}{16},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3507.png"
 ALT="$\displaystyle = \frac{15}{16},$">|; 

$key = q/displaystyle=frac{15}{2}left[frac{1}{1+25slash(5-alpha)^2}right]zeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4419.png"
 ALT="$\displaystyle = \frac{15}{2}\left[\frac{1}{1+25/(5-\alpha)^2}\right]\zeta,$">|; 

$key = q/displaystyle=frac{15}{32}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3517.png"
 ALT="$\displaystyle =\frac{15}{32}.$">|; 

$key = q/displaystyle=frac{15}{38},frac{X}{mu}=frac{15}{4},frac{zeta}{1+tilde{mu}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4320.png"
 ALT="$\displaystyle = \frac{15}{38} \frac{X}{\mu}= \frac{15}{4} \frac{\zeta}{1+\tilde{\mu}},$">|; 

$key = q/displaystyle=frac{15}{4}+frac{67}{4},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3570.png"
 ALT="$\displaystyle = \frac{15}{4} + \frac{67}{4} m,$">|; 

$key = q/displaystyle=frac{15}{8},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3271.png"
 ALT="$\displaystyle = \frac{15}{8},$">|; 

$key = q/displaystyle=frac{1}{1+x^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3789.png"
 ALT="$\displaystyle = \frac{1}{1+x^{ 2}}$">|; 

$key = q/displaystyle=frac{1}{1-x^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3801.png"
 ALT="$\displaystyle = \frac{1}{1-x^{ 2}}$">|; 

$key = q/displaystyle=frac{1}{2},(1+cos2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3873.png"
 ALT="$\displaystyle =\frac{1}{2} (1+\cos 2\alpha)$">|; 

$key = q/displaystyle=frac{1}{2},(1-cos2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3871.png"
 ALT="$\displaystyle =\frac{1}{2} (1-\cos 2\alpha)$">|; 

$key = q/displaystyle=frac{1}{2},(3,x^{,2}-1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img424.png"
 ALT="$\displaystyle = \frac{1}{2} (3 x^{ 2}-1),$">|; 

$key = q/displaystyle=frac{1}{2},(5,x^{,3}-3,x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3008.png"
 ALT="$\displaystyle = \frac{1}{2} (5 x^{ 3}-3 x)$">|; 

$key = q/displaystyle=frac{1}{2},(5,x^{,3}-x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img426.png"
 ALT="$\displaystyle =\frac{1}{2} (5 x^{ 3}-x),$">|; 

$key = q/displaystyle=frac{1}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3488.png"
 ALT="$\displaystyle = \frac{1}{2},$">|; 

$key = q/displaystyle=frac{1}{2},alpha,b_{1slash2}^{(0)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2530.png"
 ALT="$\displaystyle = \frac{1}{2} \alpha b_{1/2}^{(0)},$">|; 

$key = q/displaystyle=frac{1}{2},b_{1slash2}^{(0)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2503.png"
 ALT="$\displaystyle = \frac{1}{2} b_{1/2}^{(0)},$">|; 

$key = q/displaystyle=frac{1}{2},sin^2theta,sin^2theta'+cos^2theta,cos^2theta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img411.png"
 ALT="$\displaystyle = \frac{1}{2} \sin^2\theta \sin^2\theta'
+ \cos^2\theta \cos^2\theta'$">|; 

$key = q/displaystyle=frac{1}{2},v^{,2}-frac{G,M}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img941.png"
 ALT="$\displaystyle = \frac{1}{2} v^{ 2}-\frac{G M}{r},$">|; 

$key = q/displaystyle=frac{1}{2}-mu_2+deltax,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2368.png"
 ALT="$\displaystyle = \frac{1}{2}-\mu_2 + \delta x,$">|; 

$key = q/displaystyle=frac{1}{2}-mu_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2216.png"
 ALT="$\displaystyle = \frac{1}{2}-\mu_2,$">|; 

$key = q/displaystyle=frac{1}{2}left(frac{r_1+r_2+s}{a}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img917.png"
 ALT="$\displaystyle =\frac{1}{2}\left(\frac{r_1+r_2+s}{a}\right)^{1/2},$">|; 

$key = q/displaystyle=frac{1}{2}left(frac{r_1+r_2-s}{a}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img919.png"
 ALT="$\displaystyle = \frac{1}{2}\left(\frac{r_1+r_2-s}{a}\right)^{1/2}.$">|; 

$key = q/displaystyle=frac{1}{2}left[cos(alpha-beta)+cos(alpha+beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3849.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cos(\alpha-\beta)+\cos(\alpha+\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[cos(alpha-beta)-cos(alpha+beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3847.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cos(\alpha-\beta)-\cos(\alpha+\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[cosh(alpha+beta)+cosh(alpha-beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3906.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cosh(\alpha+\beta)+\cosh(\alpha-\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[cosh(alpha+beta)-cosh(alpha-beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3904.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\cosh(\alpha+\beta)-\cosh(\alpha-\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[sin(alpha-beta)+sin(alpha+beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3851.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\sin(\alpha-\beta)+\sin(\alpha+\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}left[sinh(alpha+beta)+sinh(alpha-beta)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3908.png"
 ALT="$\displaystyle =\frac{1}{2}\left[\sinh(\alpha+\beta)+\sinh(\alpha-\beta)\right]$">|; 

$key = q/displaystyle=frac{1}{2}sum_{j=-infty,infty}b_{1slash2}^{(j)}(alpha),cos[j,(vartheta-vartheta')],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img4971.png"
 ALT="$\displaystyle = \frac{1}{2}\sum_{j=-\infty,\infty}b_{1/2}^{(j)}(\alpha) \cos[j (\vartheta-\vartheta')],$">|; 

$key = q/displaystyle=frac{1}{2}sum_{j=-infty,infty}b_{3slash2}^{(j)}(alpha),cos[j,(vartheta-vartheta')],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img4973.png"
 ALT="$\displaystyle = \frac{1}{2}\sum_{j=-\infty,\infty}b_{3/2}^{(j)}(\alpha) \cos[j (\vartheta-\vartheta')],$">|; 

$key = q/displaystyle=frac{1}{2}sum_{j=-infty,infty}left{k,(-2,j-alpha,D),b^{(j)}_{1slash2},cos[(1-j),skew{5}bar{lambda}+j,skew{5}bar{lambda}']right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img2456.png"
 ALT="$\displaystyle = \frac{1}{2}\sum_{j=-\infty,\infty}\left\{k (-2 j-\alpha D) ...
...}_{1/2}
 \cos[ (1-j) \skew{5}\bar{\lambda}+ j \skew{5}\bar{\lambda}']\right.$">|; 

$key = q/displaystyle=frac{1}{3}+frac{2}{3}left(frac{3}{2},cos^2theta-frac{1}{2}right)left(frac{3}{2},cos^2theta'-frac{1}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img412.png"
 ALT="$\displaystyle = \frac{1}{3}+ \frac{2}{3}\left(\frac{3}{2} \cos^2\theta-\frac{1}{2}\right)\left(\frac{3}{2} \cos^2\theta'-\frac{1}{2}\right).$">|; 

$key = q/displaystyle=frac{1}{4,alpha}leftlanglefrac{skew{0}dot{r_a}}{r_a}rightrangle.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2917.png"
 ALT="$\displaystyle =\frac{1}{4 \alpha}\left\langle\frac{\skew{0}\dot{r_a}}{r_a}\right\rangle.$">|; 

$key = q/displaystyle=frac{1}{4},(3,cosalpha+cos3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3877.png"
 ALT="$\displaystyle =\frac{1}{4} (3 \cos\alpha+\cos 3\alpha)$">|; 

$key = q/displaystyle=frac{1}{4},(3,sinalpha-sin3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3875.png"
 ALT="$\displaystyle = \frac{1}{4} (3 \sin\alpha-\sin 3\alpha)$">|; 

$key = q/displaystyle=frac{1}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3578.png"
 ALT="$\displaystyle =\frac{1}{4},$">|; 

$key = q/displaystyle=frac{1}{4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3580.png"
 ALT="$\displaystyle =\frac{1}{4}.$">|; 

$key = q/displaystyle=frac{1}{8},(3+4,cos2alpha+cos4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3881.png"
 ALT="$\displaystyle = \frac{1}{8} (3+4 \cos 2\alpha+\cos 4\alpha)$">|; 

$key = q/displaystyle=frac{1}{8},(3-4,cos2alpha+cos4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3879.png"
 ALT="$\displaystyle = \frac{1}{8} (3-4 \cos 2\alpha+\cos 4\alpha)$">|; 

$key = q/displaystyle=frac{1}{8},(h^{,2}+k^{,2}+h'^{,2}+k'^{,2}),(2,alpha,D+alpha^{,2},D^{,2}),b^{(0)}_{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img5072.png"
 ALT="$\displaystyle = \frac{1}{8} (h^{ 2}+k^{ 2}+h'^{ 2}+k'^{ 2}) (2 \alpha D + \alpha^{ 2} D^{ 2}) b^{(0)}_{1/2}$">|; 

$key = q/displaystyle=frac{1}{8},(h^{,2}+k^{,2}+h'^{,2}+k'^{,2}),alpha,(2,alpha,D+alpha^{,2},D^{,2}),b^{(0)}_{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img5080.png"
 ALT="$\displaystyle = \frac{1}{8} (h^{ 2}+k^{ 2}+h'^{ 2}+k'^{ 2}) \alpha (2 \alpha D + \alpha^{ 2} D^{ 2}) b^{(0)}_{1/2}$">|; 

$key = q/displaystyle=frac{1}{cos^2x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img3783.png"
 ALT="$\displaystyle = \frac{1}{\cos^2 x}$">|; 

$key = q/displaystyle=frac{1}{cosh^2x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.92ex; " SRC="|."$dir".q|img3795.png"
 ALT="$\displaystyle = \frac{1}{\cosh^2 x}$">|; 

$key = q/displaystyle=frac{1}{n,a^{,2},(1-e^{,2})^{1slash2},sinI},frac{partial{calR}}{partialI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4855.png"
 ALT="$\displaystyle = \frac{1}{n a^{ 2} (1-e^{ 2})^{1/2} \sin I} \frac{\partial{\cal R}}{\partial I},$">|; 

$key = q/displaystyle=frac{1}{n,a^{,2},(1-e^{,2})^{1slash2},sinI},frac{partial{calR}}{partialI}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4843.png"
 ALT="$\displaystyle = \frac{1}{n a^{ 2} (1-e^{ 2})^{1/2} \sin I} \frac{\partial{\cal R}}{\partial I}.$">|; 

$key = q/displaystyle=frac{1}{r,sintheta},frac{d}{dt}(r^{,2},sin^2theta,,skew{5}dot{phi}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1476.png"
 ALT="$\displaystyle = \frac{1}{r \sin\theta} \frac{d}{dt}(r^{ 2} \sin^2\theta  \skew{5}\dot{\phi}).$">|; 

$key = q/displaystyle=frac{1}{r},frac{d}{dt}(r^{,2},skew{5}dot{theta})-r,sintheta,costheta,,skew{5}dot{phi}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1474.png"
 ALT="$\displaystyle = \frac{1}{r} \frac{d}{dt}(r^{ 2} \skew{5}\dot{\theta})-r \sin\theta \cos\theta  \skew{5}\dot{\phi}^{ 2},$">|; 

$key = q/displaystyle=frac{1}{r}frac{partial{calR}}{partialtheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4163.png"
 ALT="$\displaystyle = \frac{1}{r}\frac{\partial{\cal R}}{\partial\theta},$">|; 

$key = q/displaystyle=frac{1}{r}left[1+left(frac{r'}{r}right)costheta,costheta'right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img414.png"
 ALT="$\displaystyle = \frac{1}{r}\left[
1 + \left(\frac{r'}{r}\right)\cos\theta \cos\theta' \right.$">|; 

$key = q/displaystyle=frac{1}{sqrt{1+x^{,2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3797.png"
 ALT="$\displaystyle = \frac{1}{\sqrt{1+x^{ 2}}}$">|; 

$key = q/displaystyle=frac{1}{sqrt{1-x^{,2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3785.png"
 ALT="$\displaystyle = \frac{1}{\sqrt{1-x^{ 2}}}$">|; 

$key = q/displaystyle=frac{1}{sqrt{x^{,2}-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img3799.png"
 ALT="$\displaystyle = \frac{1}{\sqrt{x^{ 2}-1}}$">|; 

$key = q/displaystyle=frac{1}{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3777.png"
 ALT="$\displaystyle = \frac{1}{x}$">|; 

$key = q/displaystyle=frac{2,(dot{bfr}cdot{bfF})-({bfr}cdotdot{bfr}),{bfF}-({bfr}cdot{bfF}),dot{bfr}}{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img5106.png"
 ALT="$\displaystyle = \frac{2 (\dot{\bf r}\cdot {\bf F}) - ({\bf r}\cdot\dot{\bf r}) {\bf F} - ({\bf r}\cdot{\bf F}) \dot{\bf r}}{\mu}$">|; 

$key = q/displaystyle=frac{2,h,F_theta,{bfe}_r-(h,F_r+r,skew{5}dot{r},F_theta),{bfe}_theta-r,skew{5}dot{r},F_z,{bfe}_z}{mu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img5107.png"
 ALT="$\displaystyle = \frac{2 h F_\theta {\bf e}_r - (h F_r + r \skew{5}\dot{r} F_\theta) {\bf e}_\theta - r \skew{5}\dot{r} F_z {\bf e}_z}{\mu},$">|; 

$key = q/displaystyle=frac{2,h}{mu,(1-e^{,2})}left[e,sintheta,F_r+(1+e,costheta),F_thetaright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2754.png"
 ALT="$\displaystyle = \frac{2 h}{\mu (1-e^{ 2})}\left[e \sin\theta F_r + (1+e \cos\theta) F_\theta\right],$">|; 

$key = q/displaystyle=frac{21}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3265.png"
 ALT="$\displaystyle = \frac{21}{4},$">|; 

$key = q/displaystyle=frac{25}{256},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3454.png"
 ALT="$\displaystyle =\frac{25}{256},$">|; 

$key = q/displaystyle=frac{25}{256}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3456.png"
 ALT="$\displaystyle =\frac{25}{256}.$">|; 

$key = q/displaystyle=frac{2601}{1024}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3549.png"
 ALT="$\displaystyle = \frac{2601}{1024}.$">|; 

$key = q/displaystyle=frac{2pi}{a^{,3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img792.png"
 ALT="$\displaystyle =\frac{2\pi}{a^{ 3/2}},$">|; 

$key = q/displaystyle=frac{2}{3},r,frac{drho}{dr},epsilon(r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4340.png"
 ALT="$\displaystyle =\frac{2}{3} r \frac{d\rho}{dr} \epsilon(r),$">|; 

$key = q/displaystyle=frac{2}{3}-frac{8}{15}left(1-frac{15}{8},frac{J_2}{epsilon_0}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4410.png"
 ALT="$\displaystyle = \frac{2}{3} -\frac{8}{15}\left(1-\frac{15}{8} \frac{J_2}{\epsilon_0}\right)^{1/2}.$">|; 

$key = q/displaystyle=frac{2}{3}left(frac{3-alpha}{5-alpha}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4417.png"
 ALT="$\displaystyle = \frac{2}{3}\left(\frac{3-\alpha}{5-\alpha}\right),$">|; 

$key = q/displaystyle=frac{2}{5},M,R^{,2}+gamma,R^{,4},frac{4sqrt{pi}}{3}ointleft(Y_0^{,0}-frac{1}{sqrt{5}},Y_2^{,0}right)delta,d{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4481.png"
 ALT="$\displaystyle = \frac{2}{5} M R^{ 2} + \gamma R^{ 4} \frac{4\sqrt{\pi}}{3}\oint\left(Y_0^{ 0}-\frac{1}{\sqrt{5}} Y_2^{ 0}\right)\delta d{\mit\Omega},$">|; 

$key = q/displaystyle=frac{2}{5},epsilon.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img483.png"
 ALT="$\displaystyle = \frac{2}{5} \epsilon.$">|; 

$key = q/displaystyle=frac{2}{n,a},frac{partial{calR}}{partialskew{5}bar{lambda}_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.10ex; " SRC="|."$dir".q|img4835.png"
 ALT="$\displaystyle =\frac{2}{n a} \frac{\partial {\cal R}}{\partial\skew{5}\bar{\lambda}_0},$">|; 

$key = q/displaystyle=frac{2}{n,a},frac{partial{calR}}{partialskew{5}bar{lambda}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.78ex; " SRC="|."$dir".q|img4849.png"
 ALT="$\displaystyle =\frac{2}{n a} \frac{\partial {\cal R}}{\partial\skew{5}\bar{\lambda}},$">|; 

$key = q/displaystyle=frac{2}{n,a},frac{partial{calR}}{partialskew{5}bar{lambda}},displaybreak[0];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.78ex; " SRC="|."$dir".q|img4865.png"
 ALT="$\displaystyle =\frac{2}{n a} \frac{\partial {\cal R}}{\partial\skew{5}\bar{\lambda}},\displaybreak[0]$">|; 

$key = q/displaystyle=frac{2}{n,a},frac{partial{calR}}{partial{calM}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.72ex; " SRC="|."$dir".q|img2694.png"
 ALT="$\displaystyle = \frac{2}{n a} \frac{\partial{\cal R}}{\partial{\cal M}},$">|; 

$key = q/displaystyle=frac{3,(-6,x_1+17,y_1)}{32}+left(frac{522,x_1-72,c,x_1+2225,y_1+204,c,y_1}{256}right)m.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3534.png"
 ALT="$\displaystyle =\frac{3 (-6 x_1+17 y_1)}{32}+\left(\frac{522 x_1-72 c x_1+2225 y_1+204 c y_1}{256}\right)m.$">|; 

$key = q/displaystyle=frac{3,(6,x_1-17,y_1)}{64}+left(frac{-1146,x_1+72,c,x_1-1985,y_1-204,c,y_1}{512}right)m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3532.png"
 ALT="$\displaystyle =\frac{3 (6 x_1-17 y_1)}{64} +\left( \frac{-1146 x_1+72 c x_1-1985 y_1-204 c y_1}{512}\right)m,$">|; 

$key = q/displaystyle=frac{3,J_3}{8}left(frac{R}{a}right)^3frac{e,(5,cos^2I-1)}{(1-e^{,2})^{,3}},cosI,cosomega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2901.png"
 ALT="$\displaystyle = \frac{3 J_3}{8}\left(\frac{R}{a}\right)^3 \frac{e (5 \cos^2 I-1)}{(1-e^{ 2})^{ 3}} \cos I \cos\omega,$">|; 

$key = q/displaystyle=frac{3}{16}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3611.png"
 ALT="$\displaystyle = \frac{3}{16}.$">|; 

$key = q/displaystyle=frac{3}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3263.png"
 ALT="$\displaystyle = \frac{3}{2},$">|; 

$key = q/displaystyle=frac{3}{2},frac{skew{3}tilde{epsilon},(n_s^{,2}+mu_m,n_m^{,2})}{omega},costheta_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1795.png"
 ALT="$\displaystyle = \frac{3}{2} \frac{\skew{3}\tilde{\epsilon} (n_s^{ 2}+\mu_m n_m^{ 2})}{\omega} \cos\theta_0,$">|; 

$key = q/displaystyle=frac{3}{2},frac{skew{3}tilde{epsilon},I_m,mu_m,T_n({rmyr})}{T_s({rmday}),[T_m({rmyr})]^2},costheta_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.10ex; " SRC="|."$dir".q|img1811.png"
 ALT="$\displaystyle = \frac{3}{2} \frac{\skew{3}\tilde{\epsilon} I_m \mu_m T_n({\rm yr})}{T_s({\rm day}) [T_m({\rm yr})]^2} \cos\theta_0,$">|; 

$key = q/displaystyle=frac{3}{2},frac{skew{3}tilde{epsilon},I_m,mu_m,T_n({rmyr})}{T_s({rmday}),[T_m({rmyr})]^2},frac{cos(2,theta_0)}{sintheta_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.10ex; " SRC="|."$dir".q|img1812.png"
 ALT="$\displaystyle =\frac{3}{2} \frac{\skew{3}\tilde{\epsilon} I_m \mu_m T_n({\r...
...})}{T_s({\rm day}) [T_m({\rm yr})]^2} \frac{\cos(2 \theta_0)}{\sin\theta_0},$">|; 

$key = q/displaystyle=frac{3}{2},frac{skew{3}tilde{epsilon},I_m,mu_m,n_m^{,2}}{omega,{mitOmega}_n},costheta_0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1799.png"
 ALT="$\displaystyle = \frac{3}{2} \frac{\skew{3}\tilde{\epsilon} I_m \mu_m n_m^{ 2}}{\omega {\mit\Omega}_n} \cos\theta_0.$">|; 

$key = q/displaystyle=frac{3}{2},frac{skew{3}tilde{epsilon},I_m,mu_m,n_m^{,2}}{omega,{mitOmega}_n},frac{cos(2,theta_0)}{sintheta_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1797.png"
 ALT="$\displaystyle =\frac{3}{2} \frac{\skew{3}\tilde{\epsilon} I_m \mu_m n_m^{ 2}}{\omega {\mit\Omega}_n} \frac{\cos(2 \theta_0)}{\sin\theta_0},$">|; 

$key = q/displaystyle=frac{3}{2},frac{skew{3}tilde{epsilon}}{omega,(1-e^{,2})^{,3slash2}},frac{G,m}{a^{,3}}left(1-frac{3}{2},sin^2Iright)costheta_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4557.png"
 ALT="$\displaystyle =\frac{3}{2} \frac{\skew{3}\tilde{\epsilon}}{\omega (1-e^{ 2})^{ 3/2}} \frac{G m}{a^{ 3}}\left(1-\frac{3}{2} \sin^2 I\right)\cos\theta_0,$">|; 

$key = q/displaystyle=frac{3}{2},h_2,zeta,{calI}_0,l,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4496.png"
 ALT="$\displaystyle = \frac{3}{2} h_2 \zeta {\cal I}_0 l,$">|; 

$key = q/displaystyle=frac{3}{2},h_2,zeta,{calI}_0,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4497.png"
 ALT="$\displaystyle = \frac{3}{2} h_2 \zeta {\cal I}_0 m,$">|; 

$key = q/displaystyle=frac{3}{2},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3478.png"
 ALT="$\displaystyle = \frac{3}{2} m,$">|; 

$key = q/displaystyle=frac{3}{2},m^{,2},e',cos{calM}'-frac{7}{2},m^{,2},e',cos(2,D-{calM}')+frac{1}{2},m^{,2},e',cos(2,D+{calM}'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3496.png"
 ALT="$\displaystyle =\frac{3}{2} m^{ 2} e' \cos{\cal M}' -\frac{7}{2} m^{ 2} e' \cos(2 D-{\cal M}')+\frac{1}{2} m^{ 2} e' \cos(2 D+{\cal M}'),$">|; 

$key = q/displaystyle=frac{3}{2},x_1,y_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3275.png"
 ALT="$\displaystyle = \frac{3}{2} x_1 y_1,$">|; 

$key = q/displaystyle=frac{3}{2},x_1,y_1=-3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3576.png"
 ALT="$\displaystyle =\frac{3}{2} x_1 y_1=-3,$">|; 

$key = q/displaystyle=frac{3}{2},x_1,z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3297.png"
 ALT="$\displaystyle = \frac{3}{2} x_1 z_1,$">|; 

$key = q/displaystyle=frac{3}{2},x_4,z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3302.png"
 ALT="$\displaystyle =\frac{3}{2} x_4 z_1,$">|; 

$key = q/displaystyle=frac{3}{2}-frac{1}{4},m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3255.png"
 ALT="$\displaystyle = \frac{3}{2}-\frac{1}{4} m^{ 2},$">|; 

$key = q/displaystyle=frac{3}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3289.png"
 ALT="$\displaystyle = \frac{3}{4},$">|; 

$key = q/displaystyle=frac{3}{4},x_1+frac{3}{4},y_1-3,x_1,x_4-frac{3}{2},y_1,y_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3261.png"
 ALT="$\displaystyle = \frac{3}{4} x_1+\frac{3}{4} y_1-3 x_1 x_4-\frac{3}{2} y_1 y_4,$">|; 

$key = q/displaystyle=frac{3}{4},x_1-frac{3}{4},y_1-3,x_1,x_4+frac{3}{2},y_1,y_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3259.png"
 ALT="$\displaystyle = \frac{3}{4} x_1-\frac{3}{4} y_1-3 x_1 x_4+\frac{3}{2} y_1 y_4,$">|; 

$key = q/displaystyle=frac{3}{4},x_4+frac{3}{4},y_4-frac{3}{2},x_4^{,2}-frac{3}{4},y_4^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3257.png"
 ALT="$\displaystyle = \frac{3}{4} x_4+\frac{3}{4} y_4-\frac{3}{2} x_4^{ 2}-\frac{3}{4} y_4^{ 2},$">|; 

$key = q/displaystyle=frac{3}{4},x_4+frac{3}{4},y_4-frac{3}{2},x_4^{,2}-frac{3}{4},y_4^{,2}=-frac{675}{256},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3451.png"
 ALT="$\displaystyle =\frac{3}{4} x_4 + \frac{3}{4} y_4-\frac{3}{2} x_4^{ 2}-\frac{3}{4} y_4^{ 2} = -\frac{675}{256},$">|; 

$key = q/displaystyle=frac{3}{4},x_4-frac{3}{4},y_4-frac{3}{2},x_4^{,2}+frac{3}{4},y_4^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3243.png"
 ALT="$\displaystyle = \frac{3}{4} x_4-\frac{3}{4} y_4 -\frac{3}{2} x_4^{ 2} + \frac{3}{4} y_4^{ 2},$">|; 

$key = q/displaystyle=frac{3}{4},x_6-frac{3}{4},y_6-3,x_4,x_6+frac{3}{2},y_4,y_6,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3249.png"
 ALT="$\displaystyle =\frac{3}{4} x_6 -\frac{3}{4} y_6-3 x_4 x_6+\frac{3}{2} y_4 y_6,$">|; 

$key = q/displaystyle=frac{3}{4},z_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3247.png"
 ALT="$\displaystyle = \frac{3}{4} z_1^{ 2},$">|; 

$key = q/displaystyle=frac{3}{4},{calI}_parallel,I_m,mu_m,n_m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1769.png"
 ALT="$\displaystyle = \frac{3}{4} {\cal I}_\parallel I_m \mu_m n_m^{ 2},$">|; 

$key = q/displaystyle=frac{3}{4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3486.png"
 ALT="$\displaystyle =\frac{3}{4}.$">|; 

$key = q/displaystyle=frac{3}{8}+frac{41}{32},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3609.png"
 ALT="$\displaystyle = \frac{3}{8}+\frac{41}{32} m,$">|; 

$key = q/displaystyle=frac{3}{8},frac{skew{3}tilde{epsilon}}{(1-e^{,2})^{,3slash2}},frac{G,m}{a^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4541.png"
 ALT="$\displaystyle = \frac{3}{8} \frac{\skew{3}\tilde{\epsilon}}{(1-e^{ 2})^{ 3/2}} \frac{G m}{a^{ 3}},$">|; 

$key = q/displaystyle=frac{3}{8},{calI}_parallel,mu_m,n_m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1767.png"
 ALT="$\displaystyle = \frac{3}{8} {\cal I}_\parallel \mu_m n_m^{ 2},$">|; 

$key = q/displaystyle=frac{4sqrt{pi}}{3},r^{,2}left(Y_0^{,0}-frac{1}{sqrt{5}},Y_2^{,0}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4467.png"
 ALT="$\displaystyle = \frac{4\sqrt{\pi}}{3} r^{ 2}\left(Y_0^{ 0} - \frac{1}{\sqrt{5}} Y_2^{ 0}\right),$">|; 

$key = q/displaystyle=frac{5}{12},frac{omega^{,2},R^{,3}}{G,m},frac{1}{1+tilde{mu}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1354.png"
 ALT="$\displaystyle = \frac{5}{12} \frac{\omega^{ 2} R^{ 3}}{G m} \frac{1}{1+\tilde{\mu}},$">|; 

$key = q/displaystyle=frac{5}{16},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3571.png"
 ALT="$\displaystyle = \frac{5}{16},$">|; 

$key = q/displaystyle=frac{5}{2},frac{omega^{,2},R^{,3}}{G,m},frac{1}{1+tilde{mu}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1358.png"
 ALT="$\displaystyle = \frac{5}{2} \frac{\omega^{ 2} R^{ 3}}{G m} \frac{1}{1+\tilde{\mu}},$">|; 

$key = q/displaystyle=frac{5}{42},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4304.png"
 ALT="$\displaystyle = \frac{5}{42},$">|; 

$key = q/displaystyle=frac{7}{16}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3572.png"
 ALT="$\displaystyle =\frac{7}{16}.$">|; 

$key = q/displaystyle=frac{7}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3483.png"
 ALT="$\displaystyle = \frac{7}{2},$">|; 

$key = q/displaystyle=frac{81}{256},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3544.png"
 ALT="$\displaystyle = \frac{81}{256},$">|; 

$key = q/displaystyle=frac{9}{8}+frac{3}{4},x_{11},m-frac{3}{4},y_{11},m-3,x_4,x_{11},m+frac{3}{2},y_4,y_{11},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3269.png"
 ALT="$\displaystyle = \frac{9}{8}+\frac{3}{4} x_{11} m-\frac{3}{4} y_{11} m-3 x_4 x_{11} m+\frac{3}{2} y_4 y_{11} m,$">|; 

$key = q/displaystyle=frac{9}{8}+frac{3}{4},x_{11},m-frac{3}{4},y_{11},m-3,x_4,x_{11},m+frac{3}{2},y_4,y_{11},m=frac{9}{8}+frac{135}{128},m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3510.png"
 ALT="$\displaystyle = \frac{9}{8}+\frac{3}{4} x_{11} m-\frac{3}{4} y_{11} m-3 x_4 x_{11} m+\frac{3}{2} y_4 y_{11} m=\frac{9}{8}+\frac{135}{128} m,$">|; 

$key = q/displaystyle=frac{9}{8},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3504.png"
 ALT="$\displaystyle = \frac{9}{8},$">|; 

$key = q/displaystyle=frac{C_D,A,a,rho(a)}{m},n,e^{,-1},{rme}^{,alpha,cosE},frac{(1+e,cosE)^{1slash2}}{(1-e,cosE)^{3slash2}},(1-e^{,3},cosE),sinE,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2766.png"
 ALT="$\displaystyle = \frac{C_D A a \rho(a)}{m} n e^{ -1} {\rm e}^{ \alpha \...
...\frac{(1+e \cos E)^{1/2}}{(1-e  \cos E)^{3/2}}  (1-e^{ 3} \cos E) \sin E,$">|; 

$key = q/displaystyle=frac{G,M}{a^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2093.png"
 ALT="$\displaystyle = \frac{G M}{a^{ 3}},$">|; 

$key = q/displaystyle=frac{Y}{X},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img773.png"
 ALT="$\displaystyle = \frac{Y}{X},$">|; 

$key = q/displaystyle=frac{Z}{sqrt{X^{,2}+Y^{,2}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img775.png"
 ALT="$\displaystyle =\frac{Z}{\sqrt{X^{ 2} + Y^{ 2}}},$">|; 

$key = q/displaystyle=frac{a',(1-e'^{,2})}{1+e',costheta'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4171.png"
 ALT="$\displaystyle = \frac{a' (1-e'^{ 2})}{1+e' \cos\theta'}.$">|; 

$key = q/displaystyle=frac{a,(1-e^{,2})}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img645.png"
 ALT="$\displaystyle = \frac{a (1-e^{ 2})}{1+e \cos\theta},$">|; 

$key = q/displaystyle=frac{a,(1-e^{,2})}{1+e,costheta}=a,(1-e,cosE),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img5090.png"
 ALT="$\displaystyle = \frac{a (1-e^{ 2})}{1+e \cos\theta}=a (1-e \cos E),$">|; 

$key = q/displaystyle=frac{a,n}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4790.png"
 ALT="$\displaystyle =\frac{a n}{2},$">|; 

$key = q/displaystyle=frac{a}{a'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4900.png"
 ALT="$\displaystyle =\frac{a}{a'}.$">|; 

$key = q/displaystyle=frac{cos(omega+theta),r,F_z}{h},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2762.png"
 ALT="$\displaystyle = \frac{\cos(\omega+\theta) r F_z}{h},$">|; 

$key = q/displaystyle=frac{cosE-e}{1-e,cosE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img898.png"
 ALT="$\displaystyle = \frac{\cos E-e}{1-e \cos E},$">|; 

$key = q/displaystyle=frac{costheta+e}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img894.png"
 ALT="$\displaystyle = \frac{\cos\theta+e}{1+e \cos\theta},$">|; 

$key = q/displaystyle=frac{ddot{bfr}times{bfh}+dot{bfr}timesdot{bfh}}{mu}+frac{({bfr}cdotdot{bfr}),{bfr}-r^{,2},dot{bfr}}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img5105.png"
 ALT="$\displaystyle = \frac{\ddot{\bf r}\times {\bf h} +\dot{\bf r}\times \dot{\bf h}}{\mu} + \frac{({\bf r}\cdot\dot{\bf r}) {\bf r} - r^{ 2} \dot{\bf r}}{r^{ 3}}$">|; 

$key = q/displaystyle=frac{d{bfL}}{dt'}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1556.png"
 ALT="$\displaystyle = \frac{d{\bf L}}{dt'} +$">|; 

$key = q/displaystyle=frac{d{bfL}}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1553.png"
 ALT="$\displaystyle = \frac{d{\bf L}}{dt},$">|; 

$key = q/displaystyle=frac{e,r_c}{e^{,2}-1}=e,a.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4020.png"
 ALT="$\displaystyle = \frac{e r_c}{e^{ 2}-1}=e a.$">|; 

$key = q/displaystyle=frac{epsilon,eta}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4381.png"
 ALT="$\displaystyle =\frac{\epsilon \eta}{a},$">|; 

$key = q/displaystyle=frac{h,e,sintheta}{a,(1-e^{,2})}=frac{h,e}{a,(1-e^{,2})^{1slash2}},frac{sinE}{1-e,cosE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img5091.png"
 ALT="$\displaystyle = \frac{h e \sin\theta}{a (1-e^{ 2})}=\frac{h e}{a (1-e^{ 2})^{1/2}} \frac{\sin E}{1-e \cos E},$">|; 

$key = q/displaystyle=frac{h,e}{a,(1-e^{,2})^{1slash2}},frac{sinE}{1-e,cosE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2743.png"
 ALT="$\displaystyle = \frac{h e}{a (1-e^{ 2})^{1/2}} \frac{\sin E}{1-e \cos E},$">|; 

$key = q/displaystyle=frac{h}{mu}left[sintheta,F_r+(costheta+cosE),F_thetaright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2758.png"
 ALT="$\displaystyle = \frac{h}{\mu}\left[\sin\theta F_r+(\cos\theta+\cos E) F_\theta \right],$">|; 

$key = q/displaystyle=frac{m^{,alpha},(omega_j,a_j-2,b_j)}{omega_j,(1-3,m^{,2}slash2-omega_j^{,2})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.72ex; " SRC="|."$dir".q|img3398.png"
 ALT="$\displaystyle = \frac{m^{ \alpha} (\omega_j a_j-2 b_j)}{\omega_j (1-3 m^{ 2}/2-\omega_j^{ 2})},$">|; 

$key = q/displaystyle=frac{m^{,alpha}left[(omega_j^{,2}+3+3,m^{,2}slash2),b_j-2,omega_j,a_jright]}{omega_j^{,2},(1-3,m^{,2}slash2-omega_j^{,2})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.97ex; vertical-align: -2.72ex; " SRC="|."$dir".q|img3400.png"
 ALT="$\displaystyle = \frac{m^{ \alpha}\left[(\omega_j^{ 2}+3+3 m^{ 2}/2) b_j-2 \omega_j a_j\right]}{\omega_j^{ 2} (1-3 m^{ 2}/2-\omega_j^{ 2})},$">|; 

$key = q/displaystyle=frac{m_1}{m_1+m_2},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img861.png"
 ALT="$\displaystyle = \frac{m_1}{m_1+m_2} {\bf r},$">|; 

$key = q/displaystyle=frac{m_2}{m_1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2095.png"
 ALT="$\displaystyle = \frac{m_2}{m_1},$">|; 

$key = q/displaystyle=frac{m_j}{M+m_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2559.png"
 ALT="$\displaystyle = \frac{m_j}{M+m_i},$">|; 

$key = q/displaystyle=frac{mu_1}{rho_1^{,3}}+frac{mu_2}{rho_2^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2270.png"
 ALT="$\displaystyle = \frac{\mu_1}{\rho_1^{ 3}} + \frac{\mu_2}{\rho_2^{ 3}},$">|; 

$key = q/displaystyle=frac{n'^{,2},a'^{,3}}{r'^{,3}}left[frac{3,({bfr}cdot{bfr}'),{bfr}'}{r'^{,2}}-{bfr}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3022.png"
 ALT="$\displaystyle = \frac{n'^{ 2} a'^{ 3}}{r'^{ 3}}\left[\frac{3 ({\bf r}\cdot{\bf r}') {\bf r}'}{r'^{ 2}}-{\bf r}\right],$">|; 

$key = q/displaystyle=frac{n,a}{2},(1-e^{,2})^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4804.png"
 ALT="$\displaystyle = \frac{n a}{2} (1-e^{ 2})^{1/2},$">|; 

$key = q/displaystyle=frac{n,a}{2},(1-e^{,2})^{1slash2},cosI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4808.png"
 ALT="$\displaystyle = \frac{n a}{2} (1-e^{ 2})^{1/2} \cos I,$">|; 

$key = q/displaystyle=frac{n,a}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4802.png"
 ALT="$\displaystyle = \frac{n a}{2},$">|; 

$key = q/displaystyle=frac{n_i}{4},epsilon_{ij},alpha_{ij},bar{alpha}_{ij},b^{(1)}_{3slash2}(alpha_{ij}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2578.png"
 ALT="$\displaystyle = \frac{n_i}{4} \epsilon_{ij} \alpha_{ij} \bar{\alpha}_{ij} b^{(1)}_{3/2}(\alpha_{ij}),$">|; 

$key = q/displaystyle=frac{n}{4},epsilon_i,alpha_i,bar{alpha}_i,b_{3slash2}^{(1)}(alpha_i).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2654.png"
 ALT="$\displaystyle = \frac{n}{4} \epsilon_i \alpha_i \bar{\alpha}_i b_{3/2}^{(1)}(\alpha_i).$">|; 

$key = q/displaystyle=frac{partial(a,e)}{partial(p,q)}left[frac{partial(x,dot{x})}{partial(a,e)}+frac{partial(y,dot{y})}{partial(a,e)}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4784.png"
 ALT="$\displaystyle =\frac{\partial(a,e)}{\partial(p,q)}\left[\frac{\partial(x,\dot{x})}{\partial(a,e)}+\frac{\partial(y,\dot{y})}{\partial(a,e)}\right]$">|; 

$key = q/displaystyle=frac{partial(x',dot{x}')}{partial(p,q)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4738.png"
 ALT="$\displaystyle =\frac{\partial (x',\dot{x}')}{\partial (p,q)}$">|; 

$key = q/displaystyle=frac{partialU}{partialrho_1},frac{partialrho_1}{partialx}+frac{partialU}{partialrho_2},frac{partialrho_2}{partialx}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2183.png"
 ALT="$\displaystyle =\frac{\partial U}{\partial \rho_1} \frac{\partial \rho_1}{\partial x}+\frac{\partial U}{\partial \rho_2} \frac{\partial \rho_2}{\partial x}=0,$">|; 

$key = q/displaystyle=frac{partialU}{partialrho_1},frac{partialrho_1}{partialy}+frac{partialU}{partialrho_2},frac{partialrho_2}{partialy}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2185.png"
 ALT="$\displaystyle = \frac{\partial U}{\partial \rho_1} \frac{\partial \rho_1}{\partial y}+\frac{\partial U}{\partial \rho_2} \frac{\partial \rho_2}{\partial y}=0,$">|; 

$key = q/displaystyle=frac{partialU}{partial{bfr}'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2972.png"
 ALT="$\displaystyle =\frac{\partial U}{\partial {\bf r}'},$">|; 

$key = q/displaystyle=frac{partialU}{partial{bfr}}-left(frac{m_2}{m_1+m_2}right)frac{partialU}{partial{bfr}'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2970.png"
 ALT="$\displaystyle = \frac{\partial U}{\partial {\bf r}}-\left(\frac{m_2}{m_1+m_2}\right)\frac{\partial U}{\partial{\bf r}'},$">|; 

$key = q/displaystyle=frac{partial^{,2}f_1}{partialt^{,2}}+sum_{k=1,6}frac{partialg_1}{partialc_k},frac{dc_k}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4659.png"
 ALT="$\displaystyle = \frac{\partial^{ 2} f_1}{\partial t^{ 2}} +\sum_{k=1,6} \frac{\partial g_1}{\partial c_k} \frac{d c_k}{dt},$">|; 

$key = q/displaystyle=frac{partial^{,2}f_2}{partialt^{,2}}+sum_{k=1,6}frac{partialg_2}{partialc_k},frac{dc_k}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4661.png"
 ALT="$\displaystyle = \frac{\partial^{ 2} f_2}{\partial t^{ 2}}+\sum_{k=1,6} \frac{\partial g_2}{\partial c_k} \frac{d c_k}{dt},$">|; 

$key = q/displaystyle=frac{partial^{,2}f_3}{partialt^{,2}}+sum_{k=1,6}frac{partialg_3}{partialc_k},frac{dc_k}{dt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4663.png"
 ALT="$\displaystyle = \frac{\partial^{ 2} f_3}{\partial t^{ 2}}+\sum_{k=1,6} \frac{\partial g_3}{\partial c_k} \frac{d c_k}{dt}.$">|; 

$key = q/displaystyle=frac{partialbeta}{partialtheta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4177.png"
 ALT="$\displaystyle = \frac{\partial\beta}{\partial\theta}.$">|; 

$key = q/displaystyle=frac{partialdot{x}'}{partialp}-dot{y}',frac{partial{mitOmega}}{partialp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4725.png"
 ALT="$\displaystyle = \frac{\partial \dot{x}'}{\partial p} - \dot{y}' \frac{\partial {\mit\Omega}}{\partial p},$">|; 

$key = q/displaystyle=frac{partialdot{y}'}{partialp}+dot{x}',frac{partial{mitOmega}}{partialp}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4727.png"
 ALT="$\displaystyle = \frac{\partial \dot{y}'}{\partial p} + \dot{x}' \frac{\partial {\mit\Omega}}{\partial p}.$">|; 

$key = q/displaystyle=frac{partialf_1}{partialt}=g_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4653.png"
 ALT="$\displaystyle = \frac{\partial f_1}{\partial t} = g_1,$">|; 

$key = q/displaystyle=frac{partialf_2}{partialt}=g_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4655.png"
 ALT="$\displaystyle = \frac{\partial f_2}{\partial t} = g_2,$">|; 

$key = q/displaystyle=frac{partialf_3}{partialt}=g_3.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4657.png"
 ALT="$\displaystyle = \frac{\partial f_3}{\partial t} = g_3.$">|; 

$key = q/displaystyle=frac{partialphi}{partialx},{bfe}_x+frac{partialphi}{partialy},{bfe}_y+frac{partialphi}{partialz},{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3939.png"
 ALT="$\displaystyle = \frac{\partial\phi}{\partial x} {\bf e}_x+\frac{\partial\phi}{\partial y} {\bf e}_y+\frac{\partial\phi}{\partial z} {\bf e}_z$">|; 

$key = q/displaystyle=frac{partialx'}{partialp}-y',frac{partial{mitOmega}}{partialp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4722.png"
 ALT="$\displaystyle = \frac{\partial x'}{\partial p} - y' \frac{\partial {\mit\Omega}}{\partial p},$">|; 

$key = q/displaystyle=frac{partialy'}{partialp}+x',frac{partial{mitOmega}}{partialp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4724.png"
 ALT="$\displaystyle = \frac{\partial y'}{\partial p} + x' \frac{\partial {\mit\Omega}}{\partial p},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4830.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial I},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialX},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4629.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial X},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialY},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4631.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial Y},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialZ},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4633.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial Z},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialZ}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4677.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial Z}.$">|; 

$key = q/displaystyle=frac{partial{calR}}{partiala}+frac{partial{calR}}{partialskew{5}bar{lambda}}int_0^tfrac{dn}{da},dt'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4848.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial a}
+ \frac{\partial {\cal R}}{\partial \skew{5}\bar{\lambda}}\int_0^t\frac{dn}{da} dt'.$">|; 

$key = q/displaystyle=frac{partial{calR}}{partiala},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4824.png"
 ALT="$\displaystyle =\frac{\partial {\cal R}}{\partial a},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partiale},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4826.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial e},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialskew{5}bar{lambda}_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.10ex; " SRC="|."$dir".q|img4828.png"
 ALT="$\displaystyle =\frac{\partial {\cal R}}{\partial\skew{5}\bar{\lambda}_0},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialskew{5}bar{lambda}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.78ex; " SRC="|."$dir".q|img4846.png"
 ALT="$\displaystyle =\frac{\partial {\cal R}}{\partial \skew{5}\bar{\lambda}},$">|; 

$key = q/displaystyle=frac{partial{calR}}{partialvarpi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4834.png"
 ALT="$\displaystyle = \frac{\partial {\cal R}}{\partial \varpi}.$">|; 

$key = q/displaystyle=frac{partial{calR}}{partial{mitOmega}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4832.png"
 ALT="$\displaystyle =
\frac{\partial {\cal R}}{\partial {\mit\Omega}},$">|; 

$key = q/displaystyle=frac{partial{{calR}}}{partialr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4162.png"
 ALT="$\displaystyle = \frac{\partial{{\cal R}}}{\partial r},$">|; 

$key = q/displaystyle=frac{r'-a'}{a'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4954.png"
 ALT="$\displaystyle = \frac{r'-a'}{a'},$">|; 

$key = q/displaystyle=frac{r-a}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4952.png"
 ALT="$\displaystyle = \frac{r-a}{a},$">|; 

$key = q/displaystyle=frac{r_c}{1-e^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4006.png"
 ALT="$\displaystyle = \frac{r_c}{1-e^{ 2}},$">|; 

$key = q/displaystyle=frac{r_c}{e^{,2}-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4018.png"
 ALT="$\displaystyle = \frac{r_c}{e^{ 2}-1},$">|; 

$key = q/displaystyle=frac{r_c}{sqrt{1-e^{,2}}}=sqrt{1-e^{,2}},a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4008.png"
 ALT="$\displaystyle = \frac{r_c}{\sqrt{1-e^{ 2}}}=\sqrt{1-e^{ 2}} a,$">|; 

$key = q/displaystyle=frac{r_c}{sqrt{e^{,2}-1}}=sqrt{e^{,2}-1},a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4019.png"
 ALT="$\displaystyle = \frac{r_c}{\sqrt{e^{ 2}-1}}=\sqrt{e^{ 2}-1} a,$">|; 

$key = q/displaystyle=frac{r}{a}-1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3180.png"
 ALT="$\displaystyle = \frac{r}{a}-1,$">|; 

$key = q/displaystyle=frac{sin(omega+theta),r,F_z}{h,sinI}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2764.png"
 ALT="$\displaystyle =\frac{\sin(\omega+\theta) r F_z}{h \sin I}.$">|; 

$key = q/displaystyle=frac{sqrt{3}}{2}+deltay,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2369.png"
 ALT="$\displaystyle = \frac{\sqrt{3}}{2}+ \delta y,$">|; 

$key = q/displaystyle=frac{tanalphapmtanbeta}{1mptanalpha,tanbeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3837.png"
 ALT="$\displaystyle =\frac{\tan\alpha\pm \tan\beta}{1\mp \tan\alpha \tan\beta}$">|; 

$key = q/displaystyle=frac{tanhalphapmtanhbeta}{1pmtanhalpha,tanhbeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img3894.png"
 ALT="$\displaystyle = \frac{\tanh\alpha\pm\tanh\beta}{1\pm\tanh\alpha \tanh\beta}$">|; 

$key = q/displaystyle=frac{tilde{mu}'}{mu}=frac{m'}{M+m},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4899.png"
 ALT="$\displaystyle =\frac{\tilde{\mu}'}{\mu}= \frac{m'}{M+m},$">|; 

$key = q/displaystyle=frac{x^{,2}}{8}+{calO}(x^{,4}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4037.png"
 ALT="$\displaystyle =\frac{x^{ 2}}{8}+{\cal O}(x^{ 4}),$">|; 

$key = q/displaystyle=frac{x^{,3}}{48}+{calO}(x^{,5}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4039.png"
 ALT="$\displaystyle =\frac{x^{ 3}}{48}+{\cal O}(x^{ 5}).$">|; 

$key = q/displaystyle=frac{x}{2}-frac{x^{,3}}{16}+{calO}(x^{,5}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4035.png"
 ALT="$\displaystyle =\frac{x}{2}-\frac{x^{ 3}}{16} + {\cal O}(x^{ 5}),$">|; 

$key = q/displaystyle=frac{{bfe}_ycdotskew{1}dot{bfe}}{e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4150.png"
 ALT="$\displaystyle = \frac{{\bf e}_y\cdot\skew{1}\dot{\bf e}}{e}.$">|; 

$key = q/displaystyle=frac{{bfe}timesskew{1}dot{bfe}}{e^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4146.png"
 ALT="$\displaystyle = \frac{{\bf e}\times \skew{1}\dot{\bf e}}{e^{ 2}}.$">|; 

$key = q/displaystyle=frac{{bfr}cdot{bfr}'}{r,r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4175.png"
 ALT="$\displaystyle =\frac{{\bf r}\cdot{\bf r}'}{r r'},$">|; 

$key = q/displaystyle=frac{{calI}_parallel-{calI}_perp}{{calI}_parallel}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img4542.png"
 ALT="$\displaystyle = \frac{{\cal I}_\parallel-{\cal I}_\perp}{{\cal I}_\parallel}.$">|; 

$key = q/displaystyle=frac{{calI}_{xx},x^{,2}+{calI}_{yy},y^{,2}+{calI}_{zz},z^{,2}}{r^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1693.png"
 ALT="$\displaystyle = \frac{ {\cal I}_{xx} x^{ 2}+ {\cal I}_{yy} y^{ 2}+{\cal I}_{zz} z^{ 2} }{ r^{ 2} }.$">|; 

$key = q/displaystyle=frac{{calI}_{zz}-{calI}_{xx}}{{calI}_{yy}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1985.png"
 ALT="$\displaystyle =\frac{{\cal I}_{zz}-{\cal I}_{xx}}{{\cal I}_{yy}}.$">|; 

$key = q/displaystyle=frac{{calI}_{zz}-{calI}_{yy}}{{calI}_{xx}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img1983.png"
 ALT="$\displaystyle =\frac{{\cal I}_{zz}-{\cal I}_{yy}}{{\cal I}_{xx}},$">|; 

$key = q/displaystyle=g_1(c_1,c_2,c_3,c_4,c_5,c_6,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4638.png"
 ALT="$\displaystyle =g_1(c_1,c_2,c_3,c_4,c_5,c_6,t),$">|; 

$key = q/displaystyle=g_2(c_1,c_2,c_3,c_4,c_5,c_6,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4640.png"
 ALT="$\displaystyle =g_2(c_1,c_2,c_3,c_4,c_5,c_6,t),$">|; 

$key = q/displaystyle=g_3(c_1,c_2,c_3,c_4,c_5,c_6,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4642.png"
 ALT="$\displaystyle =g_3(c_1,c_2,c_3,c_4,c_5,c_6,t).$">|; 

$key = q/displaystyle=gamma,(E-{bfv}cdot{bfp}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2787.png"
 ALT="$\displaystyle =\gamma (E-{\bf v}\cdot{\bf p}),$">|; 

$key = q/displaystyle=gamma,R^{,4},{rmi}sqrt{frac{2pi}{15}}ointleft(Y_2^{,2}-Y_2^{,-2}right)delta,d{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4488.png"
 ALT="$\displaystyle = \gamma R^{ 4} {\rm i}\sqrt{\frac{2\pi}{15}}\oint\left(Y_2^{ 2}-Y_2^{ -2}\right)\delta  d{\mit\Omega},$">|; 

$key = q/displaystyle=h,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1435.png"
 ALT="$\displaystyle = h,$">|; 

$key = q/displaystyle=h,cosI.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img5127.png"
 ALT="$\displaystyle = h \cos I.$">|; 

$key = q/displaystyle=h,sin{mitOmega},sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img5123.png"
 ALT="$\displaystyle = h \sin{\mit\Omega} \sin I,$">|; 

$key = q/displaystyle=int(y^{,2}+z^{,2}),gamma,d^{,3}{bfr}=intr^{,2},gamma,(sin^2theta,sin^2phi+cos^2theta),d^{,3}{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1664.png"
 ALT="$\displaystyle = \int (y^{ 2}+z^{ 2}) \gamma d^{ 3}{\bf r} = \int r^{ 2} \gamma (\sin^2\theta \sin^2 \phi + \cos^2\theta) d^{ 3}{\bf r}$">|; 

$key = q/displaystyle=int_0^inftyointrho({bfr}),(x'^{,2}+y'^{,2}),r^{,2},d{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4479.png"
 ALT="$\displaystyle = \int_0^\infty \oint \rho({\bf r}) (x'^{ 2}+y'^{ 2}) r^{ 2} d{\mit\Omega}$">|; 

$key = q/displaystyle=intr^{,2},gamma,left(frac{1}{2},sin^2theta+cos^2thetaright),d^{,3}{bfr}=frac{1}{2}intr^{,2},gamma,(1+cos^2theta),d^{,3}{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1665.png"
 ALT="$\displaystyle = \int r^{ 2} \gamma \left(\frac{1}{2} \sin^2\theta+ \cos^2\t...
...3}{\bf r} = \frac{1}{2}\int r^{ 2} \gamma (1+ \cos^2\theta) d^{ 3}{\bf r},$">|; 

$key = q/displaystyle=l_1,e,sin{calM}+l_2,,e^{,2},sin(2,{calM})+l_3,I^{,2},sin(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3232.png"
 ALT="$\displaystyle = l_1 e \sin{\cal M} +l_2  e^{ 2} \sin(2 {\cal M}) + l_3 I^{ 2} \sin(2 F)$">|; 

$key = q/displaystyle=lambda-skew{5}bar{lambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3182.png"
 ALT="$\displaystyle =\lambda - \skew{5}\bar{\lambda},$">|; 

$key = q/displaystyle=lambda_i,{bfx}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4090.png"
 ALT="$\displaystyle = \lambda_i {\bf x}_i,$">|; 

$key = q/displaystyle=lambda_i,{bfx}_i^T{bfx}_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4097.png"
 ALT="$\displaystyle = \lambda_i {\bf x}_i^T{\bf x}_j,$">|; 

$key = q/displaystyle=lambda_j,{bfx}_i^T{bfx}_j.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4098.png"
 ALT="$\displaystyle = \lambda_j {\bf x}_i^T{\bf x}_j.$">|; 

$key = q/displaystyle=lambda_j,{bfx}_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4092.png"
 ALT="$\displaystyle = \lambda_j {\bf x}_j,$">|; 

$key = q/displaystyle=left(1+frac{1}{6}m^{,2}right),z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3357.png"
 ALT="$\displaystyle =\left(1+\frac{1}{6}m^{ 2}\right) z_1,$">|; 

$key = q/displaystyle=left(1+frac{m^{,2}}{6}right),y_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3333.png"
 ALT="$\displaystyle =\left(1+\frac{m^{ 2}}{6}\right) y_1,$">|; 

$key = q/displaystyle=left(1+frac{m^{,2}}{6}right),y_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3339.png"
 ALT="$\displaystyle =\left(1+\frac{m^{ 2}}{6}\right) y_4 ,$">|; 

$key = q/displaystyle=left(1-frac{e^{,2}}{8}right)sin{calM}+frac{e}{2}left(1-frac{e^{,2}}{3}right)sin2{calM}+frac{3,e^{,2}}{8},sin3{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4052.png"
 ALT="$\displaystyle = \left(1-\frac{e^{ 2}}{8}\right)\sin {\cal M}+\frac{e}{2}\left(1-\frac{e^{ 2}}{3}\right)\sin 2{\cal M} +\frac{3 e^{ 2}}{8} \sin
3{\cal M}$">|; 

$key = q/displaystyle=left(a_x^{,2}+a_y^{,2}+a_z^{,2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3924.png"
 ALT="$\displaystyle = \left(a_x^{ 2}+a_y^{ 2}+a_z^{ 2}\right)^{1/2}$">|; 

$key = q/displaystyle=left(frac{-46,x_1-3,y_1}{128}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3537.png"
 ALT="$\displaystyle =\left(\frac{-46 x_1-3 y_1}{128}\right),$">|; 

$key = q/displaystyle=left(frac{1+e}{1-e}right)^{1slash2}tan(Eslash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img730.png"
 ALT="$\displaystyle =\left(\frac{1+e}{1-e}\right)^{1/2} \tan (E/2).$">|; 

$key = q/displaystyle=left(frac{11}{8},m^{,2}+frac{59}{12},m^{,3}+frac{893}{72},m^{,4}right)sin(2,D)+frac{201}{256},m^{,4},sin(4,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3463.png"
 ALT="$\displaystyle = \left(\frac{11}{8} m^{ 2}+\frac{59}{12} m^{ 3}+\frac{893}{72} m^{ 4}\right)\sin(2 D)+\frac{201}{256} m^{ 4} \sin(4 D),$">|; 

$key = q/displaystyle=left(frac{6,x_1+17,y_1}{64}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3539.png"
 ALT="$\displaystyle =\left(\frac{6 x_1+17 y_1}{64}\right).$">|; 

$key = q/displaystyle=left(frac{G,M}{2,r_p^{,3}}right)^{1slash2}(t-tau),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.47ex; " SRC="|."$dir".q|img836.png"
 ALT="$\displaystyle = \left(\frac{G M}{2 r_p^{ 3}}\right)^{1/2} (t-\tau),$">|; 

$key = q/displaystyle=left(frac{G,M}{a^{,3}}right)^{1slash2}(t-tau),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img843.png"
 ALT="$\displaystyle = \left(\frac{G M}{a^{ 3}}\right)^{1/2} (t-\tau),$">|; 

$key = q/displaystyle=left(frac{coshalpha+1}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3912.png"
 ALT="$\displaystyle =\left(\frac{\cosh\alpha+1}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=left(frac{coshalpha-1}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3910.png"
 ALT="$\displaystyle = \left(\frac{\cosh\alpha-1}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=left(frac{coshalpha-1}{coshalpha+1}right)^{1slash2}=frac{coshalpha-1}{sinhalpha}=frac{sinhalpha}{coshalpha+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3914.png"
 ALT="$\displaystyle = \left(\frac{\cosh\alpha-1}{\cosh\alpha+1}\right)^{1/2}=\frac{\cosh\alpha-1}{\sinh\alpha}=
\frac{\sinh\alpha}{\cosh\alpha+1}$">|; 

$key = q/displaystyle=left(frac{e+1}{e-1}right)^{1slash2}tanh(Hslash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img845.png"
 ALT="$\displaystyle = \left(\frac{e+1}{e-1}\right)^{1/2} \tanh (H/2).$">|; 

$key = q/displaystyle=left(frac{m_1+m_2}{m_1+m_2+m_3}right){bfr}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2978.png"
 ALT="$\displaystyle = \left(\frac{m_1+m_2}{m_1+m_2+m_3}\right){\bf r}',$">|; 

$key = q/displaystyle=left(frac{m_1}{m_1+m_2}right){bfr}-left(frac{m_3}{m_1+m_2+m_3}right){bfr}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2976.png"
 ALT="$\displaystyle = \left(\frac{m_1}{m_1+m_2}\right){\bf r} -\left(\frac{m_3}{m_1+m_2+m_3}\right){\bf r}',$">|; 

$key = q/displaystyle=left[frac{1}{a},frac{deta}{da}+frac{eta,(eta-1)}{a^{,2}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4383.png"
 ALT="$\displaystyle =\left[\frac{1}{a} \frac{d\eta}{da}+\frac{\eta (\eta-1)}{a^{ 2}}\right].$">|; 

$key = q/displaystyle=left[frac{4-25slash(5-alpha)^2}{1+25slash(5-alpha)^2}right]zeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4420.png"
 ALT="$\displaystyle = \left[\frac{4-25/(5-\alpha)^2}{1+25/(5-\alpha)^2}\right]\zeta,$">|; 

$key = q/displaystyle=left|{array}{ccc}{bfe}_x,&{bfe}_y,&{bfe}_z[0.5ex]a_x,&a_y,&a_z[0.5ex]b_x,&b_y,&b_z{array}right|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.70ex; vertical-align: -3.92ex; " SRC="|."$dir".q|img3928.png"
 ALT="$\displaystyle =\left\vert\begin{array}{ccc}{\bf e}_x,&amp; {\bf e}_y,&amp; {\bf e}_z\ [0.5ex]
a_x,&amp; a_y, &amp;a_z\ [0.5ex]
b_x,&amp; b_y,&amp; b_z
\end{array}\right\vert$">|; 

$key = q/displaystyle=m,(m+2,n+1),r^{,m-2},{calR}_n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4225.png"
 ALT="$\displaystyle = m (m+2 n+1) r^{ m-2} {\cal R}_n.$">|; 

$key = q/displaystyle=m,dot{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1420.png"
 ALT="$\displaystyle = m \dot{r},$">|; 

$key = q/displaystyle=m,r,skew{5}dot{theta}^{,2}-frac{dU}{dr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1422.png"
 ALT="$\displaystyle = m r \skew{5}\dot{\theta}^{ 2} - \frac{dU}{dr},$">|; 

$key = q/displaystyle=m,r^{,2},skew{5}dot{theta},phantom{123};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1424.png"
 ALT="$\displaystyle = m r^{ 2} \skew{5}\dot{\theta},\phantom{123}$">|; 

$key = q/displaystyle=m^{,2},zetaleft(frac{3,X'}{R'^{,5}},X,Z+frac{3,Y'}{R'^{,5}},Y,Zright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3112.png"
 ALT="$\displaystyle = m^{ 2} \zeta\left(\frac{3 X'}{R'^{ 5}} X Z+ \frac{3 Y'}{R'^{ 5}} Y Z\right),$">|; 

$key = q/displaystyle=m^{,2}left(-frac{Z}{R'^{,3}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3104.png"
 ALT="$\displaystyle = m^{ 2}\left(-\frac{Z}{R'^{ 3}}\right),$">|; 

$key = q/displaystyle=m^{,2}left[left(frac{3,X'^{,2}}{R'^{,5}}-frac{1}{R'^{,3}}right)X+left(frac{3,X',Y'}{R'^{,5}}right)Yright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3100.png"
 ALT="$\displaystyle = m^{ 2}\left[\left(\frac{3 X'^{ 2}}{R'^{ 5}}-\frac{1}{R'^{ 3}}\right)X +\left(
\frac{3 X' Y'}{R'^{ 5}}\right)Y\right],$">|; 

$key = q/displaystyle=m^{,2}left[left(frac{3,Y'^{,2}}{R'^{,5}}-frac{1}{R'^{,3}}right)Y+left(frac{3,X',Y'}{R'^{,5}}right)Xright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3102.png"
 ALT="$\displaystyle = m^{ 2}\left[\left(\frac{3 Y'^{ 2}}{R'^{ 5}}-\frac{1}{R'^{ 3}}\right)Y +\left(
\frac{3 X' Y'}{R'^{ 5}}\right)X\right],$">|; 

$key = q/displaystyle=mu,{bfh},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img943.png"
 ALT="$\displaystyle = \mu {\bf h},$">|; 

$key = q/displaystyle=mu,{calE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img945.png"
 ALT="$\displaystyle = \mu {\cal E},$">|; 

$key = q/displaystyle=mu_m,n_m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4581.png"
 ALT="$\displaystyle = \mu_m n_m^{ 2},$">|; 

$key = q/displaystyle=n',t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3174.png"
 ALT="$\displaystyle = n' t,$">|; 

$key = q/displaystyle=n+frac{(1-e^{,2})^{1slash2}}{e,sintheta}left(costheta,skew{3}dot{e}-frac{r}{a},frac{skew{3}dot{a}}{a}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img5119.png"
 ALT="$\displaystyle = n + \frac{(1-e^{ 2})^{1/2}}{e \sin\theta}\left(\cos\theta \skew{3}\dot{e} - \frac{r}{a} \frac{\skew{3}\dot{a}}{a}\right),$">|; 

$key = q/displaystyle=n+frac{1}{e,sinE}left[(cosE-e),skew{3}dot{e}-left(frac{r}{a}right)^2,frac{skew{3}dot{a}}{a}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5118.png"
 ALT="$\displaystyle = n + \frac{1}{e \sin E}\left[(\cos E - e) \skew{3}\dot{e} - \left(\frac{r}{a}\right)^2 \frac{\skew{3}\dot{a}}{a}\right]$">|; 

$key = q/displaystyle=n,(t-tau),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img725.png"
 ALT="$\displaystyle = n (t-\tau),$">|; 

$key = q/displaystyle=n,a^{,2},e,(1-e^{,2})^{-1slash2},(1-cosI),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4820.png"
 ALT="$\displaystyle =n a^{ 2} e (1-e^{ 2})^{-1/2} (1-\cos I),$">|; 

$key = q/displaystyle=n,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3173.png"
 ALT="$\displaystyle = n t,$">|; 

$key = q/displaystyle=n,{bfw},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1972.png"
 ALT="$\displaystyle = n {\bf w},$">|; 

$key = q/displaystyle=n-frac{2}{n,a},frac{partial{calR}}{partiala}-frac{1-e^{,2}}{n,a^{,2},e},frac{partial{calR}}{partiale},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2696.png"
 ALT="$\displaystyle = n -\frac{2}{n a} \frac{\partial {\cal R}}{\partial a}- \frac{1-e^{ 2}}{n a^{ 2} e} \frac{\partial{\cal R}}{\partial e},$">|; 

$key = q/displaystyle=n^2,a^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img649.png"
 ALT="$\displaystyle = n^2 a^{ 3},$">|; 

$key = q/displaystyle=n^{(0)}left[1-(3slash2),epsilon',a^{(1)}(t)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4906.png"
 ALT="$\displaystyle = n^{(0)}\left[1-(3/2) \epsilon' a^{(1)}(t)\right],$">|; 

$key = q/displaystyle=n^{,2},a^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3010.png"
 ALT="$\displaystyle = n^{ 2} a^{ 3},$">|; 

$key = q/displaystyle=nabla'{calR}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2417.png"
 ALT="$\displaystyle = \nabla' {\cal R}',$">|; 

$key = q/displaystyle=nablacdot({calR}_n,nablax_i+x_i,nabla{calR}_n)=2,nablax_icdotnabla{calR}_n=2,frac{partial{calR}_n}{partialx_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4222.png"
 ALT="$\displaystyle = \nabla\cdot({\cal R}_n \nabla x_i + x_i \nabla{\cal R}_n) = 2 \nabla x_i\cdot\nabla{\cal R}_n = 2 \frac{\partial {\cal R}_n}{\partial x_i},$">|; 

$key = q/displaystyle=nabla{calR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2416.png"
 ALT="$\displaystyle =\nabla {\cal R},$">|; 

$key = q/displaystyle=omega,(-sintheta,sinphi,,sintheta,cosphi,,costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4527.png"
 ALT="$\displaystyle = \omega (-\sin\theta \sin\phi, \sin\theta \cos\phi, \cos\theta)$">|; 

$key = q/displaystyle=omega,(0,,sintheta,,costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1709.png"
 ALT="$\displaystyle = \omega (0, \sin\theta, \cos\theta),$">|; 

$key = q/displaystyle=omega,cosalpha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1591.png"
 ALT="$\displaystyle = \omega \cos\alpha,$">|; 

$key = q/displaystyle=omega,left(-sintheta,sinphi,,sintheta,cosphi,,costhetaright);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1746.png"
 ALT="$\displaystyle = \omega \left(-\sin\theta \sin\phi, \sin\theta \cos\phi, \cos\theta\right)$">|; 

$key = q/displaystyle=omega,sinalpha,cos({mitOmega},t'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1588.png"
 ALT="$\displaystyle = \omega \sin\alpha \cos({\mit\Omega} t'),$">|; 

$key = q/displaystyle=omega,sinalpha,sin({mitOmega},t'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1589.png"
 ALT="$\displaystyle = \omega \sin\alpha \sin({\mit\Omega} t'),$">|; 

$key = q/displaystyle=omega_1^{,2}+3left(1+frac{1}{2},m^{,2}right)+a_{1,x},m^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3552.png"
 ALT="$\displaystyle = \omega_1^{ 2}+3\left(1+\frac{1}{2} m^{ 2}\right) + a_{1 x} m^{ 3},$">|; 

$key = q/displaystyle=omega_1^{,2}+b_{1,y},m^{,3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3558.png"
 ALT="$\displaystyle = \omega_1^{ 2}+b_{1 y} m^{ 3}.$">|; 

$key = q/displaystyle=omega_perp,cos({mitOmega},t'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1581.png"
 ALT="$\displaystyle = \omega_\perp \cos({\mit\Omega} t'),$">|; 

$key = q/displaystyle=omega_perp,sin({mitOmega},t'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1583.png"
 ALT="$\displaystyle =\omega_\perp \sin({\mit\Omega} t'),$">|; 

$key = q/displaystyle=p_x+I,sinpsi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2014.png"
 ALT="$\displaystyle = p_x+ I \sin\psi,$">|; 

$key = q/displaystyle=p_y+I,cospsi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2016.png"
 ALT="$\displaystyle = p_y+I \cos\psi,$">|; 

$key = q/displaystyle=phi,nablapsi+psi,nablaphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3941.png"
 ALT="$\displaystyle =\phi \nabla\psi+\psi \nabla\phi$">|; 

$key = q/displaystyle=pmfrac{sqrt{3}}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2217.png"
 ALT="$\displaystyle = \pm \frac{\sqrt{3}}{2},$">|; 

$key = q/displaystyle=pmleft(frac{1+cosalpha}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3855.png"
 ALT="$\displaystyle = \pm \left(\frac{1+\cos\alpha}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=pmleft(frac{1-cosalpha}{1+cosalpha}right)^{1slash2}=frac{1-cosalpha}{sinalpha}=frac{sinalpha}{1+cosalpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3857.png"
 ALT="$\displaystyle = \pm\left(\frac{1-\cos\alpha}{1+\cos\alpha}\right)^{1/2} = \frac{1-\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1+\cos\alpha}$">|; 

$key = q/displaystyle=pmleft(frac{1-cosalpha}{2}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3853.png"
 ALT="$\displaystyle =\pm\left(\frac{1-\cos\alpha}{2}\right)^{1/2}$">|; 

$key = q/displaystyle=r',left[cos{mitOmega}',cos(omega'+theta')-sin{mitOmega}',sin(omega'+theta'),cosI'right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img4166.png"
 ALT="$\displaystyle = r' \left[\cos{\mit\Omega}' \cos(\omega'+\theta') - \sin{\mit\Omega}' \sin(\omega'+\theta') \cos I'\right],$">|; 

$key = q/displaystyle=r',left[sin{mitOmega}',cos(omega'+theta')+cos{mitOmega}',sin(omega'+theta'),cosI'right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img4167.png"
 ALT="$\displaystyle = r' \left[ \sin{\mit\Omega}' \cos(\omega'+\theta') +\cos{\mit\Omega}' \sin(\omega'+\theta') \cos I'\right],$">|; 

$key = q/displaystyle=r',sin(omega'+theta'),sinI',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4168.png"
 ALT="$\displaystyle = r' \sin (\omega' + \theta') \sin I',$">|; 

$key = q/displaystyle=r,(coseta,,sineta,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1845.png"
 ALT="$\displaystyle = r (\cos\eta,  \sin\eta,  0),$">|; 

$key = q/displaystyle=r,F_theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img5102.png"
 ALT="$\displaystyle =r F_\theta.$">|; 

$key = q/displaystyle=r,costheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img389.png"
 ALT="$\displaystyle = r \cos\theta.$">|; 

$key = q/displaystyle=r,frac{partial{calR}_n}{partialr}=n,{calR}_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4220.png"
 ALT="$\displaystyle = r \frac{\partial {\cal R}_n}{\partial r} = n {\cal R}_n,$">|; 

$key = q/displaystyle=r,left[cos{mitOmega},cos(omega+theta)-sin{mitOmega},sin(omega+theta),cosIright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img745.png"
 ALT="$\displaystyle = r \left[\cos{\mit\Omega} \cos(\omega+\theta) - \sin{\mit\Omega} \sin(\omega+\theta) \cos I\right],$">|; 

$key = q/displaystyle=r,left[sin{mitOmega},cos(omega+theta)+cos{mitOmega},sin(omega+theta),cosIright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img747.png"
 ALT="$\displaystyle = r \left[ \sin{\mit\Omega} \cos(\omega+\theta) +\cos{\mit\Omega} \sin(\omega+\theta) \cos I\right],$">|; 

$key = q/displaystyle=r,sin(omega+theta),sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4165.png"
 ALT="$\displaystyle = r \sin (\omega + \theta) \sin I,$">|; 

$key = q/displaystyle=r,sin(omega+theta),sinI.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img749.png"
 ALT="$\displaystyle = r \sin (\omega + \theta) \sin I.$">|; 

$key = q/displaystyle=r,sin(tilde{omega}+f),sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4530.png"
 ALT="$\displaystyle = r \sin(\tilde{\omega}+f) \sin I,$">|; 

$key = q/displaystyle=r,sintheta,F_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5098.png"
 ALT="$\displaystyle = r \sin\theta F_z,$">|; 

$key = q/displaystyle=r,sintheta,cosphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img385.png"
 ALT="$\displaystyle = r \sin\theta \cos\phi,$">|; 

$key = q/displaystyle=r,sintheta,sinphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img387.png"
 ALT="$\displaystyle =r \sin\theta \sin\phi,$">|; 

$key = q/displaystyle=r,{bfe}_r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4151.png"
 ALT="$\displaystyle = r {\bf e}_r,$">|; 

$key = q/displaystyle=r_p,(1+P^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img837.png"
 ALT="$\displaystyle = r_p (1+P^{ 2}),$">|; 

$key = q/displaystyle=r_p,(1-P^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img908.png"
 ALT="$\displaystyle = r_p (1-P^{ 2}),$">|; 

$key = q/displaystyle=rho(r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4338.png"
 ALT="$\displaystyle =\rho(r),$">|; 

$key = q/displaystyle=rho,g,aleft(zeta-frac{4}{15},epsilonright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4318.png"
 ALT="$\displaystyle = \rho g a\left(\zeta-\frac{4}{15} \epsilon\right),$">|; 

$key = q/displaystyle=rho,gleft(frac{2}{5},delta_2-zeta_2right)(x_i)_{r=a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4294.png"
 ALT="$\displaystyle = \rho g\left(\frac{2}{5} \delta_2-\zeta_2\right) (x_i)_{r=a},$">|; 

$key = q/displaystyle=rho,gleft(frac{2}{5},delta_2-zeta_2right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4299.png"
 ALT="$\displaystyle = \rho g\left( \frac{2}{5} \delta_2-\zeta_2 \right),$">|; 

$key = q/displaystyle=rho,gleft(frac{2}{5},delta_2-zeta_2right)left(frac{x_i}{r}right)_{r=a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4280.png"
 ALT="$\displaystyle = \rho g
\left(\frac{2}{5} \delta_2-\zeta_2\right)\left(\frac{x_i}{r}\right)_{r=a},$">|; 

$key = q/displaystyle=rho_2-frac{rho_2^{,2}}{3}+frac{rho_2^{,3}}{3}+frac{rho_2^{,4}}{81}+{calO}(rho_2^{,5}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2201.png"
 ALT="$\displaystyle = \rho_2 -\frac{\rho_2^{ 2}}{3} + \frac{\rho_2^{ 3}}{3} + \frac{\rho_2^{ 4}}{81}+ {\cal O}(\rho_2^{ 5}),$">|; 

$key = q/displaystyle=rleft[cos{mitOmega},cos(tilde{omega}+f)-sin{mitOmega},sin(tilde{omega}+f),cosIright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img4528.png"
 ALT="$\displaystyle = r\left[\cos{\mit\Omega} \cos(\tilde{\omega}+f)-\sin{\mit\Omega} \sin(\tilde{\omega}+f) \cos I\right],$">|; 

$key = q/displaystyle=rleft[sin{mitOmega},cos(tilde{omega}+f)+cos{mitOmega},sin(tilde{omega}+f),cosIright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img4529.png"
 ALT="$\displaystyle = r\left[\sin{\mit\Omega} \cos(\tilde{\omega}+f)+\cos{\mit\Omega} \sin(\tilde{\omega}+f) \cos I\right],$">|; 

$key = q/displaystyle=sin2{calM}+2,e,(sin3{calM}-sin{calM})+{calO}(e^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1859.png"
 ALT="$\displaystyle =\sin 2{\cal M} +2 e (\sin 3{\cal M} - \sin {\cal M})+{\cal O}(e^{ 2}),$">|; 

$key = q/displaystyle=sinI,cos{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4864.png"
 ALT="$\displaystyle = \sin I \cos{\mit\Omega}.$">|; 

$key = q/displaystyle=sinI,sin{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4862.png"
 ALT="$\displaystyle = \sin I \sin{\mit\Omega},$">|; 

$key = q/displaystyle=sinI_{rmfree},cos(B,t+gamma_{rmfree})+q_{rmforced}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2662.png"
 ALT="$\displaystyle = \sin I_{\rm free} \cos(B t+\gamma_{\rm free})+ q_{\rm forced}(t),$">|; 

$key = q/displaystyle=sinI_{rmfree},sin(B,t+gamma_{rmfree})+p_{rmforced}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2660.png"
 ALT="$\displaystyle = \sin I_{\rm free} \sin(B t+\gamma_{\rm free})+ p_{\rm forced}(t),$">|; 

$key = q/displaystyle=sinalpha,cosbetapmcosalpha,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3833.png"
 ALT="$\displaystyle =\sin\alpha \cos\beta\pm \cos\alpha \sin\beta$">|; 

$key = q/displaystyle=sinhalpha,coshbetapmcoshalpha,sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3890.png"
 ALT="$\displaystyle =\sinh\alpha \cosh\beta\pm \cosh\alpha \sinh\beta$">|; 

$key = q/displaystyle=sinhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3793.png"
 ALT="$\displaystyle = \sinh x$">|; 

$key = q/displaystyle=sinomega,sinIleft[sintheta,F_r+(costheta+cosE),F_thetaright]+frac{mu}{h},e,cosomega,sinI,skew{5}dot{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img5145.png"
 ALT="$\displaystyle =\sin\omega \sin I\left[\sin\theta F_r+(\cos\theta+\cos E) F_\theta\right]
+ \frac{\mu}{h} e \cos\omega \sin I \skew{5}\dot{\omega}$">|; 

$key = q/displaystyle=sinomega,sinIleft[sintheta,F_r+(costheta+cosE),F_thetaright];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5147.png"
 ALT="$\displaystyle =\sin\omega \sin I\left[\sin\theta F_r+(\cos\theta+\cos E) F_\theta\right]$">|; 

$key = q/displaystyle=sinpsi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2012.png"
 ALT="$\displaystyle =\sin\psi,$">|; 

$key = q/displaystyle=sinpsi,sintheta,,skew{5}dot{phi}+cospsi,,skew{5}dot{theta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1636.png"
 ALT="$\displaystyle = \sin\psi \sin\theta  \skew{5}\dot{\phi} +\cos\psi  \skew{5}\dot{\theta},$">|; 

$key = q/displaystyle=sinpsi,sintheta,{bfe}_{x'}+cospsi,sintheta,{bfe}_{y'}+costheta,{bfe}_{z'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1628.png"
 ALT="$\displaystyle = \sin\psi \sin\theta {\bf e}_{x'} + \cos\psi \sin\theta {\bf e}_{y'}
+ \cos\theta {\bf e}_{z'},$">|; 

$key = q/displaystyle=sin{mitOmega},sinI,r,F_theta+left[cos{mitOmega},sin(omega+theta)+sin{mitOmega},cos(omega+theta),cosIright]r,F_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5134.png"
 ALT="$\displaystyle = \sin{\mit\Omega} \sin I r F_\theta +\left[\cos{\mit\Omega} \sin(\omega+\theta)+\sin{\mit\Omega} \cos(\omega+\theta) \cos I\right]r F_z,$">|; 

$key = q/displaystyle=sin{mitOmega},x'+cos{mitOmega},y',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4712.png"
 ALT="$\displaystyle =\sin{\mit\Omega} x' + \cos{\mit\Omega} y',$">|; 

$key = q/displaystyle=skew{2}dot{r},{bfe}_r+r,skew{5}dot{theta},{bfe}_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4153.png"
 ALT="$\displaystyle = \skew{2}\dot{r} {\bf e}_r + r \skew{5}\dot{\theta} {\bf e}_\theta,$">|; 

$key = q/displaystyle=skew{3}ddot{r}-r,skew{5}dot{theta}^{,2}-r,sin^2theta,,skew{5}dot{phi}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1472.png"
 ALT="$\displaystyle = \skew{3}\ddot{r} - r \skew{5}\dot{\theta}^{ 2} -r \sin^2\theta  \skew{5}\dot{\phi}^{ 2},$">|; 

$key = q/displaystyle=skew{3}dot{h},cosI-h,sinI,dot{I}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img5133.png"
 ALT="$\displaystyle = \skew{3}\dot{h} \cos I -h \sin I \dot{I}.$">|; 

$key = q/displaystyle=skew{3}dot{h},sin{mitOmega},sinI+h,cos{mitOmega},sinI,skew{5}dot{mitOmega}+h,sin{mitOmega},cosI,dot{I},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img5129.png"
 ALT="$\displaystyle = \skew{3}\dot{h} \sin{\mit\Omega} \sin I + h \cos{\mit\Omega} \sin I \skew{5}\dot{\mit\Omega} + h \sin{\mit\Omega} \cos I \dot{I},$">|; 

$key = q/displaystyle=skew{3}hat{nu}_x,sin(s,n,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2022.png"
 ALT="$\displaystyle =\skew{3}\hat{\nu}_x \sin(s n t-\phi),$">|; 

$key = q/displaystyle=skew{3}hat{nu}_x,sin[(n+g),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2056.png"
 ALT="$\displaystyle =\skew{3}\hat{\nu}_x \sin[(n+g) t],$">|; 

$key = q/displaystyle=skew{3}hat{nu}_y,cos(s,n,t-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2024.png"
 ALT="$\displaystyle =\skew{3}\hat{\nu}_y \cos(s n t-\phi),$">|; 

$key = q/displaystyle=skew{3}hat{nu}_y,cos[(n+g),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2057.png"
 ALT="$\displaystyle =\skew{3}\hat{\nu}_y \cos[(n+g) t],$">|; 

$key = q/displaystyle=skew{3}tilde{epsilon},phi_1(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1782.png"
 ALT="$\displaystyle = \skew{3}\tilde{\epsilon} \phi_1(t),$">|; 

$key = q/displaystyle=skew{5}bar{lambda}_0'+n'left[1-epsilon,Dleft(alpha,b_{1slash2}^{(0)}right)right]t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2542.png"
 ALT="$\displaystyle =\skew{5}\bar{\lambda}_0'+n'\left[1-\epsilon D\left(\alpha b_{1/2}^{(0)}\right)\right] t,$">|; 

$key = q/displaystyle=skew{5}bar{lambda}_0+n,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img794.png"
 ALT="$\displaystyle =\skew{5}\bar{\lambda}_0 + n t,$">|; 

$key = q/displaystyle=skew{5}bar{lambda}_0+n^{(0)},t+skew{5}bar{lambda}^{(1)}(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4902.png"
 ALT="$\displaystyle = \skew{5}\bar{\lambda}_0+n^{(0)} t+ \skew{5}\bar{\lambda}^{(1)}(t),$">|; 

$key = q/displaystyle=skew{5}bar{lambda}_0+nleft[1-epsilon',alpha^{,2},D,b_{1slash2}^{(0)}right]t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2523.png"
 ALT="$\displaystyle =\skew{5}\bar{\lambda}_0+ n\left[1-\epsilon' \alpha^{ 2} D b_{1/2}^{(0)}\right] t,$">|; 

$key = q/displaystyle=skew{5}dot{D}=1-m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3425.png"
 ALT="$\displaystyle = \skew{5}\dot{D}=1-m,$">|; 

$key = q/displaystyle=skew{5}dot{F}+skew{5}dot{{calM}}=2+(g-c),m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3441.png"
 ALT="$\displaystyle = \skew{5}\dot{F}+\skew{5}\dot{{\cal M}} = 2+(g-c) m^{ 2},$">|; 

$key = q/displaystyle=skew{5}dot{F}-skew{5}dot{{calM}}=(g+c),m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3439.png"
 ALT="$\displaystyle = \skew{5}\dot{F}-\skew{5}\dot{{\cal M}} = (g+c) m^{ 2},$">|; 

$key = q/displaystyle=skew{5}dot{F}=1+g,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3437.png"
 ALT="$\displaystyle = \skew{5}\dot{F} = 1+g m^{ 2},$">|; 

$key = q/displaystyle=skew{5}dot{r},{bfe}_r+r,skew{5}dottheta,{bfe}_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img5082.png"
 ALT="$\displaystyle = \skew{5}\dot{r} {\bf e}_r + r \skew{5}\dot\theta {\bf e}_\theta,$">|; 

$key = q/displaystyle=skew{5}dot{r},{bfe}_r+r,skew{5}dot{theta},{bfe}_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2739.png"
 ALT="$\displaystyle = \skew{5}\dot{r} {\bf e}_r + r \skew{5}\dot{\theta} {\bf e}_\theta,$">|; 

$key = q/displaystyle=skew{5}dot{{calM}}'=m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3419.png"
 ALT="$\displaystyle = \skew{5}\dot{{\cal M}}'=m,$">|; 

$key = q/displaystyle=skew{5}dot{{calM}}=1-c,m^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3405.png"
 ALT="$\displaystyle = \skew{5}\dot{{\cal M}}= 1-c m^{ 2},$">|; 

$key = q/displaystyle=sqrt{frac{15}{32pi}},sin^2theta,,{rme}^{,{rmi},2,phi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img4135.png"
 ALT="$\displaystyle = \sqrt{\frac{15}{32\pi}} \sin^2\theta  {\rm e}^{ {\rm i} 2 \phi}.$">|; 

$key = q/displaystyle=sqrt{frac{15}{32pi}},sin^2theta,,{rme}^{-{rmi},2,phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img4127.png"
 ALT="$\displaystyle = \sqrt{\frac{15}{32\pi}} \sin^2\theta  {\rm e}^{-{\rm i} 2 \phi},$">|; 

$key = q/displaystyle=sqrt{frac{15}{8pi}},sintheta,costheta,,{rme}^{-{rmi},phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img4129.png"
 ALT="$\displaystyle = \sqrt{\frac{15}{8\pi}} \sin\theta \cos\theta  {\rm e}^{-{\rm i} \phi},$">|; 

$key = q/displaystyle=sqrt{frac{1}{4pi}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4119.png"
 ALT="$\displaystyle = \sqrt{\frac{1}{4\pi}},$">|; 

$key = q/displaystyle=sqrt{frac{2pi}{15}},r^{,2}left(-Y_2^{,1}+Y_2^{,-1}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4475.png"
 ALT="$\displaystyle = \sqrt{\frac{2\pi}{15}} r^{ 2}\left(-Y_2^{ 1}+Y_2^{ -1}\right),$">|; 

$key = q/displaystyle=sqrt{frac{2pi}{15}},{mitOmega}^{,2},r^{,2}left[(l+{rmi},m),Y_2^{,-1}-(l-{rmi},m),Y_2^{,1}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4460.png"
 ALT="$\displaystyle = \sqrt{\frac{2\pi}{15}} {\mit\Omega}^{ 2} r^{ 2}\left[(l+{\rm i} m) Y_2^{ -1}-(l-{\rm i} m) Y_2^{ 1}\right],$">|; 

$key = q/displaystyle=sqrt{frac{3}{4pi}},costheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4123.png"
 ALT="$\displaystyle = \sqrt{\frac{3}{4\pi}} \cos\theta,$">|; 

$key = q/displaystyle=sqrt{frac{3}{8pi}},sintheta,,{rme}^{-{rmi},phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4121.png"
 ALT="$\displaystyle = \sqrt{\frac{3}{8\pi}} \sin\theta  {\rm e}^{-{\rm i} \phi},$">|; 

$key = q/displaystyle=sqrt{frac{5}{16pi}},(3,cos^2theta-1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img4131.png"
 ALT="$\displaystyle = \sqrt{\frac{5}{16\pi}} (3 \cos^2\theta-1),$">|; 

$key = q/displaystyle=sum_{i=1,8}A_i,e_{il},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2672.png"
 ALT="$\displaystyle = \sum_{i=1,8} A_i e_{il},$">|; 

$key = q/displaystyle=sum_{i=1,8}B_i,I_{il}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2674.png"
 ALT="$\displaystyle =\sum_{i=1,8} B_i I_{il}.$">|; 

$key = q/displaystyle=sum_{i=1,8}frac{n}{4},epsilon_i,alpha_i,bar{alpha}_i,b_{3slash2}^{(1)}(alpha_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2649.png"
 ALT="$\displaystyle = \sum_{i=1,8} \frac{n}{4} \epsilon_i \alpha_i \bar{\alpha}_i b_{3/2}^{(1)}(\alpha_i),$">|; 

$key = q/displaystyle=sum_{i=1,N}(x_i^{,2}+y_i^{,2}),m_i=int(x^{,2}+y^{,2}),dm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1504.png"
 ALT="$\displaystyle = \sum_{i=1,N}(x_i^{ 2}+y_i^{ 2})  m_i= \int(x^{ 2}+ y^{ 2}) dm,$">|; 

$key = q/displaystyle=sum_{i=1,N}(x_i^{,2}+z_i^{,2}),m_i=int(x^{,2}+z^{,2}),dm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1502.png"
 ALT="$\displaystyle = \sum_{i=1,N}(x_i^{ 2}+z_i^{ 2})  m_i= \int(x^{ 2}+ z^{ 2}) dm,$">|; 

$key = q/displaystyle=sum_{i=1,N}(y_i^{,2}+z_i^{,2}),m_i=int(y^{,2}+z^{,2}),dm,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1500.png"
 ALT="$\displaystyle = \sum_{i=1,N}(y_i^{ 2}+z_i^{ 2})  m_i= \int(y^{ 2}+ z^{ 2}) dm,$">|; 

$key = q/displaystyle=sum_{i=1,N}m_i,(x_i^{,2}+y_i^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1674.png"
 ALT="$\displaystyle = \sum_{i=1,N}m_i (x_i^{ 2}+y_i^{ 2}),$">|; 

$key = q/displaystyle=sum_{i=1,N}m_i,(x_i^{,2}+z_i^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1673.png"
 ALT="$\displaystyle = \sum_{i=1,N}m_i (x_i^{ 2}+z_i^{ 2}),$">|; 

$key = q/displaystyle=sum_{i=1,N}m_i,(y_i^{,2}+z_i^{,2})+sum_{i=1,N}m_i,(x_i^{,2}+z_i^{,2})+sum_{i=1,N}m_i,(x_i^{,2}+y_i^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1687.png"
 ALT="$\displaystyle =\sum_{i=1,N} m_i (y_i^{ 2}+z_i^{ 2})+\sum_{i=1,N}m_i (x_i^{ 2}+z_i^{ 2})
+ \sum_{i=1,N}m_i (x_i^{ 2}+y_i^{ 2})$">|; 

$key = q/displaystyle=sum_{i=1,N}m_i,(y_i^{,2}+z_i^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1672.png"
 ALT="$\displaystyle = \sum_{i=1,N}m_i (y_i^{ 2}+z_i^{ 2}),$">|; 

$key = q/displaystyle=sum_{i=1,N}m_i,frac{(y_i^{,2}+z_i^{,2}),x^{,2}+(x_i^{,2}+z_i^{,2}),y^{,2}+(x_i^{,2}+y_i^{,2}),z^{,2}}{r^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.25ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1692.png"
 ALT="$\displaystyle =\sum_{i=1,N}m_i 
\frac{ (y_i^{ 2}+z_i^{ 2}) x^{ 2} + (x_i^{ 2}+z_i^{ 2}) y^{ 2}
+(x_i^{ 2}+y_i^{ 2}) z^{ 2} }{ r^{ 2} }$">|; 

$key = q/displaystyle=sum_{i=1,N}{bfF}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img276.png"
 ALT="$\displaystyle =\sum_{i=1,N} {\bf F}_i,$">|; 

$key = q/displaystyle=sum_{i=1,N}{bfr}_itimes{bfF}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img277.png"
 ALT="$\displaystyle =\sum_{i=1,N} {\bf r}_i\times{\bf F}_i,$">|; 

$key = q/displaystyle=sum_{i=1,N}{bfr}_itimes{bfF}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img191.png"
 ALT="$\displaystyle = \sum_{i=1,N} {\bf r}_i\times {\bf F}_i$">|; 

$key = q/displaystyle=sum_{j=1,8}A_{ij},k_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2564.png"
 ALT="$\displaystyle =\sum_{j=1,8} A_{ij} k_j,$">|; 

$key = q/displaystyle=sum_{j=1,8}B_{ij},q_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2568.png"
 ALT="$\displaystyle =\sum_{j=1,8} B_{ij} q_j,$">|; 

$key = q/displaystyle=sum_{jneqi}frac{n_i}{4},epsilon_{ij},alpha_{ij},bar{alpha}_{ij},b^{(1)}_{3slash2}(alpha_{ij}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img2572.png"
 ALT="$\displaystyle = \sum_{j\neq i} \frac{n_i}{4} \epsilon_{ij} \alpha_{ij} \bar{\alpha}_{ij}  b^{(1)}_{3/2}(\alpha_{ij}),$">|; 

$key = q/displaystyle=sum_{l=1,8}I_{il},cos(f_l,t+gamma_l).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2586.png"
 ALT="$\displaystyle =\sum_{l=1,8} I_{il} \cos(f_l t+\gamma_l).$">|; 

$key = q/displaystyle=sum_{l=1,8}I_{il},sin(f_l,t+gamma_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2584.png"
 ALT="$\displaystyle =\sum_{l=1,8} I_{il} \sin(f_l t+\gamma_l),$">|; 

$key = q/displaystyle=sum_{l=1,8}e_{il},cos(g_l,t+beta_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2582.png"
 ALT="$\displaystyle =\sum_{l=1,8} e_{il} \cos(g_l t+\beta_l),$">|; 

$key = q/displaystyle=sum_{l=1,8}e_{il},sin(g_l,t+beta_l),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2580.png"
 ALT="$\displaystyle =\sum_{l=1,8} e_{il} \sin(g_l t+\beta_l),$">|; 

$key = q/displaystyle=theta_0+deltatheta,cos({mitOmega}_n,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1793.png"
 ALT="$\displaystyle = \theta_0 + \delta\theta \cos({\mit\Omega}_n t),$">|; 

$key = q/displaystyle=theta_0+deltatheta_1,cos{mitOmega}-deltatheta_2,cos(2,{mitOmega}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4556.png"
 ALT="$\displaystyle = \theta_0 + \delta\theta_1 \cos{\mit\Omega}-\delta\theta_2 \cos(2 {\mit\Omega}),$">|; 

$key = q/displaystyle=theta_0+skew{3}tilde{epsilon},theta_1(t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1780.png"
 ALT="$\displaystyle =\theta_0+ \skew{3}\tilde{\epsilon} \theta_1(t),$">|; 

$key = q/displaystyle=tilde{mu}'left(frac{1}{|{bfr}-{bfr}'|}-frac{{bfr}cdot{bfr}'}{r'^{,3}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2419.png"
 ALT="$\displaystyle = \tilde{\mu}'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert} - \frac{{\bf r}\cdot{\bf r}'}{r'^{ 3}}\right),$">|; 

$key = q/displaystyle=tilde{mu}left(frac{1}{|{bfr}-{bfr}'|}-frac{{bfr}cdot{bfr}'}{r^{,3}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2421.png"
 ALT="$\displaystyle =\tilde{\mu}\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert} - \frac{{\bf r}\cdot{\bf r}'}{r^{ 3}}\right),$">|; 

$key = q/displaystyle=varv_x-u,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle = \varv_x - u,$">|; 

$key = q/displaystyle=varv_y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle = \varv_y ,$">|; 

$key = q/displaystyle=varv_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img102.png"
 ALT="$\displaystyle =\varv_z.$">|; 

$key = q/displaystyle=x+frac{x^{,3}}{3!}+frac{x^{,5}}{5!}+frac{x^{,7}}{7!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3819.png"
 ALT="$\displaystyle = x + \frac{x^{ 3}}{3!} +\frac{x^{ 5}}{5!} + \frac{x^{ 7}}{7!} + \cdots$">|; 

$key = q/displaystyle=x+frac{x^{,3}}{3}+frac{2,x^{,5}}{15}+frac{17,x^{,7}}{315}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3817.png"
 ALT="$\displaystyle = x + \frac{x^{ 3}}{3} + \frac{2 x^{ 5}}{15} + \frac{17 x^{ 7}}{315}+\cdots$">|; 

$key = q/displaystyle=x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img422.png"
 ALT="$\displaystyle = x,$">|; 

$key = q/displaystyle=x,f_y-y,f_x=-frac{3,G,m_p,({calI}_{yy}-{calI}_{xx}),y,x}{r^{,5}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1834.png"
 ALT="$\displaystyle =x f_y-y f_x= -\frac{3 G m_p ({\cal I}_{yy}-{\cal I}_{xx}) y x}{r^{ 5}}.$">|; 

$key = q/displaystyle=x-frac{x^{,2}}{2}+frac{x^{,3}}{3}-frac{x^{,4}}{4}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3811.png"
 ALT="$\displaystyle = x - \frac{x^{ 2}}{2}+\frac{x^{ 3}}{3}-\frac{x^{ 4}}{4}+\cdots$">|; 

$key = q/displaystyle=x-frac{x^{,3}}{3!}+frac{x^{,5}}{5!}-frac{x^{,7}}{7!}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3813.png"
 ALT="$\displaystyle = x - \frac{x^{ 3}}{3!} +\frac{x^{ 5}}{5!} - \frac{x^{ 7}}{7!} + \cdots$">|; 

$key = q/displaystyle=x-frac{x^{,3}}{3}+frac{2,x^{,5}}{15}-frac{17,x^{,7}}{315}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3823.png"
 ALT="$\displaystyle = x - \frac{x^{ 3}}{3} + \frac{2 x^{ 5}}{15} - \frac{17 x^{ 7}}{315}+\cdots$">|; 

$key = q/displaystyle=x-u,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle = x - u t,$">|; 

$key = q/displaystyle=x_0+deltax,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2250.png"
 ALT="$\displaystyle = x_0 + \delta x,$">|; 

$key = q/displaystyle=x_1'slasha',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3081.png"
 ALT="$\displaystyle = x_1'/a',$">|; 

$key = q/displaystyle=x_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3310.png"
 ALT="$\displaystyle =x_1,$">|; 

$key = q/displaystyle=x_1slasha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3077.png"
 ALT="$\displaystyle = x_1/a,$">|; 

$key = q/displaystyle=x_2-frac{1}{4},y_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3312.png"
 ALT="$\displaystyle = x_2-\frac{1}{4} y_1^{ 2},$">|; 

$key = q/displaystyle=x_3-frac{1}{4},z_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3314.png"
 ALT="$\displaystyle = x_3-\frac{1}{4} z_1^{ 2},$">|; 

$key = q/displaystyle=x_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3316.png"
 ALT="$\displaystyle = x_4,$">|; 

$key = q/displaystyle=x_5-frac{1}{4},y_4^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3318.png"
 ALT="$\displaystyle =x_5-\frac{1}{4} y_4^{ 2},$">|; 

$key = q/displaystyle=x_6+frac{1}{2},y_1,y_4,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3320.png"
 ALT="$\displaystyle = x_6+\frac{1}{2} y_1 y_4 m,$">|; 

$key = q/displaystyle=x_7-frac{1}{2},y_1,y_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3322.png"
 ALT="$\displaystyle =x_7-\frac{1}{2} y_1 y_4,$">|; 

$key = q/displaystyle=x_8,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3324.png"
 ALT="$\displaystyle =x_8,$">|; 

$key = q/displaystyle=x_9,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3326.png"
 ALT="$\displaystyle = x_9,$">|; 

$key = q/displaystyle=x_{01}+frac{1}{18}+frac{1}{4},y_4^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3304.png"
 ALT="$\displaystyle = x_{01} + \frac{1}{18}+\frac{1}{4} y_4^{ 2},$">|; 

$key = q/displaystyle=x_{01},m^{,4}+x_{02},e^{,2}+x_{03},I^{,2}+x_1,e,cos{calM}+x_2,e^{,2},cos(2,{calM})+x_3,I^{,2},cos(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3206.png"
 ALT="$\displaystyle = x_{01} m^{ 4}+ x_{02} e^{ 2}+x_{03} I^{ 2} + x_1 e \cos{\cal M} +x_2 e^{ 2} \cos(2 {\cal M}) + x_3 I^{ 2} \cos(2 F)$">|; 

$key = q/displaystyle=x_{02}+frac{1}{4},y_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3306.png"
 ALT="$\displaystyle = x_{02} + \frac{1}{4} y_1^{ 2},$">|; 

$key = q/displaystyle=x_{03}+frac{1}{4},z_1^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3308.png"
 ALT="$\displaystyle = x_{03}+\frac{1}{4} z_1^{ 2},$">|; 

$key = q/displaystyle=x_{10},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3328.png"
 ALT="$\displaystyle = x_{10},$">|; 

$key = q/displaystyle=x_{11},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3330.png"
 ALT="$\displaystyle = x_{11},$">|; 

$key = q/displaystyle=x_{12},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3331.png"
 ALT="$\displaystyle = x_{12},$">|; 

$key = q/displaystyle=y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle = y,$">|; 

$key = q/displaystyle=y,f_z-z,f_y=-frac{3,G,m_p,({calI}_{zz}-{calI}_{yy}),z,y}{r^{,5}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1830.png"
 ALT="$\displaystyle =y f_z-z f_y= -\frac{3 G m_p ({\cal I}_{zz}-{\cal I}_{yy}) z y}{r^{ 5}},$">|; 

$key = q/displaystyle=y_0+deltay,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2251.png"
 ALT="$\displaystyle =y_0 + \delta y,$">|; 

$key = q/displaystyle=y_1'slasha',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3083.png"
 ALT="$\displaystyle =y_1'/a',$">|; 

$key = q/displaystyle=y_1,e,sin{calM}+y_2,e^{,2},sin(2,{calM})+y_3,I^{,2},sin(2,F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3211.png"
 ALT="$\displaystyle = y_1 e \sin{\cal M} +y_2 e^{ 2} \sin(2 {\cal M}) + y_3 I^{ 2} \sin(2 F)$">|; 

$key = q/displaystyle=y_1slasha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3078.png"
 ALT="$\displaystyle =y_1/a,$">|; 

$key = q/displaystyle=y_2-frac{1}{2},x_1,y_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3335.png"
 ALT="$\displaystyle = y_2-\frac{1}{2} x_1 y_1,$">|; 

$key = q/displaystyle=y_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3337.png"
 ALT="$\displaystyle = y_3,$">|; 

$key = q/displaystyle=y_5-frac{1}{2},x_4,y_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3341.png"
 ALT="$\displaystyle =y_5-\frac{1}{2} x_4 y_4,$">|; 

$key = q/displaystyle=y_6-frac{1}{2},x_1,y_4,m+frac{1}{2},y_1,x_4,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3343.png"
 ALT="$\displaystyle =y_6-\frac{1}{2} x_1 y_4 m+\frac{1}{2} y_1 x_4 m,$">|; 

$key = q/displaystyle=y_7-frac{1}{2},x_1,y_4-frac{1}{2},y_1,x_4,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3345.png"
 ALT="$\displaystyle =y_7-\frac{1}{2} x_1 y_4-\frac{1}{2} y_1 x_4,$">|; 

$key = q/displaystyle=y_8,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3347.png"
 ALT="$\displaystyle = y_8,$">|; 

$key = q/displaystyle=y_9,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3349.png"
 ALT="$\displaystyle =y_9,$">|; 

$key = q/displaystyle=y_{10},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3351.png"
 ALT="$\displaystyle = y_{10},$">|; 

$key = q/displaystyle=y_{11},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3353.png"
 ALT="$\displaystyle = y_{11},$">|; 

$key = q/displaystyle=y_{12},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3355.png"
 ALT="$\displaystyle =y_{12},$">|; 

$key = q/displaystyle=z'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img3048.png"
 ALT="$\displaystyle =z'.$">|; 

$key = q/displaystyle=z,f_x-x,f_z=-frac{3,G,m_p,({calI}_{xx}-{calI}_{zz}),x,z}{r^{,5}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1832.png"
 ALT="$\displaystyle =z f_x-x f_z=-\frac{3 G m_p ({\cal I}_{xx}-{\cal I}_{zz}) x z}{r^{ 5}},$">|; 

$key = q/displaystyle=z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle = z.$">|; 

$key = q/displaystyle=z_1'slasha',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3085.png"
 ALT="$\displaystyle = z_1'/a',$">|; 

$key = q/displaystyle=z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3042.png"
 ALT="$\displaystyle =z_1,$">|; 

$key = q/displaystyle=z_1,I,sinF+z_2,e,I,sin(F-{calM})+z_3,e,I,sin(F+{calM})+z_4,m,I,sin(2,D-F);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3216.png"
 ALT="$\displaystyle = z_1 I \sin F + z_2 e I \sin (F-{\cal M}) + z_3 e I \sin(F+{\cal M}) + z_4 m I \sin(2 D-F)$">|; 

$key = q/displaystyle=z_1slasha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3079.png"
 ALT="$\displaystyle = z_1/a,$">|; 

$key = q/displaystyle=z_2-frac{1}{2},x_1,z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3359.png"
 ALT="$\displaystyle =z_2-\frac{1}{2} x_1 z_1,$">|; 

$key = q/displaystyle=z_3-frac{1}{2},x_1,z_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3361.png"
 ALT="$\displaystyle =z_3-\frac{1}{2} x_1 z_1,$">|; 

$key = q/displaystyle=z_4+frac{1}{2},z_1,x_4,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3363.png"
 ALT="$\displaystyle = z_4+\frac{1}{2} z_1 x_4 m,$">|; 

$key = q/displaystyle=z_5-frac{1}{2},z_1,x_4.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3365.png"
 ALT="$\displaystyle =z_5-\frac{1}{2} z_1 x_4.$">|; 

$key = q/displaystyle={bff}({bfr},{bfr}')+{bfg}({bfr},{bfr}'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3018.png"
 ALT="$\displaystyle = {\bf f}({\bf r},{\bf r}')+{\bf g}({\bf r},{\bf r}'),$">|; 

$key = q/displaystyle={bff},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle ={\bf f},$">|; 

$key = q/displaystyle={bfg}'({bfr},{bfr}'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3020.png"
 ALT="$\displaystyle = {\bf g}'({\bf r},{\bf r}'),$">|; 

$key = q/displaystyle={bfp}+left[(gamma-1),frac{{bfv}cdot{bfp}}{v^{,2}}-frac{gamma,E}{c^{,2}}right]{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2789.png"
 ALT="$\displaystyle = {\bf p} +\left[(\gamma-1) \frac{{\bf v}\cdot{\bf p}}{v^{ 2}}-\frac{\gamma E}{c^{ 2}}\right]{\bf v},$">|; 

$key = q/displaystyle={bfr}'+left(frac{m_2}{m_1+m_2}right){bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2982.png"
 ALT="$\displaystyle = {\bf r}'+\left(\frac{m_2}{m_1+m_2}\right){\bf r},$">|; 

$key = q/displaystyle={bfr}'-left(frac{m_1}{m_1+m_2}right){bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2984.png"
 ALT="$\displaystyle = {\bf r}' -\left(\frac{m_1}{m_1+m_2}\right){\bf r}.$">|; 

$key = q/displaystyle={bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2980.png"
 ALT="$\displaystyle ={\bf r},$">|; 

$key = q/displaystyle={bfr}_{cm}+frac{m_1}{m_1+m_2},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img270.png"
 ALT="$\displaystyle = {\bf r}_{cm} + \frac{m_1}{m_1+m_2} {\bf r},$">|; 

$key = q/displaystyle={bfr}_{cm}-frac{m_2}{m_1+m_2},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img268.png"
 ALT="$\displaystyle = {\bf r}_{cm} - \frac{m_2}{m_1+m_2} {\bf r},$">|; 

$key = q/displaystyle={bfr}timesdot{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img939.png"
 ALT="$\displaystyle = {\bf r}\times \dot{\bf r},$">|; 

$key = q/displaystyle={bfx}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4104.png"
 ALT="$\displaystyle = {\bf x}_i,$">|; 

$key = q/displaystyle={bfx}_j-left(frac{{bfx}_i^T{bfx}_j}{{bfx}_i^T{bfx}_i}right){bfx}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.40ex; " SRC="|."$dir".q|img4106.png"
 ALT="$\displaystyle = {\bf x}_j - \left(\frac{{\bf x}_i^T{\bf x}_j}{{\bf x}_i^T{\bf x}_i}\right) {\bf x}_i.$">|; 

$key = q/displaystyle={calI}_0left(1+frac{2,epsilon}{3}right)={calI}_parallel,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4494.png"
 ALT="$\displaystyle = {\cal I}_0\left(1+\frac{2 \epsilon}{3}\right)= {\cal I}_\parallel,$">|; 

$key = q/displaystyle={calI}_0left(1-frac{epsilon}{3}right)={calI}_perp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4495.png"
 ALT="$\displaystyle = {\cal I}_0\left(1-\frac{\epsilon}{3}\right)={\cal I}_\perp,$">|; 

$key = q/displaystyle={calI}_parallel,omega,cosalpha.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1598.png"
 ALT="$\displaystyle = {\cal I}_\parallel \omega \cos\alpha.$">|; 

$key = q/displaystyle={calI}_perp,omega,sinalpha,cos({mitOmega},t'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1594.png"
 ALT="$\displaystyle = {\cal I}_\perp \omega \sin\alpha \cos({\mit\Omega} t'),$">|; 

$key = q/displaystyle={calI}_perp,omega,sinalpha,sin({mitOmega},t'),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1596.png"
 ALT="$\displaystyle = {\cal I}_\perp \omega \sin\alpha \sin({\mit\Omega} t'),$">|; 

$key = q/displaystyle={calI}_{x'x'},skew{3}dot{omega}_{x'}-({calI}_{y'y'}-{calI}_{z'z'}),omega_{y'},omega_{z'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1564.png"
 ALT="$\displaystyle = {\cal I}_{x'x'} \skew{3}\dot{\omega}_{x'} - ({\cal I}_{y'y'}-{\cal I}_{z'z'}) \omega_{y'} \omega_{z'},$">|; 

$key = q/displaystyle={calI}_{x'z'},{mitOmega}_{x'}+{calI}_{y'z'},{mitOmega}_{y'}+{calI}_{z'z'},{mitOmega}_{z'}simeq{mitOmega},{calI}_parallel.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4500.png"
 ALT="$\displaystyle = {\cal I}_{x'z'} {\mit \Omega}_{x'} + {\cal I}_{y'z'} {\mit\Om...
...{y'}+{\cal I}_{z'z'} {\mit\Omega}_{z'}\simeq {\mit\Omega} {\cal I}_\parallel.$">|; 

$key = q/displaystyle={calI}_{xx}+{calI}_{yy}+{calI}_{zz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1688.png"
 ALT="$\displaystyle = {\cal I}_{xx} + {\cal I}_{yy} + {\cal I}_{zz},$">|; 

$key = q/displaystyle={calI}_{y'y'},skew{3}dot{omega}_{y'}-({calI}_{z'z'}-{calI}_{x'x'}),omega_{z'},omega_{x'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1566.png"
 ALT="$\displaystyle = {\cal I}_{y'y'} \skew{3}\dot{\omega}_{y'} - ({\cal I}_{z'z'}-{\cal I}_{x'x'}) \omega_{z'} \omega_{x'},$">|; 

$key = q/displaystyle={calI}_{z'z'},skew{3}dot{omega}_{z'}-({calI}_{x'x'}-{calI}_{y'y'}),omega_{x'},omega_{y'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1568.png"
 ALT="$\displaystyle = {\cal I}_{z'z'} \skew{3}\dot{\omega}_{z'} - ({\cal I}_{x'x'}-{\cal I}_{y'y'}) \omega_{x'} \omega_{y'},$">|; 

$key = q/displaystyle={calM}+2,e,sin{calM}+frac{5,e^{,2}}{4},sin2{calM}+e^{,3}left(frac{13}{12},sin3{calM}-frac{1}{4},sin{calM}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4069.png"
 ALT="$\displaystyle = {\cal M} + 2 e \sin{\cal M} + \frac{5 e^{ 2}}{4} \sin 2{\c...
... e^{ 3}\left(
\frac{13}{12} \sin 3{\cal M} - \frac{1}{4} \sin{\cal M}\right)$">|; 

$key = q/displaystyle={calM}+2,e,sin{calM}+frac{5,e^{,2}}{4},sin2{calM}+frac{e^{,3}}{12}left(13,sin3{calM}-3,sin{calM}right)+{calO}(e^4),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img788.png"
 ALT="$\displaystyle = {\cal M} +2 e \sin {\cal M} + \frac{5 e^{ 2}}{4} \sin 2{\c...
...c{e^{ 3}}{12}\left(13 \sin 3{\cal M} -3  \sin{\cal M}\right)+ {\cal O}(e^4),$">|; 

$key = q/displaystyle={calM}+2,e,sin{calM}+{calO}(e^{,2}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1855.png"
 ALT="$\displaystyle ={\cal M} + 2 e \sin{\cal M}+{\cal O}(e^{ 2}),$">|; 

$key = q/displaystyle={calM}+e,sin{calM}+frac{e^{,2}}{2},sin2{calM}+frac{e^{,3}}{8}left(3,sin3{calM}-sin{calM}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4056.png"
 ALT="$\displaystyle = {\cal M} + e \sin{\cal M} + \frac{e^{ 2}}{2} \sin 2{\cal M} + \frac{e^{ 3}}{8}\left(3 \sin 3{\cal M}-\sin{\cal M}\right)$">|; 

$key = q/displaystyle={calM},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img727.png"
 ALT="$\displaystyle = {\cal M},$">|; 

$key = q/displaystyle={calS}_D+alpha,{calS}_E,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4943.png"
 ALT="$\displaystyle = {\cal S}_D + \alpha {\cal S}_E,$">|; 

$key = q/displaystyle={mitOmega},(coslambda,,0,,sinlambda),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1107.png"
 ALT="$\displaystyle = {\mit\Omega} (\cos\lambda, 0, \sin\lambda),$">|; 

$key = q/displaystyle={mitOmega}^{,2},(l,x'+m,y'),z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4458.png"
 ALT="$\displaystyle = {\mit\Omega}^{ 2} (l x'+m y') z'$">|; 

$key = q/displaystyle={mitOmega}^{,2},r^{,2},(l,cosphi+m,sinphi),sintheta,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4459.png"
 ALT="$\displaystyle ={\mit\Omega}^{ 2} r^{ 2} (l \cos\phi+m \sin\phi) \sin\theta \cos\theta$">|; 

$key = q/displaystyle={mitchi}_2-frac{3}{5},g,delta_2left(frac{r}{a}right)^{-3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4254.png"
 ALT="$\displaystyle ={\mit\chi}_2-\frac{3}{5} g \delta_2\left(\frac{r}{a}\right)^{-3},$">|; 

$key = q/displaystyle={mitchi}_2-frac{3}{5},g,delta_2left(frac{r}{a}right)^{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4252.png"
 ALT="$\displaystyle = {\mit\chi}_2-\frac{3}{5} g \delta_2\left(\frac{r}{a}\right)^{2},$">|; 

$key = q/displaystyle={rme}^x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3775.png"
 ALT="$\displaystyle = {\rm e}^x$">|; 

$key = q/displaystyle={rmi},sqrt{frac{2pi}{15}},r^{,2}left(Y_2^{,1}+Y_2^{,-1}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img4477.png"
 ALT="$\displaystyle = {\rm i} \sqrt{\frac{2\pi}{15}} r^{ 2}\left(Y_2^{ 1}+Y_2^{ -1}\right).$">|; 

$key = q/displaystyle=|{bfr}_2-{bfr}_1|=r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2987.png"
 ALT="$\displaystyle = \vert{\bf r}_2-{\bf r}_1\vert = r,$">|; 

$key = q/displaystyleA,mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4303.png"
 ALT="$\displaystyle A \mu$">|; 

$key = q/displaystyleA;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2269.png"
 ALT="$\displaystyle A$">|; 

$key = q/displaystyleA=aleft(1-frac{1}{6},m^{,2}+frac{331}{288},m^{,4}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3474.png"
 ALT="$\displaystyle A = a\left(1-\frac{1}{6} m^{ 2}+\frac{331}{288} m^{ 4}\right).$">|; 

$key = q/displaystyleA_0=e,J_{-1}'(0)=-e,J_1'(0)=-frac{e}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4047.png"
 ALT="$\displaystyle A_0 = e J_{-1}'(0)=-e J_1'(0) = -\frac{e}{2},$">|; 

$key = q/displaystyleA_1,C_2-A_2,C_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4736.png"
 ALT="$\displaystyle A_1 C_2-A_2 C_1$">|; 

$key = q/displaystyleA_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4721.png"
 ALT="$\displaystyle A_1$">|; 

$key = q/displaystyleA_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2650.png"
 ALT="$\displaystyle A_i$">|; 

$key = q/displaystyleA_n=frac{1}{2pi,n}oint{rme}^{,{rmi},(E-n,{calM})},dE.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4042.png"
 ALT="$\displaystyle A_n = \frac{1}{2\pi n}\oint{\rm e}^{ {\rm i} (E-n {\cal M})}  dE.$">|; 

$key = q/displaystyleA_n=frac{1}{2pi,n}oint{rme}^{-{rmi},[(n-1),E-n,e,sinE]},dE.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4044.png"
 ALT="$\displaystyle A_n = \frac{1}{2\pi n} \oint {\rm e}^{-{\rm i} [(n-1) E - n e \sin E]} dE.$">|; 

$key = q/displaystyleA_n=frac{1}{2pi}oint{rme}^{,{rmi},(E-n,{calM})},d{calM}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4041.png"
 ALT="$\displaystyle A_n = \frac{1}{2\pi}\oint {\rm e}^{ {\rm i} (E-n {\cal M})}  d{\cal M}.$">|; 

$key = q/displaystyleA_n=frac{J_{n-1}(n,e)}{n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4045.png"
 ALT="$\displaystyle A_n = \frac{J_{n-1}(n e)}{n}.$">|; 

$key = q/displaystyleA_{ii};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2571.png"
 ALT="$\displaystyle A_{ii}$">|; 

$key = q/displaystyleA_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2573.png"
 ALT="$\displaystyle A_{ij}$">|; 

$key = q/displaystyleA_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3551.png"
 ALT="$\displaystyle A_{xx}$">|; 

$key = q/displaystyleA_{xy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3553.png"
 ALT="$\displaystyle A_{xy}$">|; 

$key = q/displaystyleA_{yx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3555.png"
 ALT="$\displaystyle A_{yx}$">|; 

$key = q/displaystyleA_{yy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3557.png"
 ALT="$\displaystyle A_{yy}$">|; 

$key = q/displaystyleB,mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4305.png"
 ALT="$\displaystyle B \mu$">|; 

$key = q/displaystyleB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2271.png"
 ALT="$\displaystyle B$">|; 

$key = q/displaystyleB_1,D_2-B_2,D_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4740.png"
 ALT="$\displaystyle B_1 D_2-B_2 D_1$">|; 

$key = q/displaystyleB_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4723.png"
 ALT="$\displaystyle B_1$">|; 

$key = q/displaystyleB_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2653.png"
 ALT="$\displaystyle B_i$">|; 

$key = q/displaystyleB_{ii};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2575.png"
 ALT="$\displaystyle B_{ii}$">|; 

$key = q/displaystyleB_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2577.png"
 ALT="$\displaystyle B_{ij}$">|; 

$key = q/displaystyleC;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2273.png"
 ALT="$\displaystyle C$">|; 

$key = q/displaystyleC=-2,U-varv^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img2172.png"
 ALT="$\displaystyle C = - 2 U - \varv^{ 2}$">|; 

$key = q/displaystyleC=x^{,2}+y^{,2}+2left(frac{mu_1}{rho_1}+frac{mu_2}{rho_2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2334.png"
 ALT="$\displaystyle C = x^{ 2}+y^{ 2} + 2\left(\frac{\mu_1}{\rho_1}+\frac{\mu_2}{\rho_2}\right),
$">|; 

$key = q/displaystyleC_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2228.png"
 ALT="$\displaystyle C_1$">|; 

$key = q/displaystyleC_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2230.png"
 ALT="$\displaystyle C_2$">|; 

$key = q/displaystyleC_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2232.png"
 ALT="$\displaystyle C_3$">|; 

$key = q/displaystyleC_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2234.png"
 ALT="$\displaystyle C_4$">|; 

$key = q/displaystyleC_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2236.png"
 ALT="$\displaystyle C_5$">|; 

$key = q/displaystyleD;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2275.png"
 ALT="$\displaystyle D$">|; 

$key = q/displaystyleD=skew{5}bar{lambda}-skew{5}bar{lambda}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3177.png"
 ALT="$\displaystyle D = \skew{5}\bar{\lambda}-\skew{5}\bar{\lambda}',$">|; 

$key = q/displaystyleD_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4726.png"
 ALT="$\displaystyle D_1$">|; 

$key = q/displaystyleDsimeqD_1,cos^2(thetaslash2)+D_2,sin^2(thetaslash2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img890.png"
 ALT="$\displaystyle D\simeq D_1 \cos^2(\theta/2) + D_2 \sin^2(\theta/2),
$">|; 

$key = q/displaystyleE';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2786.png"
 ALT="$\displaystyle E'$">|; 

$key = q/displaystyleE-e,sinE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img726.png"
 ALT="$\displaystyle E - e \sin E$">|; 

$key = q/displaystyleE-e,sinE={calM},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4043.png"
 ALT="$\displaystyle E-e \sin E={\cal M},$">|; 

$key = q/displaystyleE-e,sinE={calM}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img691.png"
 ALT="$\displaystyle E - e \sin E = {\cal M}.$">|; 

$key = q/displaystyleE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img944.png"
 ALT="$\displaystyle E$">|; 

$key = q/displaystyleE=K+U=frac{1}{2},mleft(frac{dx}{dt}right)^2+frac{1}{2},m,omega_0^{,2},x^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img248.png"
 ALT="$\displaystyle E = K + U = \frac{1}{2} m\left(\frac{dx}{dt}\right)^2+ \frac{1}{2} m \omega_0^{ 2} x^{ 2},$">|; 

$key = q/displaystyleE=K+U={rmconstant}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle E = K + U = {\rm constant}.$">|; 

$key = q/displaystyleE=frac{1}{2},M,dot{r}_{cm}^{,2}+frac{1}{2},mu,dot{r}^{,2}+U.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img336.png"
 ALT="$\displaystyle E=\frac{1}{2} M \dot{r}_{cm}^{ 2} + \frac{1}{2} \mu \dot{r}^{ 2} + U.
$">|; 

$key = q/displaystyleE_{n+1}={calM}+e,sinE_n;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img698.png"
 ALT="$\displaystyle E_{n+1} = {\cal M}+ e \sin E_n;$">|; 

$key = q/displaystyleF(alpha,vartheta-vartheta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4970.png"
 ALT="$\displaystyle F (\alpha,\vartheta-\vartheta')$">|; 

$key = q/displaystyleF(alpha,vartheta-vartheta')=frac{1}{[1-2,alpha,cos(vartheta-vartheta')+alpha^{,2}]^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4964.png"
 ALT="$\displaystyle F(\alpha,\vartheta-\vartheta') = \frac{1}{[1-2 \alpha \cos(\vartheta-\vartheta')+\alpha^{ 2}]^{1/2}}.$">|; 

$key = q/displaystyleF=sintheta,sintheta',cosphi'+costheta,costheta'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img399.png"
 ALT="$\displaystyle F = \sin\theta \sin\theta' \cos\phi' + \cos\theta \cos\theta'.$">|; 

$key = q/displaystyleF=skew{5}bar{lambda}-gamma,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3176.png"
 ALT="$\displaystyle F = \skew{5}\bar{\lambda}-\gamma,$">|; 

$key = q/displaystyleF^{,3}(alpha,vartheta-vartheta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4972.png"
 ALT="$\displaystyle F^{ 3}(\alpha,\vartheta-\vartheta')$">|; 

$key = q/displaystyleF_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2746.png"
 ALT="$\displaystyle F_r$">|; 

$key = q/displaystyleF_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2748.png"
 ALT="$\displaystyle F_\theta$">|; 

$key = q/displaystyleF_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2750.png"
 ALT="$\displaystyle F_z$">|; 

$key = q/displaystyleF_{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3099.png"
 ALT="$\displaystyle F_{X}$">|; 

$key = q/displaystyleF_{Y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3101.png"
 ALT="$\displaystyle F_{Y}$">|; 

$key = q/displaystyleF_{Z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3103.png"
 ALT="$\displaystyle F_{Z}$">|; 

$key = q/displaystyleG,(E+M)=N^{,2},A^{,3}left(1+frac{1}{2},m^{,2}-frac{105}{32},m^{,4}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3476.png"
 ALT="$\displaystyle G (E+M) = N^{ 2} A^{ 3}\left(1+\frac{1}{2} m^{ 2} -\frac{105}{32} m^{ 4}\right).$">|; 

$key = q/displaystyleG,(m_1+m_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3009.png"
 ALT="$\displaystyle G (m_1+m_2)$">|; 

$key = q/displaystyleG,(m_1+m_2+m_3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3011.png"
 ALT="$\displaystyle G (m_1+m_2+m_3)$">|; 

$key = q/displaystyleG,M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img648.png"
 ALT="$\displaystyle G M$">|; 

$key = q/displaystyleG=6.673times10^{-11},{rmm^3,kg^{-1},s^{-2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img344.png"
 ALT="$\displaystyle G = 6.673\times 10^{-11} {\rm m^3 kg^{-1} s^{-2}}.$">|; 

$key = q/displaystyleG_{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3105.png"
 ALT="$\displaystyle G_{X}$">|; 

$key = q/displaystyleG_{Y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3108.png"
 ALT="$\displaystyle G_{Y}$">|; 

$key = q/displaystyleG_{Z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3111.png"
 ALT="$\displaystyle G_{Z}$">|; 

$key = q/displaystyleH;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4796.png"
 ALT="$\displaystyle H$">|; 

$key = q/displaystyleI'=frac{2,(gslashn),I}{2,gslashn-3,tau}=6.75^circ.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2076.png"
 ALT="$\displaystyle I' = \frac{2 (g/n) I}{2 g/n-3 \tau}=6.75^\circ.$">|; 

$key = q/displaystyleI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2905.png"
 ALT="$\displaystyle I$">|; 

$key = q/displaystyleI_{i,{rmmax}}=sin^{-1}left(|I_{ik}|+sum_{l=1,8}^{lneqk,lneq5}|I_{il}|right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2615.png"
 ALT="$\displaystyle I_{i {\rm max}} = \sin^{-1}\left(\vert I_{ik}\vert+\sum_{l=1,8}^{l\neq k, l\neq 5} \vert I_{il}\vert\right).$">|; 

$key = q/displaystyleI_{i,{rmmin}}=sin^{-1}left(|I_{ik}|-sum_{l=1,8}^{lneqk,lneq5}|I_{il}|right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2614.png"
 ALT="$\displaystyle I_{i {\rm min}} =\sin^{-1}\left( \vert I_{ik}\vert-\sum_{l=1,8}^{l\neq k, l\neq 5} \vert I_{il}\vert\right)$">|; 

$key = q/displaystyleJ_0(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4032.png"
 ALT="$\displaystyle J_0(x)$">|; 

$key = q/displaystyleJ_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img480.png"
 ALT="$\displaystyle J_0$">|; 

$key = q/displaystyleJ_1(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4034.png"
 ALT="$\displaystyle J_1(x)$">|; 

$key = q/displaystyleJ_2(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4036.png"
 ALT="$\displaystyle J_2(x)$">|; 

$key = q/displaystyleJ_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img482.png"
 ALT="$\displaystyle J_2$">|; 

$key = q/displaystyleJ_2=frac{{calI}_parallel-{calI}_perp}{M,R^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1699.png"
 ALT="$\displaystyle J_2= \frac{{\cal I}_\parallel-{\cal I}_\perp}{M R^{ 2}},$">|; 

$key = q/displaystyleJ_2=frac{{calI}_parallel-{calI}_perp}{M,R^{,2}}=1.083times10^{-3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2684.png"
 ALT="$\displaystyle J_2= \frac{{\cal I}_\parallel-{\cal I}_\perp}{M R^{ 2}} = 1.083\times 10^{-3},$">|; 

$key = q/displaystyleJ_3(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4038.png"
 ALT="$\displaystyle J_3(x)$">|; 

$key = q/displaystyleJ_n(x)=frac{1}{2pi}oint{rme}^{-{rmi},(n,phi-x,sinphi)},dphi=frac{1}{pi}int_0^picosleft(x,sinphi-n,phiright),dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4025.png"
 ALT="$\displaystyle J_n(x) = \frac{1}{2\pi}\oint {\rm e}^{-{\rm i} (n \phi-x \sin\phi)} d\phi = \frac{1}{\pi}\int_0^\pi
\cos\left(x \sin\phi-n \phi\right) d\phi$">|; 

$key = q/displaystyleJ_n(x)=left(frac{x}{2}right)^nsum_{k=0,infty}frac{(-x^{,2}slash4)^k}{k!,(n+k)!};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img4026.png"
 ALT="$\displaystyle J_n(x) = \left(\frac{x}{2}\right)^n\sum_{k=0,\infty}
\frac{(-x^{ 2}/4)^k}{k! (n+k)!}$">|; 

$key = q/displaystyleJ_n=-frac{2pi,R^{,3}}{M},intintleft(frac{r}{R}right)^{2+n},rho(r,theta),P_n(costheta),sintheta,dtheta,frac{dr}{R}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img474.png"
 ALT="$\displaystyle J_n = - \frac{2\pi R^{ 3}}{M} \int\int \left(\frac{r}{R}\right)^{2+n} \rho(r,\theta) P_n(\cos\theta) \sin\theta d\theta \frac{dr}{R}.$">|; 

$key = q/displaystyleJ_n=-frac{3}{2,(3+n)}int_0^piP_n(costheta)left[frac{R_theta(theta)}{R}right]^{3+n},sintheta,dtheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img477.png"
 ALT="$\displaystyle J_n = -\frac{3}{2 (3+n)}\int_0^\pi P_n(\cos\theta)\left[\frac{R_\theta(\theta)}{R}\right]^{3+n} \sin\theta d\theta,$">|; 

$key = q/displaystyleJ_n=-frac{3}{2}int_0^piP_n(costheta),int_0^{R_theta(theta)}frac{r^{,2+n},dr}{R^{,3+n}},sintheta,dtheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img476.png"
 ALT="$\displaystyle J_n = - \frac{3}{2}\int_0^\pi P_n(\cos\theta) \int_0^{R_\theta(\theta)}\frac{r^{ 2+n} dr}{R^{ 3+n}} \sin\theta d\theta.$">|; 

$key = q/displaystyleJ_nsimeq-frac{3}{2,(3+n)}int_0^piP_n(costheta)left[P_0(costheta)-frac{2}{3},(3+n),epsilon,P_2(costheta)right]sintheta,dtheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img478.png"
 ALT="$\displaystyle J_n \simeq -\frac{3}{2 (3+n)}\int_0^\pi P_n(\cos\theta)\left[P_0...
...theta)-\frac{2}{3} (3+n) \epsilon P_2(\cos\theta)\right]\sin\theta d\theta,$">|; 

$key = q/displaystyleJ_{-n}(-x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4030.png"
 ALT="$\displaystyle J_{-n}(-x)$">|; 

$key = q/displaystyleJ_{-n}(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4028.png"
 ALT="$\displaystyle J_{-n}(x)$">|; 

$key = q/displaystyleK(x)=E-U(x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img195.png"
 ALT="$\displaystyle K(x) = E - U(x).$">|; 

$key = q/displaystyleK=-frac{1}{2},U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img559.png"
 ALT="$\displaystyle K = - \frac{1}{2} U
$">|; 

$key = q/displaystyleK=frac{1}{2},,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1530.png"
 ALT="$\displaystyle K = \frac{1}{2}  $">|; 

$key = q/displaystyleK=frac{1}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1532.png"
 ALT="$\displaystyle K = \frac{1}{2} $">|; 

$key = q/displaystyleK=frac{1}{2},m,skew{3}dot{x}^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1437.png"
 ALT="$\displaystyle K = \frac{1}{2} m \skew{3}\dot{x}^{ 2},$">|; 

$key = q/displaystyleK=frac{1}{2},m,varv^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle K = \frac{1}{2} m \varv^{ 2}.$">|; 

$key = q/displaystyleK=frac{1}{2}left({calI}_perp,skew{5}dot{theta}^{,2}+{calI}_perp,sin^2theta,,skew{5}dot{phi}^{,2}+{calI}_parallel,omega^2right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1720.png"
 ALT="$\displaystyle K = \frac{1}{2}\left({\cal I}_\perp \skew{5}\dot{\theta}^{ 2} +...
...,\sin^2\theta  \skew{5}\dot{\phi}^{ 2} + {\cal I}_\parallel \omega^2\right)$">|; 

$key = q/displaystyleK=frac{1}{2}left({calI}_{perp},omega_{x'}^{,2}+{calI}_perp,omega_{y'}^{,2}+{calI}_parallel,omega_{z'}^{,2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1719.png"
 ALT="$\displaystyle K = \frac{1}{2}\left({\cal I}_{\perp} \omega_{x'}^{ 2} + {\cal I}_\perp \omega_{y'}^{ 2}+{\cal I}_\parallel \omega_{z'}^{ 2}\right),$">|; 

$key = q/displaystyleK=frac{1}{2}left({calI}_{xx},omega_x^{,2}+{calI}_{yy},omega_y^{,2}+{calI}_{zz},omega_z^{,2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1552.png"
 ALT="$\displaystyle K = \frac{1}{2}\left({\cal I}_{xx} \omega_x^{ 2} + {\cal I}_{yy} \omega_y^{ 2}
+ {\cal I}_{zz} \omega_z^{ 2}\right).$">|; 

$key = q/displaystyleK=frac{1}{2}sum_{i=1,N}m_i,(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1525.png"
 ALT="$\displaystyle K = \frac{1}{2}\sum_{i=1,N} m_i ($">|; 

$key = q/displaystyleK=frac{1}{2}sum_{i=1,N}m_ileft(frac{d{bfr}_i}{dt}right)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.41ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1524.png"
 ALT="$\displaystyle K = \frac{1}{2}\sum_{i=1,N} m_i\left(\frac{d{\bf r}_i}{dt}\right)^2.$">|; 

$key = q/displaystyleK=frac{1}{2}sum_{j=1,{calF}}m_j,skew{3}dot{x}_j^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.98ex; " SRC="|."$dir".q|img1395.png"
 ALT="$\displaystyle K = \frac{1}{2}\sum_{j=1,{\cal F}} m_j \skew{3}\dot{x}_j^{ 2}.$">|; 

$key = q/displaystyleL;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4794.png"
 ALT="$\displaystyle L$">|; 

$key = q/displaystyleL_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1593.png"
 ALT="$\displaystyle L_{x'}$">|; 

$key = q/displaystyleL_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1595.png"
 ALT="$\displaystyle L_{y'}$">|; 

$key = q/displaystyleL_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1597.png"
 ALT="$\displaystyle L_{z'}$">|; 

$key = q/displaystyleLsimeqfrac{2}{5},m,R^{,2},{mitOmega}+m',a^{,2},omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1300.png"
 ALT="$\displaystyle L \simeq \frac{2}{5} m R^{ 2} {\mit\Omega} + m' a^{ 2} \omega,$">|; 

$key = q/displaystyleM,ddot{bfR}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2404.png"
 ALT="$\displaystyle M \ddot{\bf R}_s$">|; 

$key = q/displaystyleM,frac{d^{,2}{bfr}_{cm}}{dt^{,2}}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle M \frac{d^{ 2} {\bf r}_{cm}}{dt^{ 2}}= {\bf0},$">|; 

$key = q/displaystyleM,frac{d^{,2}{bfr}_{cm}}{dt^{,2}}={bfF}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1487.png"
 ALT="$\displaystyle M \frac{d^{ 2}{\bf r}_{cm}}{dt^{ 2}} = {\bf F}.$">|; 

$key = q/displaystyleM=frac{4pi}{3},R^{,3},bar{rho}(R),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4366.png"
 ALT="$\displaystyle M = \frac{4\pi}{3} R^{ 3} \bar{\rho}(R),$">|; 

$key = q/displaystyleM=m_1+m_2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img853.png"
 ALT="$\displaystyle M = m_1+ m_2.$">|; 

$key = q/displaystyleN=n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3475.png"
 ALT="$\displaystyle N = n.$">|; 

$key = q/displaystyleP+frac{P^{,3}}{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img835.png"
 ALT="$\displaystyle P + \frac{P^{ 3}}{3}$">|; 

$key = q/displaystyleP+frac{P^{,3}}{3}={calM},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img901.png"
 ALT="$\displaystyle P + \frac{P^{ 3}}{3} = {\cal M},
$">|; 

$key = q/displaystyleP=frac{1}{2},Q^{,1slash3}-2,Q^{-1slash3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img903.png"
 ALT="$\displaystyle P = \frac{1}{2} Q^{ 1/3} - 2 Q^{-1/3},
$">|; 

$key = q/displaystyleP_0(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img419.png"
 ALT="$\displaystyle P_0(x)$">|; 

$key = q/displaystyleP_1(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img421.png"
 ALT="$\displaystyle P_1(x)$">|; 

$key = q/displaystyleP_2(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img423.png"
 ALT="$\displaystyle P_2(x)$">|; 

$key = q/displaystyleP_3(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img425.png"
 ALT="$\displaystyle P_3(x)$">|; 

$key = q/displaystyleP_n(x)=frac{1}{2^n,n!},frac{d^{,n}}{dx^{,n}}!left[(x^{,2}-1)^nright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img417.png"
 ALT="$\displaystyle P_n(x) = \frac{1}{2^n n!} \frac{d^{ n}}{dx^{ n}}\!\left[(x^{ 2}-1)^n\right],$">|; 

$key = q/displaystyleQ=12,{calM}+4sqrt{4+9,{calM}^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img904.png"
 ALT="$\displaystyle Q =12 {\cal M}+4\sqrt{4+9 {\cal M}^{ 2}}.
$">|; 

$key = q/displaystyleQ_i=-sum_{j=1,{calF}}frac{partialU}{partialx_j},frac{partialx_j}{partialq_i}=-frac{partialU}{partialq_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.98ex; " SRC="|."$dir".q|img1391.png"
 ALT="$\displaystyle Q_i = - \sum_{j=1,{\cal F}} \frac{\partial U}{\partial x_j} \frac{\partial x_j}{\partial q_i} = - \frac{\partial U}{\partial q_i},$">|; 

$key = q/displaystyleQ_i=sum_{j=1,{calF}}f_j,frac{partialx_j}{partialq_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.98ex; " SRC="|."$dir".q|img1386.png"
 ALT="$\displaystyle Q_i = \sum_{j=1,{\cal F}} f_j \frac{\partial x_j}{\partial q_i}.$">|; 

$key = q/displaystyleR';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3091.png"
 ALT="$\displaystyle R'$">|; 

$key = q/displaystyleR_X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3154.png"
 ALT="$\displaystyle R_X$">|; 

$key = q/displaystyleR_Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3160.png"
 ALT="$\displaystyle R_Y$">|; 

$key = q/displaystyleR_Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3165.png"
 ALT="$\displaystyle R_Z$">|; 

$key = q/displaystyleR_c=left(frac{3}{2pi},frac{p_c}{G,gamma^{,2}}right)^{1slash2}simeq230,{rmkm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img501.png"
 ALT="$\displaystyle R_c = \left(\frac{3}{2\pi} \frac{p_c}{G \gamma^{ 2}}\right)^{1/2}\simeq 230 {\rm km}.$">|; 

$key = q/displaystyleR_c=left(frac{3}{4pi},frac{sigma_c}{G,gamma^{,2}}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1174.png"
 ALT="$\displaystyle R_c = \left(\frac{3}{4\pi} \frac{\sigma_c}{G \gamma^{ 2}}\right)^{1/2}.$">|; 

$key = q/displaystyleT'=frac{2pi}{{mitOmega}}=304,,{rmdays}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1654.png"
 ALT="$\displaystyle T'= \frac{2\pi}{{\mit\Omega}} = 304  {\rm days}.$">|; 

$key = q/displaystyleT'simeqfrac{{mitOmega}'}{|skew{5}dot{{mitOmega}}'|}simeq1.5times10^6,{rmyears}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.22ex; " SRC="|."$dir".q|img1317.png"
 ALT="$\displaystyle T' \simeq \frac{{\mit\Omega}'}{\vert\skew{5}\dot{{\mit\Omega}}'\vert}\simeq 1.5\times 10^6 {\rm years}.$">|; 

$key = q/displaystyleT=2pi,sqrt{frac{V}{g,A}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img323.png"
 ALT="$\displaystyle T = 2\pi \sqrt{\frac{V}{g A}}
$">|; 

$key = q/displaystyleT=2pileft(frac{b^{,2}-a^{,2}}{u^{,2}-varv^{,2}}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img313.png"
 ALT="$\displaystyle T = 2\pi\left(\frac{b^{ 2}-a^{ 2}}{u^{ 2}-\varv^{ 2}}\right)^{1/2}.
$">|; 

$key = q/displaystyleT=2pisqrt{frac{R}{g}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.71ex; " SRC="|."$dir".q|img533.png"
 ALT="$\displaystyle T = 2\pi\sqrt{\frac{R}{g}},
$">|; 

$key = q/displaystyleT=304,,{rmdays}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4526.png"
 ALT="$\displaystyle T = 304  {\rm days}.$">|; 

$key = q/displaystyleT=445,,{rmdays},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4525.png"
 ALT="$\displaystyle T = 445  {\rm days},$">|; 

$key = q/displaystyleT=453,,{rmdays}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4520.png"
 ALT="$\displaystyle T = 453  {\rm days}.$">|; 

$key = q/displaystyleT=frac{2pi}{left[-3,f(r_c)slashr_c-f'(r_c)right]^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.54ex; " SRC="|."$dir".q|img975.png"
 ALT="$\displaystyle T = \frac{2\pi}{\left[-3 f(r_c)/r_c - f'(r_c)\right]^{1/2}}.$">|; 

$key = q/displaystyleT=frac{2pi}{skew{5}dot{phi}}=0.994,,{rmdays}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1659.png"
 ALT="$\displaystyle T = \frac{2\pi}{\skew{5}\dot{\phi}} = 0.994  {\rm days}.$">|; 

$key = q/displaystyleT=frac{3}{4},frac{G,m,m',l}{a^{,3}}-frac{1}{4},frac{G,m^{,2}}{l^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1368.png"
 ALT="$\displaystyle T = \frac{3}{4} \frac{G m m' l}{a^{ 3}} - \frac{1}{4} \frac{G m^{ 2}}{l^{ 2}}.
$">|; 

$key = q/displaystyleT=frac{A}{dAslashdt}=frac{2pi,a,b}{h}=frac{2pi,a^{,2},(1-e^{,2})^{1slash2}}{h}=frac{2pi,a^{,3slash2},r_c^{,1slash2}}{h}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img634.png"
 ALT="$\displaystyle T = \frac{A}{dA/dt} = \frac{2\pi a b}{h} = \frac{2\pi a^{ 2} (1-e^{ 2})^{1/2}}{h}=\frac{2\pi a^{ 3/2} r_c^{ 1/2}}{h}.$">|; 

$key = q/displaystyleT=sqrt{frac{4pi^{,2},a^{,3}}{G,M}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.75ex; " SRC="|."$dir".q|img858.png"
 ALT="$\displaystyle T = \sqrt{\frac{4\pi^{ 2} a^{ 3}}{G M}}.$">|; 

$key = q/displaystyleT^{,2}=frac{4pi^{,2},a^{,3}}{G,M}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img635.png"
 ALT="$\displaystyle T^{ 2} = \frac{4\pi^{ 2} a^{ 3}}{G M}.$">|; 

$key = q/displaystyleT_0=297,{rmdays}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4521.png"
 ALT="$\displaystyle T_0 = 297 {\rm days}.$">|; 

$key = q/displaystyleT_0simeqfrac{1-skew{3}tilde{epsilon}}{skew{3}tilde{epsilon}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4511.png"
 ALT="$\displaystyle T _0\simeq \frac{1-\skew{3}\tilde{\epsilon}}{\skew{3}\tilde{\epsilon} }.$">|; 

$key = q/displaystyleT_phi({rmyr})=frac{84.34}{skew{3}tilde{epsilon}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4601.png"
 ALT="$\displaystyle T_\phi({\rm yr}) = \frac{84.34}{\skew{3}\tilde{\epsilon}}.$">|; 

$key = q/displaystyleT_phi({rmyr})=frac{n_s}{{mitOmega}_phi}=frac{2,T_s({rmday})}{3,skew{3}tilde{epsilon},(1+mu_mslash[T_m({rmyr})]^2),costheta_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1802.png"
 ALT="$\displaystyle T_\phi({\rm yr}) = \frac{n_s}{{\mit\Omega}_\phi} = \frac{2 T_s({...
...day})}{3 \skew{3}\tilde{\epsilon} (1+\mu_m/[T_m({\rm yr})]^2) \cos\theta_0},$">|; 

$key = q/displaystyleT_phi({rmyr})=frac{n_s}{{mitOmega}_phi}=frac{2,T_s({rmday})}{3,skew{3}tilde{epsilon},costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1736.png"
 ALT="$\displaystyle T_\phi({\rm yr}) = \frac{n_s}{{\mit\Omega}_\phi} = \frac{2 T_s({\rm day})}{3 \skew{3}\tilde{\epsilon} \cos\theta},$">|; 

$key = q/displaystyleT_phisimeq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1739.png"
 ALT="$\displaystyle T_\phi\simeq$">|; 

$key = q/displaystyleTsimeqfrac{{mitOmega}}{|skew{5}dot{mitOmega}|}simeq4times10^9,{rmyears}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.22ex; " SRC="|."$dir".q|img1298.png"
 ALT="$\displaystyle T \simeq \frac{{\mit\Omega}}{\vert\skew{5}\dot{\mit\Omega}\vert} \simeq 4\times 10^9 {\rm years}.$">|; 

$key = q/displaystyleU(a,theta)=U_0(a)+U_2(a),P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4352.png"
 ALT="$\displaystyle U(a,\theta)= U_0(a)+U_2(a) P_2(\cos\theta),$">|; 

$key = q/displaystyleU(x)=-frac{a}{x^{,6}}+frac{b}{x^{,12}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img314.png"
 ALT="$\displaystyle U(x) = -\frac{a}{x^{ 6}}+ \frac{b}{x^{ 12}},
$">|; 

$key = q/displaystyleU(x)simeqfrac{1}{2},m,omega_0^{,2},x^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img247.png"
 ALT="$\displaystyle U(x) \simeq \frac{1}{2} m \omega_0^{ 2} x^{ 2}.$">|; 

$key = q/displaystyleU(x,y,z)=-frac{mu_1}{rho_1}-frac{mu_2}{rho_2}-frac{omega^{,2}}{2},(x^{,2}+y^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2164.png"
 ALT="$\displaystyle U(x,y,z) = - \frac{\mu_1}{\rho_1} - \frac{\mu_2}{\rho_2} - \frac{\omega^{ 2}}{2} (x^{ 2}+y^{ 2})$">|; 

$key = q/displaystyleU({bfr})=-frac{G,M,m}{r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img576.png"
 ALT="$\displaystyle U({\bf r}) = - \frac{G M m}{r}.$">|; 

$key = q/displaystyleU({bfr}_1,{bfr}_2,{bfr}_3)=-Gleft(frac{m_1,m_2}{r_{12}}+frac{m_1,m_3}{r_{13}}+frac{m_2,m_3}{r_{23}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2955.png"
 ALT="$\displaystyle U({\bf r}_1,{\bf r}_2,{\bf r}_3) = -G\left(\frac{m_1 m_2}{r_{12}}+\frac{m_1 m_3}{r_{13}}+ \frac{m_2 m_3}{r_{23}}\right).$">|; 

$key = q/displaystyleU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1758.png"
 ALT="$\displaystyle U$">|; 

$key = q/displaystyleU=-16,pi^{,2},Gint_0^Rint_0^rr'^{,2},rho(r'),r,rho(r),dr',dr.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img555.png"
 ALT="$\displaystyle U = - 16 \pi^{ 2} G\int_0^R \int_0^r r'^{ 2} \rho(r') r \rho(r) dr' dr.
$">|; 

$key = q/displaystyleU=-frac{(3-alpha)}{(5-2,alpha)},frac{G,M^{,2}}{R},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img558.png"
 ALT="$\displaystyle U = - \frac{(3-\alpha)}{(5-2 \alpha)} \frac{G M^{ 2}}{R},
$">|; 

$key = q/displaystyleU=-frac{1}{2},frac{1}{n-1}sum_{i,j=1,N}^{jneqi}frac{k_i,k_j}{|{bfr}_j-{bfr}_i|^{,n-1}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img544.png"
 ALT="$\displaystyle U = -\frac{1}{2} \frac{1}{n-1}\sum_{i,j=1,N}^{j\neq i}\frac{k_i k_j}{\vert{\bf r}_j-{\bf r}_i\vert^{ n-1}}.
$">|; 

$key = q/displaystyleU=-frac{1}{2}sum_{i,j=1,N}^{ineqj}frac{G,m_i,m_j}{|{bfr}_j-{bfr}_i|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img535.png"
 ALT="$\displaystyle U= -\frac{1}{2}\sum_{i,j=1,N}^{i\neq j} \frac{G m_i m_j}{\vert{\bf r}_j-{\bf r}_i\vert}.
$">|; 

$key = q/displaystyleU=-frac{1}{2}sum_{i,j=1,N}^{jneqi}frac{G,m_i,m_j}{|{bfr}_j-{bfr}_i|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img378.png"
 ALT="$\displaystyle U =-\frac{1}{2} \sum_{i,j=1,N}^{j\neq i}
\frac{G m_i  m_j}{\vert{\bf r}_j-{\bf r}_i\vert}.$">|; 

$key = q/displaystyleU=-frac{G,M_m,M}{a_m}+frac{G,M_m,({calI}_parallel-{calI}_perp)}{a_m^{,3}},P_2[cos(gamma_m)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1741.png"
 ALT="$\displaystyle U = - \frac{G M_m M}{a_m} + \frac{G M_m ({\cal I}_\parallel-{\cal I}_\perp)}{a_m^{ 3}} P_2[\cos(\gamma_m)],$">|; 

$key = q/displaystyleU=-frac{G,M_s,M}{a_s}+frac{G,M_s,({calI}_parallel-{calI}_perp)}{2,a_s^{,3}},(3,sin^2theta,sin^2lambda_s-1).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1712.png"
 ALT="$\displaystyle U = - \frac{G M_s M}{a_s} + \frac{G M_s ({\cal I}_\parallel-{\cal I}_\perp)}{2 a_s^{ 3}} (3 \sin^2\theta \sin^2\lambda_s -1).$">|; 

$key = q/displaystyleU=-frac{G,M_s,M}{a_s}+frac{G,M_s,({calI}_parallel-{calI}_perp)}{2,a_s^{,3}},left(frac{3}{2},sin^2theta-1right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1713.png"
 ALT="$\displaystyle U = - \frac{G M_s M}{a_s} + \frac{G M_s ({\cal I}_\parallel-{\cal I}_\perp)}{2 a_s^{ 3}} \left(\frac{3}{2} \sin^2\theta -1\right)$">|; 

$key = q/displaystyleU=-frac{G,m,M}{r}+frac{G,m,({calI}_parallel-{calI}_perp)}{r^{,3}},P_2(cosgamma).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4533.png"
 ALT="$\displaystyle U = - \frac{G m M}{r} + \frac{G m ({\cal I}_\parallel-{\cal I}_\perp)}{r^{ 3}} P_2(\cos\gamma).$">|; 

$key = q/displaystyleU=-frac{G,m_2,m_1}{|{bfr}_1-{bfr}_2|}-frac{G,m_3,m_1}{|{bfr}_1-{bfr}_3|}-frac{G,m_3,m_2}{|{bfr}_2-{bfr}_3|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img375.png"
 ALT="$\displaystyle U = - \frac{G m_2  m_1}{\vert{\bf r}_1- {\bf r}_2\vert}
-\frac{...
... r}_1 - {\bf r}_3\vert}
- \frac{G m_3  m_2}{\vert{\bf r}_2 - {\bf r}_3\vert}.$">|; 

$key = q/displaystyleU=-int_P^Q{bff}cdotd{bfr}=-mint_P^Q{bfg}cdotd{bfr}=mint_P^Qnabla{mitPhi}cdotd{bfr}=mleft[{mitPhi}(Q)-{mitPhi}(P)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle U =- \int_P^Q {\bf f} \cdot d{\bf r} =- m \int_P^Q {\bf g} \cdot ...
...\nabla{\mit\Phi} \cdot d{\bf r} = m\left[ {\mit\Phi}(Q) - {\mit\Phi}(P)\right].$">|; 

$key = q/displaystyleU=-mu_1left(frac{1}{rho_1}+frac{rho_1^{,2}}{2}right)-mu_2left(frac{1}{rho_2}+frac{rho_2^{,2}}{2}right)+frac{mu_1,mu_2}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2181.png"
 ALT="$\displaystyle U = - \mu_1\left(\frac{1}{\rho_1}+\frac{\rho_1^{ 2}}{2}\right)
-...
...2\left(\frac{1}{\rho_2}+\frac{\rho_2^{ 2}}{2}\right) + \frac{\mu_1 \mu_2}{2}.$">|; 

$key = q/displaystyleU=-sum_{i,j=1,N}^{j<i}frac{G,m_i,m_j}{|{bfr}_j-{bfr}_i|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img376.png"
 ALT="$\displaystyle U= -\sum_{i,j=1,N}^{j&lt;i}\frac{G m_i  m_j}{\vert{\bf r}_j
-{\bf r}_i\vert}.$">|; 

$key = q/displaystyleU=M_s,{mitPhi}=-frac{G,M_s,M}{a_s}+frac{G,M_s,({calI}_parallel-{calI}_perp)}{a_s^{,3}},P_2[cos(gamma_s)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1704.png"
 ALT="$\displaystyle U = M_s {\mit\Phi} = - \frac{G M_s M}{a_s} + \frac{G M_s ({\cal I}_\parallel-{\cal I}_\perp)}{a_s^{ 3}} P_2[\cos(\gamma_s)],$">|; 

$key = q/displaystyleU=U(a).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4331.png"
 ALT="$\displaystyle U=U(a).$">|; 

$key = q/displaystyleU=U(rho).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4326.png"
 ALT="$\displaystyle U=U(\rho).$">|; 

$key = q/displaystyleU=U_0''-skew{3}tilde{epsilon},alpha,cos(2,theta)+skew{3}tilde{epsilon},beta_m,sin(2,theta),cos(alpha_n-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1771.png"
 ALT="$\displaystyle U = U_0'' -\skew{3}\tilde{\epsilon} \alpha \cos(2 \theta) +\skew{3}\tilde{\epsilon} \beta_m \sin(2 \theta) \cos(\alpha_n-\phi),$">|; 

$key = q/displaystyleU=U_0-skew{3}tilde{epsilon},alpha_s,cos(2,theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1715.png"
 ALT="$\displaystyle U = U_0 - \skew{3}\tilde{\epsilon} \alpha_s \cos(2 \theta),$">|; 

$key = q/displaystyleU=frac{1}{2}intrho({bfr}),{mitPhi}({bfr}),d^{,3}{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img381.png"
 ALT="$\displaystyle U = \frac{1}{2} \int \rho({\bf r}) {\mit\Phi}({\bf r}) d^{ 3}{\bf r},$">|; 

$key = q/displaystyleU=frac{1}{2}sum_{i=1,N}m_i,{mitPhi}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img379.png"
 ALT="$\displaystyle U = \frac{1}{2} \sum_{i=1,N} m_i  {\mit\Phi}_i,$">|; 

$key = q/displaystyleU={mitPhi}+chi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4323.png"
 ALT="$\displaystyle U= {\mit\Phi} + \chi,$">|; 

$key = q/displaystyleU_2(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4353.png"
 ALT="$\displaystyle U_2(a)$">|; 

$key = q/displaystyleU_2=-frac{G,m_2,m_1}{|{bfr}_1-{bfr}_2|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img372.png"
 ALT="$\displaystyle U_2 = -\frac{G m_2  m_1}{\vert{\bf r}_1 - {\bf r}_2\vert}.$">|; 

$key = q/displaystyleU_3=-frac{G,m_3,m_1}{|{bfr}_1-{bfr}_3|}-frac{G,m_3,m_2}{|{bfr}_2-{bfr}_3|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img374.png"
 ALT="$\displaystyle U_3 = - \frac{G m_3  m_1}{\vert{\bf r}_1 - {\bf r}_3\vert}
-\frac{G m_3  m_2}{\vert{\bf r}_2 - {\bf r}_3\vert}.$">|; 

$key = q/displaystyleU_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2277.png"
 ALT="$\displaystyle U_{xx}$">|; 

$key = q/displaystyleU_{xy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2281.png"
 ALT="$\displaystyle U_{xy}$">|; 

$key = q/displaystyleU_{yy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2279.png"
 ALT="$\displaystyle U_{yy}$">|; 

$key = q/displaystyleUsimeqU_0'-skew{3}tilde{epsilon},alpha_m,cos(2,theta)+skew{3}tilde{epsilon},beta_m,sin(2,theta),cos(alpha_n-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img1761.png"
 ALT="$\displaystyle U \simeq U_0' - \skew{3}\tilde{\epsilon} \alpha_m \cos(2 \theta) + \skew{3}\tilde{\epsilon} \beta_m \sin(2 \theta) \cos(\alpha_n-\phi),$">|; 

$key = q/displaystyleUsimeqU_0+U_x,deltax+U_y,deltay+frac{1}{2},U_{xx},(deltax)^2+U_{xy},deltax,deltay+frac{1}{2},U_{yy},(deltay)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2255.png"
 ALT="$\displaystyle U \simeq U_0 + U_x \delta x+ U_y \delta y + \frac{1}{2} U_{xx} (\delta x)^2+ U_{xy} \delta x \delta y
+ \frac{1}{2} U_{yy} (\delta y)^2,$">|; 

$key = q/displaystyleUsimeqU_0+frac{1}{2},U_{xx},(deltax)^2+U_{xy},deltax,deltay+frac{1}{2},U_{yy},(deltay)^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2260.png"
 ALT="$\displaystyle U \simeq U_0 + \frac{1}{2} U_{xx} (\delta x)^2+ U_{xy} \delta x \delta y
+ \frac{1}{2} U_{yy} (\delta y)^2.$">|; 

$key = q/displaystyleV(Q+dx)=V(Q)+int_Q^{Q+dx}{bfA}cdotd{bfr}=V(Q)+A_x,dx.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.31ex; " SRC="|."$dir".q|img3950.png"
 ALT="$\displaystyle V(Q+dx) = V(Q) + \int_Q^{Q+dx} {\bf A}\cdot d{\bf r} = V(Q) + A_x dx.$">|; 

$key = q/displaystyleV(r)=-frac{G,M}{r}left(1+frac{epsilon}{5},frac{R^{,2}}{r^{,2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1061.png"
 ALT="$\displaystyle V(r) = -\frac{G M}{r}\left(1+ \frac{\epsilon}{5} \frac{R^{ 2}}{r^{ 2}}\right),
$">|; 

$key = q/displaystyleV(r)=-frac{h^{,2}}{2}left(frac{a^{,2}}{r^{,4}}+frac{1}{r^{,2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1040.png"
 ALT="$\displaystyle V(r)=-\frac{h^{ 2}}{2}\left(\frac{a^{ 2}}{r^{ 4}}+ \frac{1}{r^{ 2}}\right),
$">|; 

$key = q/displaystyleV(r)=-frac{mu}{r},{rme}^{-k,r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1055.png"
 ALT="$\displaystyle V(r)= -\frac{\mu}{r} {\rm e}^{-k r},
$">|; 

$key = q/displaystyleV(r)=-h^{,2}left(frac{2,r_0}{r^{,3}}+frac{1}{2,r^{,2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img954.png"
 ALT="$\displaystyle V(r) = - h^{ 2}\left(\frac{2 r_0}{r^{ 3}} + \frac{1}{2 r^{ 2}}\right).$">|; 

$key = q/displaystyleV(u)=-h^{,2}left(2,r_0,u^{,3}+frac{u^{,2}}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img953.png"
 ALT="$\displaystyle V(u) = -h^{ 2}\left(2 r_0 u^{ 3} + \frac{u^{ 2}}{2}\right),$">|; 

$key = q/displaystyleV(x,y,z)=-2,U=frac{2,mu_1}{rho_1}+frac{2,mu_2}{rho_2}+x^{,2}+y^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2221.png"
 ALT="$\displaystyle V(x,y,z) = - 2 U = \frac{2 \mu_1}{\rho_1}
+ \frac{2 \mu_2}{\rho_2} +x^{ 2}+y^{ 2}.$">|; 

$key = q/displaystyleV(x,y,z)=C,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2220.png"
 ALT="$\displaystyle V(x,y,z) = C,$">|; 

$key = q/displaystyleX';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3080.png"
 ALT="$\displaystyle X'$">|; 

$key = q/displaystyleX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img744.png"
 ALT="$\displaystyle X$">|; 

$key = q/displaystyleX=sigma_cleft(frac{R}{R_c}right)^{2}left(zeta-frac{4}{15},epsilonright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1171.png"
 ALT="$\displaystyle X = \sigma_c\left(\frac{R}{R_c}\right)^{2}\left(\zeta - \frac{4}{15} \epsilon\right),$">|; 

$key = q/displaystyleX_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3188.png"
 ALT="$\displaystyle X_0$">|; 

$key = q/displaystyleX_0^{,-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img3152.png"
 ALT="$\displaystyle X_0^{ -3}$">|; 

$key = q/displaystyleX_2(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4316.png"
 ALT="$\displaystyle X_2(\theta,\phi)$">|; 

$key = q/displaystyleX_i(a,theta,phi)=g,rho,delta_2left(frac{x_i}{r}right)_{r=a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.76ex; " SRC="|."$dir".q|img4277.png"
 ALT="$\displaystyle X_i(a,\theta,\phi) = g \rho \delta_2\left(\frac{x_i}{r}\right)_{r=a}.$">|; 

$key = q/displaystyleY';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3082.png"
 ALT="$\displaystyle Y'$">|; 

$key = q/displaystyleY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img746.png"
 ALT="$\displaystyle Y$">|; 

$key = q/displaystyleY_0^{,0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img4118.png"
 ALT="$\displaystyle Y_0^{ 0}$">|; 

$key = q/displaystyleY_1^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4120.png"
 ALT="$\displaystyle Y_1^{ -1}$">|; 

$key = q/displaystyleY_1^{,0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img4122.png"
 ALT="$\displaystyle Y_1^{ 0}$">|; 

$key = q/displaystyleY_1^{,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4124.png"
 ALT="$\displaystyle Y_1^{ 1}$">|; 

$key = q/displaystyleY_2^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4128.png"
 ALT="$\displaystyle Y_2^{ -1}$">|; 

$key = q/displaystyleY_2^{,-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4126.png"
 ALT="$\displaystyle Y_2^{ -2}$">|; 

$key = q/displaystyleY_2^{,0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img4130.png"
 ALT="$\displaystyle Y_2^{ 0}$">|; 

$key = q/displaystyleY_2^{,1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4132.png"
 ALT="$\displaystyle Y_2^{ 1}$">|; 

$key = q/displaystyleY_2^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4134.png"
 ALT="$\displaystyle Y_2^{ 2}$">|; 

$key = q/displaystyleY_l^{,0}(theta,phi)=sqrt{frac{2,l+1}{4pi}},P_l(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.81ex; " SRC="|."$dir".q|img4114.png"
 ALT="$\displaystyle Y_l^{ 0}(\theta,\phi) = \sqrt{\frac{2 l+1}{4\pi}} P_l(\cos\theta),$">|; 

$key = q/displaystyleY_l^{,m,ast}=(-1)^m,Y_l^{,-m},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img4116.png"
 ALT="$\displaystyle Y_l^{ m \ast} = (-1)^m Y_l^{ -m},$">|; 

$key = q/displaystyleY_l^{,m}(theta,phi)=sqrt{frac{(2,l+1)}{4pi},frac{(l-m)!}{(l+m)!}},P_l^{,m}(costheta),,{rme}^{,{rmi},m,phi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.75ex; vertical-align: -2.65ex; " SRC="|."$dir".q|img4112.png"
 ALT="$\displaystyle Y_l^{ m}(\theta,\phi) = \sqrt{\frac{(2 l+1)}{4\pi} \frac{(l-m)!}{(l+m)!}} P_l^{ m}(\cos\theta)  {\rm e}^{ {\rm i} m \phi},$">|; 

$key = q/displaystyleZ';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3084.png"
 ALT="$\displaystyle Z'$">|; 

$key = q/displaystyleZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img748.png"
 ALT="$\displaystyle Z$">|; 

$key = q/displaystyle[1-4,(A+B),mu]left.p_2right|_{r=a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img4298.png"
 ALT="$\displaystyle [1-4 (A+B) \mu]\left.p_2\right\vert _{r=a}$">|; 

$key = q/displaystyle[I,{mitOmega}],frac{d{mitOmega}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4829.png"
 ALT="$\displaystyle [I,{\mit\Omega}] \frac{d{\mit\Omega}}{d t}$">|; 

$key = q/displaystyle[a,skew{5}bar{lambda}_0],frac{dskew{5}bar{lambda}_0}{dt}+[a,varpi],frac{dvarpi}{dt}+[a,{mitOmega}],frac{d{mitOmega}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4823.png"
 ALT="$\displaystyle [a,\skew{5}\bar{\lambda}_0] \frac{d \skew{5}\bar{\lambda}_0}{ dt} + [a,\varpi] \frac{d\varpi}{d t} + [a,{\mit\Omega}] \frac{d{\mit\Omega}}{d t}$">|; 

$key = q/displaystyle[c_j,c_j];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4691.png"
 ALT="$\displaystyle [c_j,c_j]$">|; 

$key = q/displaystyle[c_j,c_k];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4692.png"
 ALT="$\displaystyle [c_j,c_k]$">|; 

$key = q/displaystyle[e,varpi],frac{dvarpi}{dt}+[e,{mitOmega}],frac{d{mitOmega}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4825.png"
 ALT="$\displaystyle [e,\varpi] \frac{d\varpi}{d t} + [e,{\mit\Omega}] \frac{d{\mit\Omega}}{d t}$">|; 

$key = q/displaystyle[p,q]''';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4783.png"
 ALT="$\displaystyle [p,q]'''$">|; 

$key = q/displaystyle[p,q]'''=frac{partial(x,dot{x})}{partial(p,q)}+frac{partial(y,dot{y})}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4757.png"
 ALT="$\displaystyle [p,q]''' = \frac{\partial(x,\dot{x})}{\partial (p,q)}+ \frac{\partial(y,\dot{y})}{\partial (p,q)}.$">|; 

$key = q/displaystyle[p,q]''=[p,q]'''+frac{partial(varpi-{mitOmega},x,dot{y}-y,dot{x})}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4758.png"
 ALT="$\displaystyle [p,q]'' = [p,q]''' + \frac{\partial(\varpi-{\mit\Omega},x \dot{y}-y \dot{x})}{\partial (p,q)}.$">|; 

$key = q/displaystyle[p,q]'=[p,q]''+frac{partial(I,y'',dot{z}''-z'',dot{y}'')}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4753.png"
 ALT="$\displaystyle [p,q]' = [p,q]'' + \frac{\partial(I,y'' \dot{z}''-z'' \dot{y}'')}{\partial(p,q)}.$">|; 

$key = q/displaystyle[p,q]'=[p,q]''.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4755.png"
 ALT="$\displaystyle [p,q]'=[p,q]''.$">|; 

$key = q/displaystyle[p,q]'=frac{partial(x',dot{x}')}{partial(p,q)}+frac{partial(y',dot{y}')}{partial(p,q)}+frac{partial(z',dot{z}')}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4743.png"
 ALT="$\displaystyle [p,q]' = \frac{\partial(x',\dot{x}')}{\partial (p,q)}+ \frac{\partial(y',\dot{y}')}{\partial (p,q)}+ \frac{\partial(z',\dot{z}')}{\partial (p,q)}.$">|; 

$key = q/displaystyle[p,q];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4746.png"
 ALT="$\displaystyle [p,q]$">|; 

$key = q/displaystyle[p,q]=A_1,C_2-A_2,C_1+B_1,D_2-B_2,D_1+frac{partial(Z,dot{Z})}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4735.png"
 ALT="$\displaystyle [p,q] = A_1 C_2-A_2 C_1 + B_1 D_2-B_2 D_1+ \frac{\partial(Z,\dot{Z})}{\partial(p,q)}.$">|; 

$key = q/displaystyle[p,q]=[p,q]'''+frac{partial(varpi-{mitOmega},H)}{partial(p,q)}+frac{partial({mitOmega},{calG})}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4760.png"
 ALT="$\displaystyle [p,q] = [p,q]''' + \frac{\partial(\varpi-{\mit\Omega},H )}{\partial (p,q)}
+ \frac{\partial({\mit\Omega}, {\cal G})}{\partial (p,q)}.$">|; 

$key = q/displaystyle[p,q]=[p,q]'+frac{partial({mitOmega},{calG})}{partial(p,q)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4751.png"
 ALT="$\displaystyle [p,q] = [p,q]' + \frac{\partial({\mit\Omega}, {\cal G})}{\partial (p,q)}.$">|; 

$key = q/displaystyle[p,q]=frac{partial(X,dot{X})}{partial(p,q)}+frac{partial(Y,dot{Y})}{partial(p,q)}+frac{partial(Z,dot{Z})}{partial(p,q)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4708.png"
 ALT="$\displaystyle [p,q] = \frac{\partial(X,\dot{X})}{\partial (p,q)}+ \frac{\partial(Y,\dot{Y})}{\partial (p,q)}+ \frac{\partial(Z,\dot{Z})}{\partial (p,q)},$">|; 

$key = q/displaystyle[skew{5}bar{lambda}_0,a],frac{da}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4827.png"
 ALT="$\displaystyle [\skew{5}\bar{\lambda}_0,a] \frac{d a}{d t}$">|; 

$key = q/displaystyle[skew{5}bar{lambda}_0,a]=-[a,skew{5}bar{lambda}_0];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4813.png"
 ALT="$\displaystyle [\skew{5}\bar{\lambda}_0,a] =-[a,\skew{5}\bar{\lambda}_0]$">|; 

$key = q/displaystyle[varpi,a],frac{da}{dt}+[varpi,e],frac{de}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4833.png"
 ALT="$\displaystyle [\varpi,a] \frac{d a}{d t} + [\varpi,e] \frac{d e}{d t}$">|; 

$key = q/displaystyle[varpi,a]=-[a,varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4814.png"
 ALT="$\displaystyle [\varpi,a]=-[a,\varpi]$">|; 

$key = q/displaystyle[varpi,e]=-[e,varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4818.png"
 ALT="$\displaystyle [\varpi,e] = -[e,\varpi]$">|; 

$key = q/displaystyle[{mitOmega},I]=-[I,{mitOmega}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4821.png"
 ALT="$\displaystyle [{\mit\Omega}, I]=-[I,{\mit\Omega}]$">|; 

$key = q/displaystyle[{mitOmega},a],frac{da}{dt}+[{mitOmega},e],frac{de}{dt}+[{mitOmega},I],frac{dI}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4831.png"
 ALT="$\displaystyle [{\mit\Omega},a] \frac{d a}{d t} + [{\mit\Omega},e] \frac{d e}{d t} + [{\mit\Omega}, I] \frac{d I}{d t}$">|; 

$key = q/displaystyle[{mitOmega},a]=-[a,{mitOmega}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4816.png"
 ALT="$\displaystyle [{\mit\Omega},a]=-[a,{\mit\Omega}]$">|; 

$key = q/displaystyle[{mitOmega},e]=-[e,{mitOmega}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4819.png"
 ALT="$\displaystyle [{\mit\Omega},e]=-[e,{\mit\Omega}]$">|; 

$key = q/displaystyle^T,textbf{emI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1533.png"
 ALT="$\displaystyle ^T \textbf{\em I} $">|; 

$key = q/displaystyle_phi+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1633.png"
 ALT="$\displaystyle _\phi
+$">|; 

$key = q/displaystyle_phi=skew{5}dot{phi},{bfe}_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1613.png"
 ALT="$\displaystyle _\phi = \skew{5}\dot{\phi} {\bf e}_z.$">|; 

$key = q/displaystyle_psi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1635.png"
 ALT="$\displaystyle _\psi,$">|; 

$key = q/displaystyle_psi=skew{5}dot{psi},{bfe}_{z'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1626.png"
 ALT="$\displaystyle _\psi= \skew{5}\dot{\psi} {\bf e}_{z'}.$">|; 

$key = q/displaystyle_theta+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1634.png"
 ALT="$\displaystyle _\theta+$">|; 

$key = q/displaystyle_theta=skew{5}dot{theta},{bfe}_{x''}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1621.png"
 ALT="$\displaystyle _\theta = \skew{5}\dot{\theta} {\bf e}_{x''}.$">|; 

$key = q/displaystylea'^{,-1}=a^{,-1}sum_{n=0,infty}left(frac{r}{a}right)^nP_n(costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1232.png"
 ALT="$\displaystyle a'^{ -1} = a^{ -1}\sum_{n=0,\infty} \left(\frac{r}{a}\right)^n P_n(\cos\theta).$">|; 

$key = q/displaystylea'^{,-1}=left(a^{,2}-2,{bfa}cdot{bfr}+r^{,2}right)^{-1slash2}=left(a^{,2}-2,a,r,costheta+r^{,2}right)^{-1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1230.png"
 ALT="$\displaystyle a'^{ -1} = \left(a^{ 2} - 2 {\bf a}\cdot{\bf r}+ r^{ 2}\right)^{-1/2}
= \left(a^{ 2} - 2 a r \cos\theta+ r^{ 2}\right)^{-1/2}.$">|; 

$key = q/displaystylea(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4903.png"
 ALT="$\displaystyle a(t)$">|; 

$key = q/displaystylea,e^{-4slash5},(1-e^{,2})=C,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2921.png"
 ALT="$\displaystyle a e^{-4/5} (1-e^{ 2}) = C,
$">|; 

$key = q/displaystylea,frac{deta}{da}+eta^{,2}+5,eta+2,frac{a}{bar{rho}},frac{dbar{rho}}{da},(1+eta)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4385.png"
 ALT="$\displaystyle a \frac{d\eta}{da} + \eta^{ 2}+5 \eta + 2 \frac{a}{\bar{\rho}} \frac{d\bar{\rho}}{da} (1+\eta)= 0.$">|; 

$key = q/displaystylea,frac{deta}{da}+eta^{,2}-eta-6+6,frac{rho}{bar{rho}},(1+eta)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4384.png"
 ALT="$\displaystyle a \frac{d\eta}{da} + \eta^{ 2} -\eta -6 + 6 \frac{\rho}{\bar{\rho}} (1+\eta)=0.$">|; 

$key = q/displaystylea;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4005.png"
 ALT="$\displaystyle a$">|; 

$key = q/displaystylea=frac{h^{,2}}{(1-e^{,2}),G,M}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img857.png"
 ALT="$\displaystyle a = \frac{h^{ 2}}{(1-e^{ 2}) G M}.$">|; 

$key = q/displaystylea=frac{r_p+r_a}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img638.png"
 ALT="$\displaystyle a = \frac{r_p+r_a}{2}.$">|; 

$key = q/displaystylea=rleft[1+frac{2}{3},epsilon(r),P_2(costheta)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4335.png"
 ALT="$\displaystyle a = r\left[1+\frac{2}{3} \epsilon(r) P_2(\cos\theta)\right].$">|; 

$key = q/displaystylea^{,2},frac{d^{,2}epsilon}{da^{,2}}-6,epsilon+6,frac{rho}{bar{rho}}left(a,frac{depsilon}{da}+epsilonright)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4362.png"
 ALT="$\displaystyle a^{ 2} \frac{d^{ 2}\epsilon}{da^{ 2}}-6 \epsilon + 6 \frac{\rho}{\bar{\rho}}\left(a \frac{d\epsilon}{da}+\epsilon\right)= 0.$">|; 

$key = q/displaystylea^{,2},frac{d^{,2}epsilon}{da^{,2}}=6left(1-frac{rho}{bar{rho}}right)epsilon.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4370.png"
 ALT="$\displaystyle a^{ 2} \frac{d^{ 2}\epsilon}{da^{ 2}}=6\left(1-\frac{\rho}{\bar{\rho}}\right)\epsilon.$">|; 

$key = q/displaystylea_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3248.png"
 ALT="$\displaystyle a_1$">|; 

$key = q/displaystylea_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3250.png"
 ALT="$\displaystyle a_2$">|; 

$key = q/displaystylea_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3252.png"
 ALT="$\displaystyle a_3$">|; 

$key = q/displaystylea_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3254.png"
 ALT="$\displaystyle a_4$">|; 

$key = q/displaystylea_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3256.png"
 ALT="$\displaystyle a_5$">|; 

$key = q/displaystylea_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3258.png"
 ALT="$\displaystyle a_6$">|; 

$key = q/displaystylea_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3260.png"
 ALT="$\displaystyle a_7$">|; 

$key = q/displaystylea_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3262.png"
 ALT="$\displaystyle a_8$">|; 

$key = q/displaystylea_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3264.png"
 ALT="$\displaystyle a_9$">|; 

$key = q/displaystylea_c=1.41left(frac{rho'}{rho}right)^{1slash3}R'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1331.png"
 ALT="$\displaystyle a_c = 1.41\left(\frac{\rho'}{\rho}\right)^{1/3} R'.$">|; 

$key = q/displaystylea_c=2.44left(frac{rho'}{rho}right)^{1slash3}R'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1332.png"
 ALT="$\displaystyle a_c = 2.44\left(\frac{\rho'}{\rho}\right)^{1/3} R'.$">|; 

$key = q/displaystylea_c=a_g.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1214.png"
 ALT="$\displaystyle a_c=a_g.$">|; 

$key = q/displaystylea_c=left(2,frac{m'}{m}right)^{1slash3}R,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1327.png"
 ALT="$\displaystyle a_c = \left(2 \frac{m'}{m}\right)^{1/3} R,$">|; 

$key = q/displaystylea_c=omega^{,2},rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1213.png"
 ALT="$\displaystyle a_c = \omega^{ 2} \rho$">|; 

$key = q/displaystylea_g=frac{G,m'}{a^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1212.png"
 ALT="$\displaystyle a_g = \frac{G m'}{a^{ 2}}$">|; 

$key = q/displaystylea_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1475.png"
 ALT="$\displaystyle a_\phi$">|; 

$key = q/displaystylea_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1471.png"
 ALT="$\displaystyle a_r$">|; 

$key = q/displaystylea_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1473.png"
 ALT="$\displaystyle a_\theta$">|; 

$key = q/displaystylea_x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img106.png"
 ALT="$\displaystyle a_x'$">|; 

$key = q/displaystylea_y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img108.png"
 ALT="$\displaystyle a_y'$">|; 

$key = q/displaystylea_z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle a_z'$">|; 

$key = q/displaystylea_{01};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3242.png"
 ALT="$\displaystyle a_{01}$">|; 

$key = q/displaystylea_{01}=frac{3}{4},x_4-frac{3}{4},y_4-frac{3}{2},x_4^{,2}+frac{3}{4},y_4^{,2}=-frac{477}{256},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3457.png"
 ALT="$\displaystyle a_{01} = \frac{3}{4} x_4 -\frac{3}{4} y_4 -\frac{3}{2} x_4^{ 2} +\frac{3}{4} y_4^{ 2}=-\frac{477}{256},$">|; 

$key = q/displaystylea_{02};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3244.png"
 ALT="$\displaystyle a_{02}$">|; 

$key = q/displaystylea_{02}=-frac{3}{2},x_1^{,2}+frac{3}{4},y_1^{,2}=frac{3}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3573.png"
 ALT="$\displaystyle a_{02} = -\frac{3}{2} x_1^{ 2}+\frac{3}{4} y_1^{ 2} =\frac{3}{2},$">|; 

$key = q/displaystylea_{03};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3246.png"
 ALT="$\displaystyle a_{03}$">|; 

$key = q/displaystylea_{03}=frac{3}{4},z_1^{,2}=frac{3}{4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3621.png"
 ALT="$\displaystyle a_{03} = \frac{3}{4} z_1^{ 2}=\frac{3}{4},$">|; 

$key = q/displaystylea_{1,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3543.png"
 ALT="$\displaystyle a_{1 x}$">|; 

$key = q/displaystylea_{1,y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3545.png"
 ALT="$\displaystyle a_{1 y}$">|; 

$key = q/displaystylea_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3266.png"
 ALT="$\displaystyle a_{10}$">|; 

$key = q/displaystylea_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3268.png"
 ALT="$\displaystyle a_{11}$">|; 

$key = q/displaystylea_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3270.png"
 ALT="$\displaystyle a_{12}$">|; 

$key = q/displaystylealpha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3661.png"
 ALT="$\displaystyle \alpha'$">|; 

$key = q/displaystylealpha'=c,m=frac{3}{4},m+frac{225}{32},m^{,2}+{calO}(m^{,3}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3648.png"
 ALT="$\displaystyle \alpha' =c m= \frac{3}{4} m+ \frac{225}{32} m^{ 2} + {\cal O}(m^{ 3}).$">|; 

$key = q/displaystylealpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2200.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/displaystylealpha<frac{b}{R}-frac{R}{b};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img933.png"
 ALT="$\displaystyle \alpha&lt; \frac{b}{R} -\frac{R}{b}
$">|; 

$key = q/displaystylealpha=0.623.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1941.png"
 ALT="$\displaystyle \alpha = 0.623.$">|; 

$key = q/displaystylealpha=2.615times10^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1930.png"
 ALT="$\displaystyle \alpha = 2.615\times 10^{-2}.$">|; 

$key = q/displaystylealpha=alpha_0+alpha',n',t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3647.png"
 ALT="$\displaystyle \alpha = \alpha_0 + \alpha' n' t,$">|; 

$key = q/displaystylealpha=alpha_0+c,m^{,2},T=alpha_0+c,m,n',t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3428.png"
 ALT="$\displaystyle \alpha = \alpha_0 + c m^{ 2} T = \alpha_0+c m n' t,$">|; 

$key = q/displaystylealpha=alpha_s+alpha_m.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1773.png"
 ALT="$\displaystyle \alpha=\alpha_s+\alpha_m.$">|; 

$key = q/displaystylealpha=left(1-frac{gamma}{1-e^{,2}}right)^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1046.png"
 ALT="$\displaystyle \alpha = \left(1-\frac{\gamma}{1-e^{ 2}}\right)^{-1/2},
$">|; 

$key = q/displaystylealpha=left(frac{mu_2}{3,mu_1}right)^{1slash3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2196.png"
 ALT="$\displaystyle \alpha = \left(\frac{\mu_2}{3 \mu_1}\right)^{1/3}.$">|; 

$key = q/displaystylealpha=left[3,left(frac{{calI}_{yy}-{calI}_{xx}}{{calI}_{zz}}right)right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1868.png"
 ALT="$\displaystyle \alpha= \left[3 \left(\frac{{\cal I}_{yy}-{\cal I}_{xx}}{{\cal I}_{zz}}\right)\right]^{1/2},$">|; 

$key = q/displaystylealpha=rho_2+frac{rho_2^{,2}}{3}+frac{rho_2^{,3}}{3}+frac{53,rho_2^{,4}}{81}+{calO}(rho_2^{,5}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2194.png"
 ALT="$\displaystyle \alpha = \rho_2 + \frac{\rho_2^{ 2}}{3} + \frac{\rho_2^{ 3}}{3} + \frac{53 \rho_2^{ 4}}{81}+ {\cal O}(\rho_2^{ 5}).$">|; 

$key = q/displaystylealpha>frac{1}{2+sqrt{14,e}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img1910.png"
 ALT="$\displaystyle \alpha &gt; \frac{1}{2+\sqrt{14 e}}.$">|; 

$key = q/displaystylealpha_1=sqrt{1+e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img668.png"
 ALT="$\displaystyle \alpha_1 = \sqrt{1+e}.$">|; 

$key = q/displaystylealpha_2=frac{1}{sqrt{1-e}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img669.png"
 ALT="$\displaystyle \alpha_2 = \frac{1}{\sqrt{1-e}}.$">|; 

$key = q/displaystylealpha_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1766.png"
 ALT="$\displaystyle \alpha_m$">|; 

$key = q/displaystylealpha_s=frac{3}{8},{calI}_parallel,n_s^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1716.png"
 ALT="$\displaystyle \alpha_s = \frac{3}{8} {\cal I}_\parallel n_s^{ 2}.$">|; 

$key = q/displaystylealphasimeq0.89;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1945.png"
 ALT="$\displaystyle \alpha\simeq 0.89$">|; 

$key = q/displaystyleb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4007.png"
 ALT="$\displaystyle b$">|; 

$key = q/displaystyleb_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3272.png"
 ALT="$\displaystyle b_1$">|; 

$key = q/displaystyleb_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3274.png"
 ALT="$\displaystyle b_2$">|; 

$key = q/displaystyleb_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3276.png"
 ALT="$\displaystyle b_3$">|; 

$key = q/displaystyleb_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3277.png"
 ALT="$\displaystyle b_4$">|; 

$key = q/displaystyleb_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3279.png"
 ALT="$\displaystyle b_5$">|; 

$key = q/displaystyleb_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3281.png"
 ALT="$\displaystyle b_6$">|; 

$key = q/displaystyleb_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3283.png"
 ALT="$\displaystyle b_7$">|; 

$key = q/displaystyleb_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3285.png"
 ALT="$\displaystyle b_8$">|; 

$key = q/displaystyleb_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3286.png"
 ALT="$\displaystyle b_9$">|; 

$key = q/displaystyleb_s^{(j)}(alpha)=frac{1}{pi}int_0^{2pi}frac{cos(j,psi),dpsi}{[1-2,alpha,cospsi+alpha^{,2}]^s},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2467.png"
 ALT="$\displaystyle b_s^{(j)}(\alpha) = \frac{1}{\pi}\int_0^{2\pi}\frac{\cos(j \psi) d\psi}{[1-2 \alpha \cos\psi+\alpha^{ 2}]^s},$">|; 

$key = q/displaystyleb_s^{(j)}(alpha)=frac{1}{pi}int_0^{2pi}frac{cos(j,psi),dpsi}{[1-2,alpha,cospsi+alpha^{,2}]^s}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4974.png"
 ALT="$\displaystyle b_s^{(j)}(\alpha) = \frac{1}{\pi}\int_0^{2\pi}\frac{\cos(j \psi) d\psi}{[1-2 \alpha \cos\psi+\alpha^{ 2}]^s}.$">|; 

$key = q/displaystyleb_{1,x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3547.png"
 ALT="$\displaystyle b_{1 x}$">|; 

$key = q/displaystyleb_{1,y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3548.png"
 ALT="$\displaystyle b_{1 y}$">|; 

$key = q/displaystyleb_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3288.png"
 ALT="$\displaystyle b_{10}$">|; 

$key = q/displaystyleb_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3290.png"
 ALT="$\displaystyle b_{11}$">|; 

$key = q/displaystyleb_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3292.png"
 ALT="$\displaystyle b_{12}$">|; 

$key = q/displaystylebar{rho}(a)=frac{3}{a^{,3}}int_0^arho(a'),a'^{,2},da';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4359.png"
 ALT="$\displaystyle \bar{\rho}(a)=\frac{3}{a^{ 3}}\int_0^a \rho(a') a'^{ 2} da'$">|; 

$key = q/displaystylebeta(theta,theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4174.png"
 ALT="$\displaystyle \beta(\theta,\theta')$">|; 

$key = q/displaystylebeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img784.png"
 ALT="$\displaystyle \beta$">|; 

$key = q/displaystylebeta_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1768.png"
 ALT="$\displaystyle \beta_m$">|; 

$key = q/displaystylebgg10^{-6},{rmm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2850.png"
 ALT="$\displaystyle b \gg 10^{-6} {\rm m}.$">|; 

$key = q/displaystylebggfrac{3}{8pi},frac{L}{G,M,rho,c}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2844.png"
 ALT="$\displaystyle b\gg \frac{3}{8\pi} \frac{L}{G M \rho c}.$">|; 

$key = q/displaystylec=frac{3}{4}+frac{255}{32},m+{calO}(m^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3562.png"
 ALT="$\displaystyle c = \frac{3}{4}+ \frac{255}{32} m+{\cal O}(m^{ 2}).$">|; 

$key = q/displaystylec_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3294.png"
 ALT="$\displaystyle c_1$">|; 

$key = q/displaystylec_1=-frac{3}{2},x_4,z_4.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3601.png"
 ALT="$\displaystyle c_1 = -\frac{3}{2} x_4 z_4.$">|; 

$key = q/displaystylec_1=frac{9}{16},z_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3602.png"
 ALT="$\displaystyle c_1 = \frac{9}{16} z_1.$">|; 

$key = q/displaystylec_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3296.png"
 ALT="$\displaystyle c_2$">|; 

$key = q/displaystylec_2=frac{3}{2},x_1,z_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3617.png"
 ALT="$\displaystyle c_2 = \frac{3}{2} x_1 z_1.$">|; 

$key = q/displaystylec_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3298.png"
 ALT="$\displaystyle c_3$">|; 

$key = q/displaystylec_3=frac{3}{2},x_1,z_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3619.png"
 ALT="$\displaystyle c_3 = \frac{3}{2} x_1 z_1.$">|; 

$key = q/displaystylec_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3299.png"
 ALT="$\displaystyle c_4$">|; 

$key = q/displaystylec_4=-frac{3}{2},x_4,z_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3597.png"
 ALT="$\displaystyle c_4 = -\frac{3}{2} x_4 z_1.$">|; 

$key = q/displaystylec_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3301.png"
 ALT="$\displaystyle c_5$">|; 

$key = q/displaystylec_5=frac{3}{2},x_4,z_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3599.png"
 ALT="$\displaystyle c_5 = \frac{3}{2} x_4 z_1.$">|; 

$key = q/displaystylecdot!!sum_{i=1,N}m_i,{bfr}_itimes(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1528.png"
 ALT="$\displaystyle \cdot\!\! \sum_{i=1,N}
m_i {\bf r}_i\times ($">|; 

$key = q/displaystylecdot{bfL}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1531.png"
 ALT="$\displaystyle \cdot {\bf L}.$">|; 

$key = q/displaystylecdot{bfh}-frac{C}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2124.png"
 ALT="$\displaystyle \cdot{\bf h} - \frac{C}{2},$">|; 

$key = q/displaystylecdot{bfh}=omega,h,cosI=sqrt{a,(1-e^{,2})},cosI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.54ex; " SRC="|."$dir".q|img2131.png"
 ALT="$\displaystyle \cdot {\bf h} = \omega h \cos I = \sqrt{a (1-e^{ 2})} \cos I,$">|; 

$key = q/displaystylechi'=frac{G,m'}{a}frac{r}{a},P_1(costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1221.png"
 ALT="$\displaystyle \chi' = \frac{G m'}{a}\frac{r}{a} P_1(\cos\theta).$">|; 

$key = q/displaystylechi'=omega^{,2},rho,z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1219.png"
 ALT="$\displaystyle \chi' = \omega^{ 2} \rho z$">|; 

$key = q/displaystylechi(r,theta)=-frac{{mitOmega}^{,2},r^{,2}}{2},sin^2theta=frac{{mitOmega}^{,2},r^{,2}}{3},left[P_2(costheta)-1right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1156.png"
 ALT="$\displaystyle \chi(r,\theta) = - \frac{{\mit\Omega}^{ 2} r^{ 2}}{2} \sin^2\theta= \frac{{\mit\Omega}^{ 2} r^{ 2}}{3} \left[P_2(\cos\theta)-1\right]$">|; 

$key = q/displaystylechi(r,theta)=frac{G,M}{R},zetaleft(frac{r}{R}right)^2left[P_2(costheta)-1right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1158.png"
 ALT="$\displaystyle \chi(r,\theta) = \frac{G M}{R} \zeta\left(\frac{r}{R}\right)^2\left[P_2(\cos\theta)-1\right],$">|; 

$key = q/displaystylechi(r,theta)=frac{G,m}{R},zetaleft(frac{r}{R}right)^2P_2(costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1240.png"
 ALT="$\displaystyle \chi(r,\theta)=\frac{G m}{R} \zeta\left(\frac{r}{R}\right)^2 P_2(\cos\theta).$">|; 

$key = q/displaystylechi=-frac{1}{2},|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4455.png"
 ALT="$\displaystyle \chi = -\frac{1}{2} \vert$">|; 

$key = q/displaystylechi=-frac{G,m'}{a^{,3}},(z^{,2}-x^{,2}slash2-y^{,2}slash2)+{rmconst}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1320.png"
 ALT="$\displaystyle \chi = - \frac{G m'}{a^{ 3}} (z^{ 2}-x^{ 2}/2-y^{ 2}/2) + {\rm const}.$">|; 

$key = q/displaystylechi=chi'+{mitPhi}'simeq-frac{G,m'}{a}left[1+frac{r^{,2}}{a^{,2}},P_2(costheta)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1236.png"
 ALT="$\displaystyle \chi=\chi'+{\mit\Phi}' \simeq - \frac{G m'}{a}\left[1 + \frac{r^{ 2}}{a^{ 2}} P_2(\cos\theta)\right],$">|; 

$key = q/displaystylechi=frac{{mitOmega}^{,2},r^{,2}}{3}left[P_2(costheta)-1right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4324.png"
 ALT="$\displaystyle \chi = \frac{{\mit\Omega}^{ 2} r^{ 2}}{3}\left[P_2(\cos\theta)-1\right].$">|; 

$key = q/displaystylechi_0=-frac{1}{2},{mitOmega}^{,2},(x'^{,2}+y'^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4454.png"
 ALT="$\displaystyle \chi_0 = -\frac{1}{2} {\mit\Omega}^{ 2} (x'^{ 2}+y'^{ 2}).$">|; 

$key = q/displaystylecos(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3826.png"
 ALT="$\displaystyle \cos(-\alpha)$">|; 

$key = q/displaystylecos(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3860.png"
 ALT="$\displaystyle \cos(2\alpha)$">|; 

$key = q/displaystylecos(3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3864.png"
 ALT="$\displaystyle \cos(3\alpha)$">|; 

$key = q/displaystylecos(4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3868.png"
 ALT="$\displaystyle \cos(4\alpha)$">|; 

$key = q/displaystylecos(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3834.png"
 ALT="$\displaystyle \cos(\alpha\pm \beta)$">|; 

$key = q/displaystylecos(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3854.png"
 ALT="$\displaystyle \cos(\alpha/2)$">|; 

$key = q/displaystylecos(j,vartheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5018.png"
 ALT="$\displaystyle \cos(j \vartheta)$">|; 

$key = q/displaystylecos(omega+theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4982.png"
 ALT="$\displaystyle \cos(\omega+\theta)$">|; 

$key = q/displaystylecos2theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1856.png"
 ALT="$\displaystyle \cos 2\theta$">|; 

$key = q/displaystylecosE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img893.png"
 ALT="$\displaystyle \cos E$">|; 

$key = q/displaystylecos[j,(vartheta-vartheta')];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5028.png"
 ALT="$\displaystyle \cos[j (\vartheta-\vartheta')]$">|; 

$key = q/displaystylecos[j,(vartheta-vartheta')]equivcos(j,vartheta),cos(j,vartheta')+sin(j,vartheta),sin(j,vartheta').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5017.png"
 ALT="$\displaystyle \cos[ j (\vartheta-\vartheta') ]\equiv \cos( j \vartheta) \cos(j \vartheta') + \sin( j \vartheta) \sin (j \vartheta').$">|; 

$key = q/displaystylecos^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3872.png"
 ALT="$\displaystyle \cos^2\alpha$">|; 

$key = q/displaystylecos^3alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3876.png"
 ALT="$\displaystyle \cos^3\alpha$">|; 

$key = q/displaystylecos^4alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3880.png"
 ALT="$\displaystyle \cos^4\alpha$">|; 

$key = q/displaystylecosalpha+cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3842.png"
 ALT="$\displaystyle \cos\alpha+\cos\beta$">|; 

$key = q/displaystylecosalpha,cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3848.png"
 ALT="$\displaystyle \cos\alpha \cos\beta$">|; 

$key = q/displaystylecosalpha-cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3844.png"
 ALT="$\displaystyle \cos\alpha-\cos\beta$">|; 

$key = q/displaystylecosgamma=frac{mbox{boldmathomega}cdot{bfr}}{|mbox{boldmathomega}|,|{bfr}|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img4534.png"
 ALT="$\displaystyle \cos\gamma = \frac{\mbox{\boldmath$\omega$}\cdot{\bf r}}{\vert\mbox{\boldmath$\omega$}\vert \vert{\bf r}\vert}$">|; 

$key = q/displaystylecosgamma_s=frac{mbox{boldmathomega}cdot{bfr}_s}{|mbox{boldmathomega}|,|{bfr}_s|}=sintheta,sinlambda_s,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img1711.png"
 ALT="$\displaystyle \cos\gamma_s =\frac{\mbox{\boldmath$\omega$}\cdot{\bf r}_s}{\vert\mbox{\boldmath$\omega$}\vert \vert{\bf r}_s\vert}= \sin\theta \sin\lambda_s,$">|; 

$key = q/displaystylecosh(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3884.png"
 ALT="$\displaystyle \cosh(-\alpha)$">|; 

$key = q/displaystylecosh(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3917.png"
 ALT="$\displaystyle \cosh(2\alpha)$">|; 

$key = q/displaystylecosh(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3891.png"
 ALT="$\displaystyle \cosh(\alpha\pm \beta)$">|; 

$key = q/displaystylecosh(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3911.png"
 ALT="$\displaystyle \cosh(\alpha/2)$">|; 

$key = q/displaystylecosh^2alpha-sinh^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3888.png"
 ALT="$\displaystyle \cosh^2\alpha-\sinh^2\alpha$">|; 

$key = q/displaystylecoshalpha+coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3899.png"
 ALT="$\displaystyle \cosh\alpha+\cosh\beta$">|; 

$key = q/displaystylecoshalpha,coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3905.png"
 ALT="$\displaystyle \cosh\alpha \cosh\beta$">|; 

$key = q/displaystylecoshalpha-coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3901.png"
 ALT="$\displaystyle \cosh\alpha-\cosh\beta$">|; 

$key = q/displaystylecoshx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3820.png"
 ALT="$\displaystyle \cosh x$">|; 

$key = q/displaystylecospsi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5002.png"
 ALT="$\displaystyle \cos\psi$">|; 

$key = q/displaystylecospsi=frac{X}{r},frac{X'}{r'}+frac{Y}{r},frac{Y'}{r'}+frac{Z}{r},frac{Z'}{r'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img5001.png"
 ALT="$\displaystyle \cos\psi = \frac{X}{r} \frac{X'}{r'} + \frac{Y}{r} \frac{Y'}{r'}
+ \frac{Z}{r} \frac{Z'}{r'},$">|; 

$key = q/displaystylecostheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img897.png"
 ALT="$\displaystyle \cos \theta$">|; 

$key = q/displaystylecostheta=-1+frac{2,r_p}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img924.png"
 ALT="$\displaystyle \cos\theta = -1 + \frac{2 r_p}{a},
$">|; 

$key = q/displaystylecostheta=frac{cosE-e}{1-e,cosE}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img718.png"
 ALT="$\displaystyle \cos\theta = \frac{\cos E - e}{1-e \cos E}.$">|; 

$key = q/displaystylecosvartheta=frac{Z}{r}=sin(omega+theta),sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2705.png"
 ALT="$\displaystyle \cos\vartheta = \frac{Z}{r} = \sin(\omega+\theta) \sin I,$">|; 

$key = q/displaystylecosx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3814.png"
 ALT="$\displaystyle \cos x$">|; 

$key = q/displaystylecos{mitOmega},skew{3}dot{h}_X+sin{mitOmega},skew{3}dot{h}_Y=sin(omega+theta),r,F_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5140.png"
 ALT="$\displaystyle \cos{\mit\Omega} \skew{3}\dot{h}_X+\sin{\mit\Omega} \skew{3}\dot{h}_Y =\sin(\omega+\theta) r F_z.$">|; 

$key = q/displaystyled_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3356.png"
 ALT="$\displaystyle d_1$">|; 

$key = q/displaystyled_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3358.png"
 ALT="$\displaystyle d_2$">|; 

$key = q/displaystyled_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3360.png"
 ALT="$\displaystyle d_3$">|; 

$key = q/displaystyled_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3362.png"
 ALT="$\displaystyle d_4$">|; 

$key = q/displaystyled_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3364.png"
 ALT="$\displaystyle d_5$">|; 

$key = q/displaystyled_{rmeast}simeqfrac{{mitOmega}}{3},coslambda,left(frac{8,h^3}{g}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1134.png"
 ALT="$\displaystyle d_{\rm east} \simeq \frac{{\mit\Omega}}{3} \cos\lambda \left(\frac{8 h^3}{g}\right)^{1/2}.$">|; 

$key = q/displaystyleddot{X}+mu,frac{X}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4628.png"
 ALT="$\displaystyle \ddot{X}+ \mu \frac{X}{r^{ 3}}$">|; 

$key = q/displaystyleddot{X}-2,dot{Y}-,X+frac{X}{R^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3093.png"
 ALT="$\displaystyle \ddot{X} -2 \dot{Y}- X+\frac{X}{R^{ 3}}$">|; 

$key = q/displaystyleddot{X}_l=frac{partialF_0}{partialX_l},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4702.png"
 ALT="$\displaystyle \ddot{X}_l = \frac{\partial F_0}{\partial X_l},$">|; 

$key = q/displaystyleddot{Y}+2,dot{X}-Y+frac{Y}{R^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3095.png"
 ALT="$\displaystyle \ddot{Y}+2 \dot{X}-Y+\frac{Y}{R^{ 3}}$">|; 

$key = q/displaystyleddot{Y}+mu,frac{Y}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4630.png"
 ALT="$\displaystyle \ddot{Y}+ \mu \frac{Y}{r^{ 3}}$">|; 

$key = q/displaystyleddot{Z}+frac{Z}{R^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3097.png"
 ALT="$\displaystyle \ddot{Z} +\frac{Z}{R^{ 3}}$">|; 

$key = q/displaystyleddot{Z}+mu,frac{Z}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4632.png"
 ALT="$\displaystyle \ddot{Z}+ \mu \frac{Z}{r^{ 3}}$">|; 

$key = q/displaystyleddot{bfr}'+mu',frac{{bfr}'}{r'^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2412.png"
 ALT="$\displaystyle \ddot{\bf r}' + \mu' \frac{{\bf r}'}{r'^{ 3}}$">|; 

$key = q/displaystyleddot{bfr}'+n'^{,2},a'^{,3},frac{{bfr}'}{r'^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3019.png"
 ALT="$\displaystyle \ddot{\bf r}' + n'^{ 2} a'^{ 3} \frac{{\bf r}'}{r'^{ 3}}$">|; 

$key = q/displaystyleddot{bfr}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2963.png"
 ALT="$\displaystyle \ddot{\bf r}'$">|; 

$key = q/displaystyleddot{bfr}+2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2150.png"
 ALT="$\displaystyle \ddot{\bf r} + 2 $">|; 

$key = q/displaystyleddot{bfr}+mu,frac{bfr}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2410.png"
 ALT="$\displaystyle \ddot{\bf r} + \mu \frac{\bf r}{r^{ 3}}$">|; 

$key = q/displaystyleddot{bfr}+mu,frac{bfr}{r^{,3}}=nabla{calR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2888.png"
 ALT="$\displaystyle \ddot{\bf r} + \mu \frac{\bf r}{r^{ 3}} = \nabla{\cal R},
$">|; 

$key = q/displaystyleddot{bfr}+mu,frac{{bfr}}{r^{,3}}=nabla{calR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2687.png"
 ALT="$\displaystyle \ddot{\bf r} + \mu \frac{{\bf r}}{r^{ 3}} = \nabla{\cal R},$">|; 

$key = q/displaystyleddot{bfr}+n^{,2},a^{,3},frac{{bfr}}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3017.png"
 ALT="$\displaystyle \ddot{\bf r}+n^{ 2} a^{ 3} \frac{{\bf r}}{r^{ 3}}$">|; 

$key = q/displaystyleddot{bfr}+n^{,2},a^{,3},frac{{bfr}}{r^{,3}}=nabla{calR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3673.png"
 ALT="$\displaystyle \ddot{\bf r} +n^{ 2} a^{ 3} \frac{{\bf r}}{r^{ 3}} =\nabla{\cal R},
$">|; 

$key = q/displaystyleddot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2961.png"
 ALT="$\displaystyle \ddot{\bf r}$">|; 

$key = q/displaystyleddot{bfr}=-nabla{mitPhi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2686.png"
 ALT="$\displaystyle \ddot{\bf r} = - \nabla {\mit\Phi}.$">|; 

$key = q/displaystyleddot{r}-r,skew{5}dot{theta}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1432.png"
 ALT="$\displaystyle \ddot{r} - r \skew{5}\dot{\theta}^{ 2}$">|; 

$key = q/displaystyleddot{x}+left[-frac{3,f(r_c)}{r_c}-f'(r_c)right]x=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img966.png"
 ALT="$\displaystyle \ddot{x} + \left[-\frac{3 f(r_c)}{r_c} - f'(r_c)\right] x = 0.$">|; 

$key = q/displaystyleddot{x}+n^{,2},a^{,3},frac{x}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3062.png"
 ALT="$\displaystyle \ddot{x} + n^{ 2} a^{ 3} \frac{x}{r^{ 3}}$">|; 

$key = q/displaystyleddot{x},';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1122.png"
 ALT="$\displaystyle \ddot{x} '$">|; 

$key = q/displaystyleddot{x}-frac{h^{,2}}{(r_c+x)^3}=f(r_c+x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img961.png"
 ALT="$\displaystyle \ddot{x} - \frac{h^{ 2}}{(r_c+x)^3} = f(r_c+x).$">|; 

$key = q/displaystyleddot{x}-frac{h^{,2}}{r_c^{,3}}left(1-3,frac{x}{r_c}right)=f(r_c)+f'(r_c),x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img964.png"
 ALT="$\displaystyle \ddot{x} - \frac{h^{ 2}}{r_c^{ 3}}\left(1-3 \frac{x}{r_c}\right)=
f(r_c) + f'(r_c) x,$">|; 

$key = q/displaystyleddot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1338.png"
 ALT="$\displaystyle \ddot{x}$">|; 

$key = q/displaystyleddot{x}_1-2,n,dot{y}_1-n^{,2},x_1+n^{,2},a^{,3},frac{x_1}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3068.png"
 ALT="$\displaystyle \ddot{x}_1-2 n \dot{y}_1-n^{ 2} x_1 +n^{ 2} a^{ 3} \frac{x_1}{r^{ 3}}$">|; 

$key = q/displaystyleddot{y}+n^{,2},a^{,3},frac{y}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3064.png"
 ALT="$\displaystyle \ddot{y} + n^{ 2} a^{ 3} \frac{y}{r^{ 3}}$">|; 

$key = q/displaystyleddot{y},';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1124.png"
 ALT="$\displaystyle \ddot{y} '$">|; 

$key = q/displaystyleddot{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1340.png"
 ALT="$\displaystyle \ddot{y}$">|; 

$key = q/displaystyleddot{y}_1+2,n,dot{x}_1-n^{,2},y_1+n^{,2},a^{,3},frac{y_1}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3070.png"
 ALT="$\displaystyle \ddot{y}_1+2 n \dot{x}_1-n^{ 2} y_1 +n^{ 2} a^{ 3} \frac{y_1}{r^{ 3}}$">|; 

$key = q/displaystyleddot{z}+n^{,2},a^{,3},frac{z}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.96ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3066.png"
 ALT="$\displaystyle \ddot{z} + n^{ 2} a^{ 3} \frac{z}{r^{ 3}}$">|; 

$key = q/displaystyleddot{z},';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1126.png"
 ALT="$\displaystyle \ddot{z} '$">|; 

$key = q/displaystyleddot{z}_1+n^{,2},a^{,3},frac{z_1}{r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.96ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3072.png"
 ALT="$\displaystyle \ddot{z}_1+n^{ 2} a^{ 3} \frac{z_1}{r^{ 3}}$">|; 

$key = q/displaystyleddot{{bfr}}+mu,frac{bfr}{r^{,3}}=nabla{calR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4626.png"
 ALT="$\displaystyle \ddot{{\bf r}} + \mu \frac{\bf r}{r^{ 3}} = \nabla {\cal R},$">|; 

$key = q/displaystyleddot{{bfr}}+mu,frac{bfr}{r^{,3}}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4625.png"
 ALT="$\displaystyle \ddot{{\bf r}} + \mu \frac{\bf r}{r^{ 3}} = {\bf0},$">|; 

$key = q/displaystyleddot{{bfr}}+mu,frac{bfr}{r^{,3}}={bfF}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img5092.png"
 ALT="$\displaystyle \ddot{{\bf r}} + \mu \frac{\bf r}{r^{ 3}} = {\bf F}.$">|; 

$key = q/displaystyleddot{{bfr}}+n'^{,2},a'^{,3},frac{{bfr}'}{r'^{,3}}=-frac{3}{4},epsilon,n'^{,2},a'^{,5},frac{{bfr}'}{r'^{,5}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3675.png"
 ALT="$\displaystyle \ddot{{\bf r}}+n'^{ 2} a'^{ 3} \frac{{\bf r}'}{r'^{ 3}}=-\frac{3}{4} \epsilon  n'^{ 2} a'^{ 5} \frac{{\bf r}'}{r'^{ 5}},
$">|; 

$key = q/displaystyledelta(a,theta)=-frac{2}{3},a,epsilon(a),P_2(costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4346.png"
 ALT="$\displaystyle \delta(a,\theta) = -\frac{2}{3} a \epsilon(a) P_2(\cos\theta).$">|; 

$key = q/displaystyledelta(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4445.png"
 ALT="$\displaystyle \delta(\theta,\phi)$">|; 

$key = q/displaystyledelta(theta,theta')=(r^{,2}+r'^{,2}-2,r,r',beta)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4192.png"
 ALT="$\displaystyle \delta(\theta,\theta') = (r^{ 2} + r'^{ 2}-2 r r' \beta)^{1/2}.$">|; 

$key = q/displaystyledelta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4955.png"
 ALT="$\displaystyle \delta$">|; 

$key = q/displaystyledeltaAsimeqfrac{1}{2},r^{,2},deltatheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img611.png"
 ALT="$\displaystyle \delta A \simeq \frac{1}{2} r^{ 2} \delta\theta,$">|; 

$key = q/displaystyledeltaR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3179.png"
 ALT="$\displaystyle \delta R$">|; 

$key = q/displaystyledeltaW=sum_{i=1,{calF}}Q_i,deltaq_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.89ex; " SRC="|."$dir".q|img1385.png"
 ALT="$\displaystyle \delta W = \sum_{i=1,{\cal F}} Q_i \delta q_i,$">|; 

$key = q/displaystyledeltaW=sum_{j=1,{calF}}f_j,deltax_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.98ex; " SRC="|."$dir".q|img1380.png"
 ALT="$\displaystyle \delta W = \sum_{j=1,{\cal F}} f_j \delta x_j$">|; 

$key = q/displaystyledeltaW=sum_{j=1,{calF}}f_jsum_{i=1,{calF}}frac{partialx_j}{partialq_i},deltaq_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.98ex; " SRC="|."$dir".q|img1384.png"
 ALT="$\displaystyle \delta W = \sum_{j=1,{\cal F}} f_j\sum_{i=1,{\cal F}}\frac{\partial x_j}{\partial q_i} \delta q_i.$">|; 

$key = q/displaystyledeltaX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3205.png"
 ALT="$\displaystyle \delta X$">|; 

$key = q/displaystyledeltaY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3210.png"
 ALT="$\displaystyle \delta Y$">|; 

$key = q/displaystyledeltaZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3215.png"
 ALT="$\displaystyle \delta Z$">|; 

$key = q/displaystyledelta_2(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4314.png"
 ALT="$\displaystyle \delta_2(\theta,\phi)$">|; 

$key = q/displaystyledelta_2=h_2,zeta_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4307.png"
 ALT="$\displaystyle \delta_2 = h_2 \zeta_2,$">|; 

$key = q/displaystyledeltabeta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3683.png"
 ALT="$\displaystyle \delta \beta'$">|; 

$key = q/displaystyledeltabeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3183.png"
 ALT="$\displaystyle \delta \beta$">|; 

$key = q/displaystyledeltachi=chi-chi_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4457.png"
 ALT="$\displaystyle \delta\chi = \chi-\chi_0$">|; 

$key = q/displaystyledeltaddot{X}-2,deltadot{Y}-3left(1+frac{1}{2},m^{,2}right),deltaX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3190.png"
 ALT="$\displaystyle \delta \ddot{X}-2 \delta \dot{Y} - 3\left(1+\frac{1}{2} m^{ 2}\right) \delta X$">|; 

$key = q/displaystyledeltaddot{X}-2,deltadot{Y}-left(2,X_0^{,-3}+1+frac{1}{2},m^{,2}right)deltaX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3146.png"
 ALT="$\displaystyle \delta \ddot{X}-2 \delta \dot{Y} - \left(2 X_0^{ -3}+1+\frac{1}{2} m^{ 2}\right)\delta X$">|; 

$key = q/displaystyledeltaddot{Y}+2,deltadot{X}+left(X_0^{,-3}-1-frac{1}{2},m^{,2}right)deltaY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3148.png"
 ALT="$\displaystyle \delta \ddot{Y}+2 \delta \dot{X} +\left(X_0^{ -3}-1-\frac{1}{2} m^{ 2}\right)\delta Y$">|; 

$key = q/displaystyledeltaddot{Y}+2,deltadot{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3192.png"
 ALT="$\displaystyle \delta \ddot{Y}+2 \delta \dot{X}$">|; 

$key = q/displaystyledeltaddot{Z}+left(1+frac{3}{2},m^{,2}right),deltaZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3194.png"
 ALT="$\displaystyle \delta\ddot{Z} + \left(1+\frac{3}{2} m^{ 2}\right) \delta Z$">|; 

$key = q/displaystyledeltaddot{Z}+left(X_0^{,-3}+m^{,2}right)deltaZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3150.png"
 ALT="$\displaystyle \delta\ddot{Z} + \left(X_0^{ -3}+m^{ 2}\right)\delta Z$">|; 

$key = q/displaystyledeltalambda';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3681.png"
 ALT="$\displaystyle \delta\lambda'$">|; 

$key = q/displaystyledeltalambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3181.png"
 ALT="$\displaystyle \delta \lambda$">|; 

$key = q/displaystyledeltalambdasimeqsum_{i=1,5}A_i,sin(n_i,t-gamma_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img3743.png"
 ALT="$\displaystyle \delta\lambda \simeq \sum_{i=1,5} A_i \sin(n_i t-\gamma_i),
$">|; 

$key = q/displaystyledeltaphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1796.png"
 ALT="$\displaystyle \delta\phi$">|; 

$key = q/displaystyledeltaphi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4562.png"
 ALT="$\displaystyle \delta\phi_1$">|; 

$key = q/displaystyledeltaphi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4617.png"
 ALT="$\displaystyle \delta\phi_2$">|; 

$key = q/displaystyledeltaskew{3}ddot{x}-2,deltaskew{3}dot{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2261.png"
 ALT="$\displaystyle \delta\skew{3}\ddot{x} - 2 \delta\skew{3}\dot{y}$">|; 

$key = q/displaystyledeltaskew{3}ddot{y}+2,deltaskew{3}dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2263.png"
 ALT="$\displaystyle \delta\skew{3}\ddot{y} + 2 \delta\skew{3}\dot{x}$">|; 

$key = q/displaystyledeltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1798.png"
 ALT="$\displaystyle \delta\theta$">|; 

$key = q/displaystyledeltatheta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4558.png"
 ALT="$\displaystyle \delta\theta_1$">|; 

$key = q/displaystyledeltatheta_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4560.png"
 ALT="$\displaystyle \delta\theta_2$">|; 

$key = q/displaystyledeltavarpisimeqfrac{6pi,G,M}{c^{,2},r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1025.png"
 ALT="$\displaystyle \delta\varpi \simeq \frac{6\pi G M}{c^{ 2}  r}$">|; 

$key = q/displaystyledeltax'(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2382.png"
 ALT="$\displaystyle \delta x'(t)$">|; 

$key = q/displaystyledeltax_j=sum_{i=1,{calF}}frac{partialx_j}{partialq_i},deltaq_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.89ex; " SRC="|."$dir".q|img1378.png"
 ALT="$\displaystyle \delta x_j = \sum_{i=1,{\cal F}} \frac{\partial x_j}{\partial q_i} \delta q_i,$">|; 

$key = q/displaystyledeltay'(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2384.png"
 ALT="$\displaystyle \delta y'(t)$">|; 

$key = q/displaystyledot{E}=frac{n}{1-e,cos,E}-frac{(1-e,cosE)}{e,sinE},frac{skew{3}dot{a}}{a}+frac{cosE}{sinE},frac{skew{3}dot{e}}{e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img5115.png"
 ALT="$\displaystyle \dot{E} =\frac{n}{1-e \cos E} - \frac{(1-e \cos E)}{e \sin E} \frac{\skew{3}\dot{a}}{a} + \frac{\cos E}{\sin E} \frac{\skew{3}\dot{e}}{e}.$">|; 

$key = q/displaystyledot{E}=tau,(omega-{mitOmega}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1306.png"
 ALT="$\displaystyle \dot{E} = \tau (\omega-{\mit\Omega}).$">|; 

$key = q/displaystyledot{I};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2761.png"
 ALT="$\displaystyle \dot{I}$">|; 

$key = q/displaystyledot{I}=frac{cos(omega+theta),r,F_z}{h}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img5137.png"
 ALT="$\displaystyle \dot{I} = \frac{\cos(\omega+\theta) r F_z}{h}.$">|; 

$key = q/displaystyledot{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4637.png"
 ALT="$\displaystyle \dot{X}$">|; 

$key = q/displaystyledot{Y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4639.png"
 ALT="$\displaystyle \dot{Y}$">|; 

$key = q/displaystyledot{Z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4641.png"
 ALT="$\displaystyle \dot{Z}$">|; 

$key = q/displaystyledot{bfe};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img5104.png"
 ALT="$\displaystyle \dot{\bf e}$">|; 

$key = q/displaystyledot{bfe}_r=skew{5}dot{theta},(-sintheta,,costheta)=skew{5}dot{theta},,{bfe}_theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img597.png"
 ALT="$\displaystyle \dot{\bf e}_r = \skew{5}\dot{\theta} (-\sin\theta, \cos\theta) = \skew{5}\dot{\theta}  {\bf e}_\theta.$">|; 

$key = q/displaystyledot{bfe}_theta=skew{5}dot{theta},(-costheta,,-sintheta)=-skew{5}dot{theta},{bfe}_r.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img600.png"
 ALT="$\displaystyle \dot{\bf e}_\theta = \skew{5}\dot{\theta} (-\cos\theta, -\sin\theta) = - \skew{5}\dot{\theta} {\bf e}_r.$">|; 

$key = q/displaystyledot{bfh}={bfr}timesddot{bfr}={bfr}times{bfF}=-r,F_z,{bfe}_theta+r,F_theta,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5096.png"
 ALT="$\displaystyle \dot{\bf h} = {\bf r}\times \ddot{\bf r} = {\bf r}\times {\bf F} = -r F_z {\bf e}_\theta + r F_\theta {\bf e}_z,$">|; 

$key = q/displaystyledot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2738.png"
 ALT="$\displaystyle \dot{\bf r}$">|; 

$key = q/displaystyledot{varpi}'=frac{3,epsilon}{4},n',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3677.png"
 ALT="$\displaystyle \dot{\varpi}' = \frac{3 \epsilon}{4} n',
$">|; 

$key = q/displaystyledot{varpi}=frac{3,epsilon}{5}left(frac{R}{a}right)^2n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1062.png"
 ALT="$\displaystyle \dot{\varpi}= \frac{3 \epsilon}{5}\left(\frac{R}{a}\right)^2 n,
$">|; 

$key = q/displaystyledot{varpi}={bfe}_zcdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4149.png"
 ALT="$\displaystyle \dot{\varpi} = {\bf e}_z\cdot$">|; 

$key = q/displaystyledot{varpi}simeqfrac{0.0383}{a,T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1027.png"
 ALT="$\displaystyle \dot{\varpi} \simeq \frac{0.0383}{a T}$">|; 

$key = q/displaystyledot{varv}_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1137.png"
 ALT="$\displaystyle \dot{\varv}_{x'}$">|; 

$key = q/displaystyledot{varv}_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1139.png"
 ALT="$\displaystyle \dot{\varv}_{y'}$">|; 

$key = q/displaystyledot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4765.png"
 ALT="$\displaystyle \dot{x}$">|; 

$key = q/displaystyledot{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4767.png"
 ALT="$\displaystyle \dot{y}$">|; 

$key = q/displaystyledr=frac{r_p}{1-e},e,sinE,dE,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.24ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img687.png"
 ALT="$\displaystyle dr = \frac{r_p}{1-e} e \sin E dE,$">|; 

$key = q/displaystylee,sinhH-H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img842.png"
 ALT="$\displaystyle e \sinh H - H$">|; 

$key = q/displaystylee;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2903.png"
 ALT="$\displaystyle e$">|; 

$key = q/displaystylee=0.123;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1946.png"
 ALT="$\displaystyle e=0.123$">|; 

$key = q/displaystylee=frac{r_2-r_1}{r_2+r_1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img667.png"
 ALT="$\displaystyle e = \frac{r_2-r_1}{r_2+r_1}.$">|; 

$key = q/displaystylee=frac{r_a-r_p}{r_a+r_p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img639.png"
 ALT="$\displaystyle e = \frac{r_a-r_p}{r_a+r_p}$">|; 

$key = q/displaystylee_Z=e,sinomega,sinI,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5142.png"
 ALT="$\displaystyle e_Z = e \sin\omega \sin I,$">|; 

$key = q/displaystylee_zsimeq-p_x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2005.png"
 ALT="$\displaystyle e_z \simeq - p_x.$">|; 

$key = q/displaystylee_{i,{rmmax}}=|e_{ik}|+sum_{l=1,8}^{lneqk}|e_{il}|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.47ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2610.png"
 ALT="$\displaystyle e_{i {\rm max}} = \vert e_{ik}\vert+\sum_{l=1,8}^{l\neq k} \vert e_{il}\vert.$">|; 

$key = q/displaystylee_{i,{rmmin}}=|e_{ik}|-sum_{l=1,8}^{lneqk}|e_{il}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.47ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2609.png"
 ALT="$\displaystyle e_{i {\rm min}} = \vert e_{ik}\vert-\sum_{l=1,8}^{l\neq k} \vert e_{il}\vert$">|; 

$key = q/displaystyleepsilon';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4898.png"
 ALT="$\displaystyle \epsilon'$">|; 

$key = q/displaystyleepsilon'=frac{3}{5},epsilon+frac{3}{2},zeta=frac{3}{2}left(frac{5slash2+tilde{mu}}{1+tilde{mu}}right)zeta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1269.png"
 ALT="$\displaystyle \epsilon' = \frac{3}{5} \epsilon + \frac{3}{2} \zeta =\frac{3}{2} \left(\frac{5/2+\tilde{\mu}}{1+\tilde{\mu}}\right)\zeta.$">|; 

$key = q/displaystyleepsilon'lle,,Ill1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4923.png"
 ALT="$\displaystyle \epsilon'\ll e, I\ll 1,$">|; 

$key = q/displaystyleepsilon(a)=epsilon_0left(frac{a}{R}right)^{eta_0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img4416.png"
 ALT="$\displaystyle \epsilon(a)= \epsilon_0\left(\frac{a}{R}\right)^{\eta_0}.$">|; 

$key = q/displaystyleepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4319.png"
 ALT="$\displaystyle \epsilon$">|; 

$key = q/displaystyleepsilon=0.101.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1204.png"
 ALT="$\displaystyle \epsilon= 0.101.$">|; 

$key = q/displaystyleepsilon=4.31times10^{-3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1192.png"
 ALT="$\displaystyle \epsilon = 4.31\times 10^{-3}.$">|; 

$key = q/displaystyleepsilon=frac{15}{38},frac{X}{mu},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1180.png"
 ALT="$\displaystyle \epsilon = \frac{15}{38} \frac{X}{\mu},$">|; 

$key = q/displaystyleepsilon=frac{15}{4},frac{zeta}{1+tilde{mu}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1182.png"
 ALT="$\displaystyle \epsilon =\frac{15}{4}  \frac{\zeta}{1+\tilde{\mu}},$">|; 

$key = q/displaystyleepsilon=frac{15}{4},zeta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1167.png"
 ALT="$\displaystyle \epsilon = \frac{15}{4} \zeta,$">|; 

$key = q/displaystyleepsilon=frac{15}{4}left(frac{zeta}{1+tilde{mu}}right)simeq-4.8times10^{-8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1252.png"
 ALT="$\displaystyle \epsilon = \frac{15}{4}\left(\frac{\zeta}{1+\tilde{\mu}}\right)\simeq -4.8\times 10^{-8}.$">|; 

$key = q/displaystyleepsilon=frac{3}{2}left(J_2+zetaright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1166.png"
 ALT="$\displaystyle \epsilon = \frac{3}{2}\left(J_2+\zeta\right).$">|; 

$key = q/displaystyleepsilon=frac{E,M}{(E+M)^{,2}}left(frac{a}{a'}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3676.png"
 ALT="$\displaystyle \epsilon =\frac{E M}{(E+M)^{ 2}}\left(\frac{a}{a'}\right)^2,
$">|; 

$key = q/displaystyleepsilon=frac{R_e-R_p}{R}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img467.png"
 ALT="$\displaystyle \epsilon = \frac{R_e-R_p}{R}.$">|; 

$key = q/displaystyleepsilon=frac{tilde{mu}}{mu}=frac{m}{M+m'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4941.png"
 ALT="$\displaystyle \epsilon =\frac{\tilde{\mu}}{\mu}= \frac{m}{M+m'}.$">|; 

$key = q/displaystyleepsilon=frac{{calI}_parallel-{calI}_perp}{{calI}_0}simeqfrac{{calI}_parallel-{calI}_perp}{{calI}_parallel}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1668.png"
 ALT="$\displaystyle \epsilon = \frac{{\cal I}_\parallel-{\cal I}_\perp}{{\cal I}_0}\simeq \frac{{\cal I}_\parallel-{\cal I}_\perp}{{\cal I}_\parallel}.$">|; 

$key = q/displaystyleepsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4418.png"
 ALT="$\displaystyle \epsilon_0$">|; 

$key = q/displaystyleepsilon_0=frac{3}{2},(J_2+zeta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4406.png"
 ALT="$\displaystyle \epsilon_0 =\frac{3}{2} (J_2+\zeta),$">|; 

$key = q/displaystyleepsilon_i=frac{m_i}{M}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2643.png"
 ALT="$\displaystyle \epsilon_i = \frac{m_i}{M}.$">|; 

$key = q/displaystyleepsilon_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2558.png"
 ALT="$\displaystyle \epsilon_{ij}$">|; 

$key = q/displaystyleequiv-alpha,b_{3slash2}^{(2)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2510.png"
 ALT="$\displaystyle \equiv- \alpha b_{3/2}^{(2)}.$">|; 

$key = q/displaystyleequivalpha,b_{3slash2}^{(1)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2508.png"
 ALT="$\displaystyle \equiv \alpha b_{3/2}^{(1)},$">|; 

$key = q/displaystyleequivcos[j,(varpi+theta)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5019.png"
 ALT="$\displaystyle \equiv \cos[j (\varpi+\theta)]$">|; 

$key = q/displaystyleequivcosomega,costheta-sinomega,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4983.png"
 ALT="$\displaystyle \equiv \cos\omega \cos \theta - \sin\omega \sin \theta$">|; 

$key = q/displaystyleequivfrac{r}{a}-1simeq-e,cos,{calM}+frac{e^{,2}}{2},(1-cos,2{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4978.png"
 ALT="$\displaystyle \equiv \frac{r}{a}-1 \simeq - e \cos {\cal M}+ \frac{e^{ 2}}{2} (1-\cos 2{\cal M})$">|; 

$key = q/displaystyleequivr^{,2},skew{5}dot{theta}=(1-e^{,2})^{1slash2},(mu,a)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2745.png"
 ALT="$\displaystyle \equiv r^{ 2} \skew{5}\dot{\theta} = (1-e^{ 2})^{1/2} (\mu a)^{1/2}.$">|; 

$key = q/displaystyleequivsin[j,(varpi+theta)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5024.png"
 ALT="$\displaystyle \equiv \sin[j (\varpi+\theta)]$">|; 

$key = q/displaystyleequivsinomega,costheta+cosomega,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4987.png"
 ALT="$\displaystyle \equiv \sin\omega \cos \theta + \cos\omega \sin \theta$">|; 

$key = q/displaystyleeta(a)=eta_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4414.png"
 ALT="$\displaystyle \eta(a)=\eta_0,$">|; 

$key = q/displaystyleeta=eta_o+eta_p,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3737.png"
 ALT="$\displaystyle \eta = \eta_o + \eta_p,
$">|; 

$key = q/displaystyleeta=frac{a}{epsilon},frac{depsilon}{da}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4379.png"
 ALT="$\displaystyle \eta = \frac{a}{\epsilon} \frac{d\epsilon}{da}.$">|; 

$key = q/displaystyleeta=theta-phi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1849.png"
 ALT="$\displaystyle \eta = \theta-\phi,$">|; 

$key = q/displaystyleeta_0=-2+frac{15}{2},frac{zeta}{epsilon_0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4403.png"
 ALT="$\displaystyle \eta_0 = -2+\frac{15}{2} \frac{\zeta}{\epsilon_0},$">|; 

$key = q/displaystyleeta_0=frac{alpha,(10-alpha)}{(5-alpha)^2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4415.png"
 ALT="$\displaystyle \eta_0 =\frac{\alpha (10-\alpha)}{(5-\alpha)^2}.$">|; 

$key = q/displaystyleeta_psimeqsum_{i=1,5}A_i',sin(n_i,t-gamma_i),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img3760.png"
 ALT="$\displaystyle \eta_p \simeq \sum_{i=1,5} A_i' \sin(n_i t-\gamma_i),
$">|; 

$key = q/displaystyleetasimeq2,e,sin{calM}+gamma_0,sin(n_0,t-varphi_0)+2,e,frac{alpha^{,2}}{1-alpha^{,2}},sin{calM}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1924.png"
 ALT="$\displaystyle \eta \simeq 2 e \sin {\cal M}+ \gamma_0 \sin(n_0 t-\varphi_0) + 2 e \frac{\alpha^{ 2}}{1-\alpha^{ 2}} \sin {\cal M}.$">|; 

$key = q/displaystyleetasimeq2,e,sin{calM}-gamma,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1923.png"
 ALT="$\displaystyle \eta \simeq 2 e \sin {\cal M} - \gamma,$">|; 

$key = q/displaystylef(0)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle f(0) = 0,$">|; 

$key = q/displaystylef(r)=-c,r^{,n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img969.png"
 ALT="$\displaystyle f(r) = -c r^{ n},$">|; 

$key = q/displaystylef(r)=-frac{k}{r^{,2}}+frac{c}{r^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1041.png"
 ALT="$\displaystyle f(r)=-\frac{k}{r^{ 2}} + \frac{c}{r^{ 3}},
$">|; 

$key = q/displaystylef(r)=-frac{mu}{r^{,2}},{rme}^{-k,r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1051.png"
 ALT="$\displaystyle f(r)= -\frac{\mu}{r^{ 2}} {\rm e}^{-k r},
$">|; 

$key = q/displaystylef(r_c)+frac{r_c}{3},f'(r_c)<0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.13ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img968.png"
 ALT="$\displaystyle f(r_c) + \frac{r_c}{3} f'(r_c)&lt;0.$">|; 

$key = q/displaystylef(t)=frac{p_0,deltat}{pi},frac{1}{(t-t_0)^{,2}+(deltat)^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img305.png"
 ALT="$\displaystyle f(t) = \frac{p_0 \delta t}{\pi}  \frac{1}{(t-t_0)^{ 2} + (\delta t)^{ 2}}.
$">|; 

$key = q/displaystylef(t,x_1,t,x_2,cdots,t,x_n)=t^{,a},f(x_1,x_2,cdots,x_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img538.png"
 ALT="$\displaystyle f(t x_1, t x_2,\cdots,t x_n) = t^{ a} f(x_1,x_2,\cdots,x_n)
$">|; 

$key = q/displaystylef(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3804.png"
 ALT="$\displaystyle f(x)$">|; 

$key = q/displaystylef(x)=-frac{dU(x)}{dx},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img193.png"
 ALT="$\displaystyle f(x) = - \frac{dU(x)}{dx},$">|; 

$key = q/displaystylef(x)=-k,x+frac{a}{x^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img309.png"
 ALT="$\displaystyle f(x) = -k x+\frac{a}{x^{ 3}},
$">|; 

$key = q/displaystylef(x)simeq-m,omega_0^{,2},x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img234.png"
 ALT="$\displaystyle f(x) \simeq - m \omega_0^{ 2} x,$">|; 

$key = q/displaystylef(x)simeqf(0)+frac{df(0)}{dx},x+{calO}(x^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle f(x) \simeq f(0) + \frac{df(0)}{dx} x + {\cal O}(x^{ 2}).$">|; 

$key = q/displaystylef_j=-frac{partialU}{partialx_j},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img1389.png"
 ALT="$\displaystyle f_j = -\frac{\partial U}{\partial x_j},$">|; 

$key = q/displaystylef_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1823.png"
 ALT="$\displaystyle f_x$">|; 

$key = q/displaystylef_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1825.png"
 ALT="$\displaystyle f_y$">|; 

$key = q/displaystylef_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1827.png"
 ALT="$\displaystyle f_z$">|; 

$key = q/displaystylefrac{(x-x_c)^2}{a^{,2}}+frac{y^{,2}}{b^{,2}}=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4004.png"
 ALT="$\displaystyle \frac{(x-x_c)^2}{a^{ 2}} + \frac{y^{ 2}}{b^{ 2}} = 1,$">|; 

$key = q/displaystylefrac{(x-x_c)^2}{a^{,2}}-frac{y^{,2}}{b^{,2}}=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4017.png"
 ALT="$\displaystyle \frac{(x-x_c)^2}{a^{ 2}} - \frac{y^{ 2}}{b^{ 2}} = 1,$">|; 

$key = q/displaystylefrac{15}{4},m,e,sin(2,D-{calM}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3687.png"
 ALT="$\displaystyle \frac{15}{4} m e \sin(2 D-{\cal M}),
$">|; 

$key = q/displaystylefrac{1}{2,a}+sqrt{a,(1-e^{,2})},cosI=frac{1}{2,a'}+sqrt{a',(1-e'^{,2})},cosI'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2135.png"
 ALT="$\displaystyle \frac{1}{2 a} + \sqrt{a (1-e^{ 2})} \cos I = \frac{1}{2 a'} + \sqrt{a' (1-e'^{ 2})} \cos I'.$">|; 

$key = q/displaystylefrac{1}{2,r_p},(1-e)+sqrt{(1+e),r_p},cosIsimeqfrac{1}{2,a'}+sqrt{(1-e'^{,2}),a'},cosI',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2312.png"
 ALT="$\displaystyle \frac{1}{2 r_p}  (1-e)+\sqrt{(1+e) r_p} \cos I \simeq \frac{1}{2 a'} + \sqrt{(1-e'^{ 2}) a'} \cos I',
$">|; 

$key = q/displaystylefrac{1}{2},frac{partialskew{3}dot{x}_j^{,2}}{partialq_i}=skew{3}dot{x}_j,frac{partialskew{3}dot{x}_j}{partialq_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img1405.png"
 ALT="$\displaystyle \frac{1}{2} \frac{\partial \skew{3}\dot{x}_j^{ 2}}{\partial q_i}
= \skew{3}\dot{x}_j \frac{\partial \skew{3}\dot{x}_j}{\partial q_i}$">|; 

$key = q/displaystylefrac{1}{2}frac{d^{,2}{calI}}{dt^{,2}}=2,K+(n-1),U,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img550.png"
 ALT="$\displaystyle \frac{1}{2}\frac{d^{ 2} {\cal I}}{dt^{ 2}} = 2 K + (n-1) U,
$">|; 

$key = q/displaystylefrac{1}{2}left(frac{dgamma}{dt}right)^2-frac{1}{4},n_0^{,2},cos2gammasimeqfrac{1}{4},n_0^{,2},{calE},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1892.png"
 ALT="$\displaystyle \frac{1}{2}\left(\frac{d\gamma}{dt}\right)^2 - \frac{1}{4} n_0^{ 2} \cos 2\gamma \simeq\frac{1}{4} n_0^{ 2} {\cal E},$">|; 

$key = q/displaystylefrac{1}{3}left(frac{2,R}{g}right)^{1slash2},left[left(1+frac{h}{R}right)^{3slash2}-1right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img529.png"
 ALT="$\displaystyle \frac{1}{3}\left(\frac{2 R}{g}\right)^{1/2} \left[\left(1+\frac{h}{R}\right)^{3/2}-1\right],
$">|; 

$key = q/displaystylefrac{1}{sqrt{1-2,x,t+t^{,2}}}=sum_{n=0,infty}t^{,n},P_n(x),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2995.png"
 ALT="$\displaystyle \frac{1}{\sqrt{1-2 x t+t^{ 2}}}=\sum_{n=0,\infty}t^{ n}  P_n(x),$">|; 

$key = q/displaystylefrac{2^{1slash2}}{3pi}left(frac{2,r_p}{a}+1right)left(1-frac{r_p}{a}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img925.png"
 ALT="$\displaystyle \frac{2^{1/2}}{3\pi}\left(\frac{2 r_p}{a}+1\right)\left(1-\frac{r_p}{a}\right)^{1/2}
$">|; 

$key = q/displaystylefrac{3}{2},J_2,nleft(frac{R}{a}right)^2cosI.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2085.png"
 ALT="$\displaystyle \frac{3}{2} J_2 n \left(\frac{R}{a}\right)^2\cos I.
$">|; 

$key = q/displaystylefrac{3}{8},m,I,sin(2,D-F),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3690.png"
 ALT="$\displaystyle \frac{3}{8} m I \sin(2 D-F),
$">|; 

$key = q/displaystylefrac{8}{9}leqAleq1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img2294.png"
 ALT="$\displaystyle \frac{8}{9}\leq A \leq 1.$">|; 

$key = q/displaystylefrac{G,m}{a^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4575.png"
 ALT="$\displaystyle \frac{G m}{a^{ 3}}$">|; 

$key = q/displaystylefrac{J_2}{epsilon_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4407.png"
 ALT="$\displaystyle \frac{J_2}{\epsilon_0}$">|; 

$key = q/displaystylefrac{L,A}{2pi,m,c,mu}ll1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2841.png"
 ALT="$\displaystyle \frac{L A}{2\pi m c \mu}\ll 1,$">|; 

$key = q/displaystylefrac{R_e-R_p}{R}=frac{5}{4},frac{{mitOmega}^{,2},R^{,3}}{G,M}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1168.png"
 ALT="$\displaystyle \frac{R_e-R_p}{R} = \frac{5}{4} \frac{{\mit\Omega}^{ 2} R^{ 3}}{G M}.$">|; 

$key = q/displaystylefrac{X}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4990.png"
 ALT="$\displaystyle \frac{X}{r}$">|; 

$key = q/displaystylefrac{Y}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4994.png"
 ALT="$\displaystyle \frac{Y}{r}$">|; 

$key = q/displaystylefrac{Z}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4998.png"
 ALT="$\displaystyle \frac{Z}{r}$">|; 

$key = q/displaystylefrac{d(r^{,2},skew{5}dot{theta})}{dt}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img606.png"
 ALT="$\displaystyle \frac{d(r^{ 2} \skew{5}\dot{\theta})}{dt} = 0,$">|; 

$key = q/displaystylefrac{dA}{dt}=lim_{deltatrightarrow0}frac{r^{,2},deltatheta}{2,delta{t}}=frac{r^{,2}}{2},frac{dtheta}{dt}=frac{h}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.70ex; " SRC="|."$dir".q|img613.png"
 ALT="$\displaystyle \frac{dA}{dt} = \lim_{\delta t\rightarrow 0}\frac{r^{ 2} \delta\theta}{2 \delta{t}}= \frac{r^{ 2}}{2} \frac{d\theta}{dt} = \frac{h}{2}.$">|; 

$key = q/displaystylefrac{dC}{dt}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2122.png"
 ALT="$\displaystyle \frac{dC}{dt} = 0.$">|; 

$key = q/displaystylefrac{dE}{d{calM}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.72ex; " SRC="|."$dir".q|img4063.png"
 ALT="$\displaystyle \frac{dE}{d{\cal M}}$">|; 

$key = q/displaystylefrac{dI}{d(n,t)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2900.png"
 ALT="$\displaystyle \frac{dI}{d(n t)}$">|; 

$key = q/displaystylefrac{dI}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2699.png"
 ALT="$\displaystyle \frac{dI}{dt}$">|; 

$key = q/displaystylefrac{dK}{dt}={bff}cdot{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \frac{d K}{dt} = {\bf f}\cdot {\bf v}.$">|; 

$key = q/displaystylefrac{dU}{dx}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img204.png"
 ALT="$\displaystyle \frac{dU}{dx} = 0.$">|; 

$key = q/displaystylefrac{dU}{dx}=frac{d^{,2}U}{dx^{,2}}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle \frac{dU}{dx}=\frac{d^{ 2} U}{dx^{ 2}}=0$">|; 

$key = q/displaystylefrac{dV}{du}=-h^{,2}left(6,r_0,u^{,2}+uright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img952.png"
 ALT="$\displaystyle \frac{d V}{du} = - h^{ 2}\left(6 r_0 u^{ 2} + u\right).$">|; 

$key = q/displaystylefrac{dX}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4652.png"
 ALT="$\displaystyle \frac{dX}{dt}$">|; 

$key = q/displaystylefrac{dX}{dt}=frac{partialf_1}{partialt}+sum_{k=1,6}frac{partialf_1}{partialc_k}frac{dc_k}{dt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4647.png"
 ALT="$\displaystyle \frac{dX}{dt} = \frac{\partial f_1}{\partial t} + \sum_{k=1,6}\frac{\partial f_1}{\partial c_k}\frac{d c_k}{dt}.$">|; 

$key = q/displaystylefrac{dY}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4654.png"
 ALT="$\displaystyle \frac{dY}{dt}$">|; 

$key = q/displaystylefrac{dZ}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4656.png"
 ALT="$\displaystyle \frac{dZ}{dt}$">|; 

$key = q/displaystylefrac{d^{,2}U}{dx^{,2}}>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img212.png"
 ALT="$\displaystyle \frac{d^{ 2} U}{dx^{ 2}}&gt;0.$">|; 

$key = q/displaystylefrac{d^{,2}X}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4658.png"
 ALT="$\displaystyle \frac{d^{ 2}X}{dt^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}Y}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4660.png"
 ALT="$\displaystyle \frac{d^{ 2}Y}{dt^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}Z}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4662.png"
 ALT="$\displaystyle \frac{d^{ 2}Z}{dt^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}epsilon}{da^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4382.png"
 ALT="$\displaystyle \frac{d^{ 2}\epsilon}{d a^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}gamma}{dt^{,2}}+n_0^{,2},gammasimeq2,e,n_0^{,2},sin(n,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1916.png"
 ALT="$\displaystyle \frac{d^{ 2}\gamma}{dt^{ 2}} +n_0^{ 2} \gamma \simeq 2 e  n_0^{ 2} \sin (n t),$">|; 

$key = q/displaystylefrac{d^{,2}gamma}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1879.png"
 ALT="$\displaystyle \frac{d^{ 2}\gamma}{dt^{ 2}}$">|; 

$key = q/displaystylefrac{d^{,2}gamma}{dt^{,2}}simeq-frac{1}{2},n_0^{,2},sin2gamma.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1883.png"
 ALT="$\displaystyle \frac{d^{ 2}\gamma}{dt^{ 2}} \simeq -\frac{1}{2} n_0^{ 2} \sin 2\gamma.$">|; 

$key = q/displaystylefrac{d^{,2}gamma}{dt^{,2}}simeq-frac{7,e}{4},n_0^{,2},sin2gamma.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1889.png"
 ALT="$\displaystyle \frac{d^{ 2}\gamma}{dt^{ 2}} \simeq -\frac{7 e}{4} n_0^{ 2} \sin 2\gamma.$">|; 

$key = q/displaystylefrac{d^{,2}gamma}{dt^{,2}}simeqfrac{e}{4},n_0^{,2},sin2gamma.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1887.png"
 ALT="$\displaystyle \frac{d^{ 2}\gamma}{dt^{ 2}} \simeq \frac{e}{4} n_0^{ 2} \sin 2\gamma.$">|; 

$key = q/displaystylefrac{d^{,2}theta}{dt^{,2}}-omega^{,2},sintheta,costheta=-frac{g}{l},sintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1454.png"
 ALT="$\displaystyle \frac{d^{ 2}\theta}{dt^{ 2}} -\omega^{ 2} \sin\theta \cos\theta = -\frac{g}{l} \sin\theta,
$">|; 

$key = q/displaystylefrac{d^{,2}u}{dtheta^{,2}}+u=-frac{1}{h^{,2}}frac{dV}{du},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img949.png"
 ALT="$\displaystyle \frac{d^{ 2} u}{d\theta^{ 2}} + u = - \frac{1}{h^{ 2}}\frac{dV}{du},$">|; 

$key = q/displaystylefrac{d^{,2}u}{dtheta^{,2}}+u=frac{G,M}{h^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img620.png"
 ALT="$\displaystyle \frac{d^{ 2} u}{d\theta^{ 2}} + u = \frac{G M}{h^{ 2}}.$">|; 

$key = q/displaystylefrac{d^{,2}x}{dt^{,2}}+omega_0^{,2},xsimeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle \frac{d^{ 2} x}{dt^{ 2}}+ \omega_0^{ 2} x\simeq 0,$">|; 

$key = q/displaystylefrac{d^{,2}x}{dt^{,2}}simeqk^{,2},x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img253.png"
 ALT="$\displaystyle \frac{d^{ 2}x}{dt^{ 2}} \simeq k^{ 2} x,$">|; 

$key = q/displaystylefrac{d^{,2}{bfr}}{dt^{,2}}=-frac{G,M}{r^{,3}},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img852.png"
 ALT="$\displaystyle \frac{d^{ 2}{\bf r}}{dt^{ 2}} =-
\frac{G M}{r^{ 3}}  {\bf r},$">|; 

$key = q/displaystylefrac{d^{,2}{bfr}}{dt^{,2}}=-frac{G,M}{r^{,3}},{bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img574.png"
 ALT="$\displaystyle \frac{d^{ 2}{\bf r}}{dt^{ 2}} = -\frac{G M}{r^{ 3}} {\bf r}.$">|; 

$key = q/displaystylefrac{d^{,2}{calI}}{dt^{,2}}=-2,U+c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img563.png"
 ALT="$\displaystyle \frac{d^{ 2} {\cal I}}{dt^{ 2}} = -2 U + c,
$">|; 

$key = q/displaystylefrac{da^{(1)'}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2474.png"
 ALT="$\displaystyle \frac{d a^{(1)'}}{dt}$">|; 

$key = q/displaystylefrac{da^{(1)}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2441.png"
 ALT="$\displaystyle \frac{d a^{(1)}}{dt}$">|; 

$key = q/displaystylefrac{da^{,2}}{dt}=-frac{L,A}{pi,m,c^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2851.png"
 ALT="$\displaystyle \frac{d a^{ 2}}{dt} = -\frac{L A}{\pi m c^{ 2}}.$">|; 

$key = q/displaystylefrac{dalpha_n}{dt}=-{mitOmega}_n,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1755.png"
 ALT="$\displaystyle \frac{d\alpha_n}{dt}= -{\mit\Omega}_n,$">|; 

$key = q/displaystylefrac{da}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2693.png"
 ALT="$\displaystyle \frac{da}{dt}$">|; 

$key = q/displaystylefrac{deltaR_x}{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1353.png"
 ALT="$\displaystyle \frac{\delta R_x}{R}$">|; 

$key = q/displaystylefrac{deltaR_y-deltaR_z}{deltaR_x-deltaR_z}=frac{1}{4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1361.png"
 ALT="$\displaystyle \frac{\delta R_y-\delta R_z}{\delta R_x-\delta R_z} = \frac{1}{4}.$">|; 

$key = q/displaystylefrac{deltaR_y}{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1355.png"
 ALT="$\displaystyle \frac{\delta R_y}{R}$">|; 

$key = q/displaystylefrac{deltaR_z}{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1356.png"
 ALT="$\displaystyle \frac{\delta R_z}{R}$">|; 

$key = q/displaystylefrac{delta_2}{a}=-frac{5}{19},frac{X_2}{mu}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4311.png"
 ALT="$\displaystyle \frac{\delta_2}{a} = -\frac{5}{19} \frac{X_2}{\mu}.$">|; 

$key = q/displaystylefrac{depsilon}{deta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4380.png"
 ALT="$\displaystyle \frac{d\epsilon}{d\eta}$">|; 

$key = q/displaystylefrac{de}{d(n,t)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2898.png"
 ALT="$\displaystyle \frac{de}{d(n t)}$">|; 

$key = q/displaystylefrac{de}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2697.png"
 ALT="$\displaystyle \frac{de}{dt}$">|; 

$key = q/displaystylefrac{df(0)}{dx}<0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle \frac{d f(0)}{dx} &lt; 0.$">|; 

$key = q/displaystylefrac{df(0)}{dx}>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle \frac{d f(0)}{dx} &gt; 0.$">|; 

$key = q/displaystylefrac{dh'}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2478.png"
 ALT="$\displaystyle \frac{dh'}{dt}$">|; 

$key = q/displaystylefrac{dh_i}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2563.png"
 ALT="$\displaystyle \frac{dh_i}{dt}$">|; 

$key = q/displaystylefrac{dh}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2445.png"
 ALT="$\displaystyle \frac{dh}{dt}$">|; 

$key = q/displaystylefrac{dk'}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2480.png"
 ALT="$\displaystyle \frac{dk'}{dt}$">|; 

$key = q/displaystylefrac{dk_i}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2565.png"
 ALT="$\displaystyle \frac{dk_i} {dt}$">|; 

$key = q/displaystylefrac{dk}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2447.png"
 ALT="$\displaystyle \frac{dk}{dt}$">|; 

$key = q/displaystylefrac{dlna}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4886.png"
 ALT="$\displaystyle \frac{d \ln a}{dt}$">|; 

$key = q/displaystylefrac{dl}{dt'}+omega,m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4502.png"
 ALT="$\displaystyle \frac{dl}{dt'} + \omega m$">|; 

$key = q/displaystylefrac{dmbox{boldmathnu}}{dt}+mbox{boldmathomega}timesmbox{boldmathnu}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1992.png"
 ALT="$\displaystyle \frac{d\mbox{\boldmath$\nu$}}{dt} + \mbox{\boldmath$\omega$}\times \mbox{\boldmath$\nu$}= {\bf0}.$">|; 

$key = q/displaystylefrac{dm}{dt'}-omega,l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4503.png"
 ALT="$\displaystyle \frac{dm}{dt'}-\omega l$">|; 

$key = q/displaystylefrac{domega_{x'}}{dt'}+{mitOmega},omega_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1577.png"
 ALT="$\displaystyle \frac{d\omega_{x'}}{dt'} + {\mit\Omega} \omega_{y'}$">|; 

$key = q/displaystylefrac{domega_{y'}}{dt'}-{mitOmega},omega_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1578.png"
 ALT="$\displaystyle \frac{d\omega_{y'}}{dt'} - {\mit\Omega} \omega_{x'}$">|; 

$key = q/displaystylefrac{domega_{z'}}{dt'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1575.png"
 ALT="$\displaystyle \frac{d\omega_{z'}}{dt'}$">|; 

$key = q/displaystylefrac{domega}{d(n,t)}=frac{3,J_2}{4}left(frac{R}{a}right)^2frac{(5,cos^2I-1)}{(1-e^{,2})^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2902.png"
 ALT="$\displaystyle \frac{d\omega}{d(n t)} = \frac{3 J_2}{4}\left(\frac{R}{a}\right)^2\frac{(5 \cos^2 I-1)}{(1-e^{ 2})^{ 2}},
$">|; 

$key = q/displaystylefrac{domega}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2701.png"
 ALT="$\displaystyle \frac{d\omega}{dt}$">|; 

$key = q/displaystylefrac{dp'}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2482.png"
 ALT="$\displaystyle \frac{dp'}{dt}$">|; 

$key = q/displaystylefrac{dp_i}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2567.png"
 ALT="$\displaystyle \frac{dp_i}{dt}$">|; 

$key = q/displaystylefrac{dp_i}{dt}=frac{partial{calL}}{partialq_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img1444.png"
 ALT="$\displaystyle \frac{d p_i}{dt} = \frac{\partial {\cal L}}{\partial q_i},$">|; 

$key = q/displaystylefrac{dp_k}{dt}=frac{partial{calL}}{partialq_k}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img1446.png"
 ALT="$\displaystyle \frac{d p_k}{dt} = \frac{\partial {\cal L}}{\partial q_k}=0.$">|; 

$key = q/displaystylefrac{dp}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2449.png"
 ALT="$\displaystyle \frac{dp}{dt}$">|; 

$key = q/displaystylefrac{dq'}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2484.png"
 ALT="$\displaystyle \frac{dq'}{dt}$">|; 

$key = q/displaystylefrac{dq_i}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2569.png"
 ALT="$\displaystyle \frac{dq_i} {dt}$">|; 

$key = q/displaystylefrac{dq}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2451.png"
 ALT="$\displaystyle \frac{dq}{dt}$">|; 

$key = q/displaystylefrac{dskew{5}bar{lambda}^{(1)'}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2476.png"
 ALT="$\displaystyle \frac{d\skew{5}\bar{\lambda}^{(1)'}}{dt}$">|; 

$key = q/displaystylefrac{dskew{5}bar{lambda}^{(1)}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2443.png"
 ALT="$\displaystyle \frac{d\skew{5}\bar{\lambda}^{(1)}}{dt}$">|; 

$key = q/displaystylefrac{dskew{5}bar{lambda}_0}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4836.png"
 ALT="$\displaystyle \frac{d\skew{5}\bar{\lambda}_0}{dt}$">|; 

$key = q/displaystylefrac{dskew{5}bar{lambda}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4850.png"
 ALT="$\displaystyle \frac{d\skew{5}\bar{\lambda}}{dt}$">|; 

$key = q/displaystylefrac{dtheta}{dt}=frac{h}{r^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img856.png"
 ALT="$\displaystyle \frac{d\theta}{dt} = \frac{h}{r^{ 2}},$">|; 

$key = q/displaystylefrac{dtheta}{dt}simeq2,{mitOmega},sinlambda.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1147.png"
 ALT="$\displaystyle \frac{d\theta}{dt} \simeq 2 {\mit\Omega} \sin\lambda.$">|; 

$key = q/displaystylefrac{dtheta}{d{calM}}=(1-e^{,2})^{1slash2}left(frac{a}{r}right)^2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.72ex; " SRC="|."$dir".q|img4061.png"
 ALT="$\displaystyle \frac{d\theta}{d{\cal M}} = (1-e^{ 2})^{1/2}\left(\frac{a}{r}\right)^2,$">|; 

$key = q/displaystylefrac{dvarpi}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4841.png"
 ALT="$\displaystyle \frac{d\varpi}{d t}$">|; 

$key = q/displaystylefrac{d{bfL}}{dt'}={bfL}times;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4501.png"
 ALT="$\displaystyle \frac{d{\bf L}}{dt'} = {\bf L}\times$">|; 

$key = q/displaystylefrac{d{bfL}}{dt}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle \frac{d{\bf L}}{dt} =$">|; 

$key = q/displaystylefrac{d{bfL}}{dt}=frac{d{bfL}}{dt'}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1554.png"
 ALT="$\displaystyle \frac{d{\bf L}}{dt} = \frac{d{\bf L}}{dt'} +$">|; 

$key = q/displaystylefrac{d{bfL}}{dt}=sum_{i,j=1,N}^{ineqj}{bfr}_itimes{bff}_{ij}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle \frac{d {\bf L}}{dt} = \sum_{i,j = 1,N}^{i\neq j} {\bf r}_i\times {\bf f}_{ij}.$">|; 

$key = q/displaystylefrac{d{bfL}}{dt}={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle \frac{d {\bf L}}{dt} = {\bf0}.$">|; 

$key = q/displaystylefrac{d{bfP}}{dt}={bfF},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle \frac{d{\bf P}}{dt} = {\bf F},$">|; 

$key = q/displaystylefrac{d{bfp}}{dt}={bff},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle \frac{d{\bf p}}{dt} = {\bf f},$">|; 

$key = q/displaystylefrac{d{bfr}_i}{dt}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1491.png"
 ALT="$\displaystyle \frac{d{\bf r}_i}{dt} =$">|; 

$key = q/displaystylefrac{d{bfr}_{cm}}{dt}=frac{sum_{i=1,N}m_i,d{bfr}_islashdt}{sum_{i=1,N}m_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle \frac{d{\bf r}_{cm} }{dt}= \frac{\sum_{i=1,N} m_i  d{\bf r}_i/dt}{\sum_{i=1,N} m_i},$">|; 

$key = q/displaystylefrac{d{bfr}}{dt}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1064.png"
 ALT="$\displaystyle \frac{d{\bf r}}{dt} =$">|; 

$key = q/displaystylefrac{d{bfr}}{dt}=frac{d{bfr}}{dt'}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1071.png"
 ALT="$\displaystyle \frac{d{\bf r}}{dt} = \frac{d{\bf r}}{dt'}+$">|; 

$key = q/displaystylefrac{d{bfr}}{dt}={bfv}'+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1067.png"
 ALT="$\displaystyle \frac{d{\bf r}}{dt} = {\bf v}'+$">|; 

$key = q/displaystylefrac{d{calM}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2695.png"
 ALT="$\displaystyle \frac{d{\cal M}}{dt}$">|; 

$key = q/displaystylefrac{d{calM}}{dt}=nleft[1+frac{3,J_2}{2}left(frac{R}{a}right)^2(1-e^{,2})^{-3slash2}left(1-frac{3}{2},sin^2Iright)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2723.png"
 ALT="$\displaystyle \frac{d{\cal M}}{dt} =n\left[1+\frac{3 J_2}{2}\left(\frac{R}{a}\right)^2(1-e^{ 2})^{-3/2}\left(1-\frac{3}{2} \sin^2 I\right)\right].$">|; 

$key = q/displaystylefrac{d{mitOmega}}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2703.png"
 ALT="$\displaystyle \frac{d{\mit\Omega}}{dt}$">|; 

$key = q/displaystylefrac{d}{da}left[bar{rho},a^{,5},(1+eta)^{1slash2}right]=5,bar{rho},a^{,4},psi(eta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4387.png"
 ALT="$\displaystyle \frac{d}{da}\left[\bar{\rho} a^{ 5} (1+\eta)^{1/2}\right] = 5 \bar{\rho} a^{ 4} \psi(\eta),$">|; 

$key = q/displaystylefrac{d}{da}left[bar{rho},a^{,5},(1+eta)^{1slash2}right]simeq5,bar{rho},a^{,4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4394.png"
 ALT="$\displaystyle \frac{d}{da}\left[\bar{\rho} a^{ 5} (1+\eta)^{1/2}\right] \simeq 5 \bar{\rho} a^{ 4},$">|; 

$key = q/displaystylefrac{d}{dr}left(p_0+rho,{mitPhi}_0right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4269.png"
 ALT="$\displaystyle \frac{d}{dr}\left(p_0+\rho {\mit\Phi}_0\right)$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partialK}{partialskew{3}dot{q}_i}right)=-frac{partialU}{partialq_i}+frac{partialK}{partialq_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1412.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial K}{\partial \skew{3}\dot{q}_i}\right) = -\frac{\partial U}{\partial q_i}+\frac{\partial K}{\partial q_i}.$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partialK}{partialskew{3}dot{q}_i}right)=Q_i+frac{partialK}{partialq_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1411.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial K}{\partial \skew{3}\dot{q}_i}\right) = Q_i + \frac{\partial K}{\partial q_i}.$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partial{calL}}{partialdot{r}}right)-frac{partial{calL}}{partialr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1427.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial {\cal L}}{\partial\dot{r}}\right)- \frac{\partial {\cal L}}{\partial r}$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partial{calL}}{partialskew{3}dot{q}_i}right)-frac{partial{calL}}{partialq_i}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1415.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial {\cal L}}{\partial \skew{3}\dot{q}_i}\right) -\frac{\partial {\cal L}}{\partial q_i} =0,$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partial{calL}}{partialskew{5}dot{phi}}right)-frac{partial{calL}}{partialphi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1775.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial {\cal L}}{\partial \skew{5}\dot{\phi}}\right)-\frac{\partial{\cal L}}{\partial \phi}$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partial{calL}}{partialskew{5}dot{theta}}right)-frac{partial{calL}}{partialtheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1429.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial {\cal L}}{\partial\skew{5}\dot{\theta}}\right)- \frac{\partial {\cal L}}{\partial \theta}$">|; 

$key = q/displaystylefrac{d}{dt}!left(frac{partial{calL}}{partialskew{5}dot{theta}}right)-frac{partial{calL}}{partialtheta}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1726.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(\frac{\partial{\cal L}}{\partial \skew{5}\dot{\theta}}\right)- \frac{\partial {\cal L}}{\partial\theta} = 0,$">|; 

$key = q/displaystylefrac{d}{dt}!left(m,dot{r}right)-m,r,skew{5}dot{theta}^{,2}+frac{dU}{dr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1430.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(m \dot{r}\right) - m r \skew{5}\dot{\theta}^{ 2} + \frac{dU}{dr}$">|; 

$key = q/displaystylefrac{d}{dt}!left(m,r^{,2},skew{5}dot{theta}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1431.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left(m r^{ 2} \skew{5}\dot{\theta}\right)$">|; 

$key = q/displaystylefrac{d}{dt}!left[frac{1}{2}left(skew{3}dot{x}^{,2}+skew{3}dot{y}^{,2}+skew{3}dot{z}^{,2}right)+Uright]=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2171.png"
 ALT="$\displaystyle \frac{d}{dt}\!\left[\frac{1}{2}\left(\skew{3}\dot{x}^{ 2}+\skew{3}\dot{y}^{ 2}+\skew{3}\dot{z}^{ 2}\right) + U\right] = 0.$">|; 

$key = q/displaystylefrac{d}{dt}=frac{d}{dt'}+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1073.png"
 ALT="$\displaystyle \frac{d}{dt} =\frac{d}{dt'}+$">|; 

$key = q/displaystylefrac{d}{dt}left(frac{partial{calL}}{partialskew{5}dot{phi}}right)-frac{partial{calL}}{partialphi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4546.png"
 ALT="$\displaystyle \frac{d}{dt}\left(\frac{\partial{\cal L}}{\partial\skew{5}\dot{\phi}}\right)- \frac{\partial{\cal L}}{\partial \phi}$">|; 

$key = q/displaystylefrac{d}{dt}left(frac{partial{calL}}{partialskew{5}dot{theta}}right)-frac{partial{calL}}{partialtheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4545.png"
 ALT="$\displaystyle \frac{d}{dt}\left(\frac{\partial{\cal L}}{\partial\skew{5}\dot{\theta}}\right)-\frac{\partial{\cal L}}{\partial \theta}$">|; 

$key = q/displaystylefrac{d}{dx},cos^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3786.png"
 ALT="$\displaystyle \frac{d}{dx} \cos^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},cosh^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3798.png"
 ALT="$\displaystyle \frac{d}{dx} \cosh^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},coshx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3792.png"
 ALT="$\displaystyle \frac{d}{dx} \cosh x$">|; 

$key = q/displaystylefrac{d}{dx},cosx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3780.png"
 ALT="$\displaystyle \frac{d}{dx} \cos x$">|; 

$key = q/displaystylefrac{d}{dx},lnx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3776.png"
 ALT="$\displaystyle \frac{d}{dx} \ln x$">|; 

$key = q/displaystylefrac{d}{dx},sin^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3784.png"
 ALT="$\displaystyle \frac{d}{dx} \sin^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},sinh^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3796.png"
 ALT="$\displaystyle \frac{d}{dx} \sinh^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},sinhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3790.png"
 ALT="$\displaystyle \frac{d}{dx} \sinh x$">|; 

$key = q/displaystylefrac{d}{dx},sinx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3778.png"
 ALT="$\displaystyle \frac{d}{dx} \sin x$">|; 

$key = q/displaystylefrac{d}{dx},tan^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3788.png"
 ALT="$\displaystyle \frac{d}{dx} \tan^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},tanh^{-1}x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3800.png"
 ALT="$\displaystyle \frac{d}{dx} \tanh^{-1} x$">|; 

$key = q/displaystylefrac{d}{dx},tanhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3794.png"
 ALT="$\displaystyle \frac{d}{dx} \tanh x$">|; 

$key = q/displaystylefrac{d}{dx},tanx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3782.png"
 ALT="$\displaystyle \frac{d}{dx} \tan x$">|; 

$key = q/displaystylefrac{d}{dx},{rme}^x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3774.png"
 ALT="$\displaystyle \frac{d}{dx} {\rm e}^x$">|; 

$key = q/displaystylefrac{f}{n^{,2},a}simleft(frac{n'}{n}right)^2=left(7.48times10^{-2}right)^{,2}=5.6times10^{-3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3026.png"
 ALT="$\displaystyle \frac{f}{n^{ 2} a} \sim \left(\frac{n'}{n}\right)^2= \left(7.48\times 10^{-2}\right)^{ 2} = 5.6\times 10^{-3}.$">|; 

$key = q/displaystylefrac{g'}{n'^{,2},a'}simleft(frac{m_2}{m_1}right)left(frac{a}{a'}right)^{,2}=frac{1}{81.3,(389.2)^{,2}}=8.1times10^{-8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3028.png"
 ALT="$\displaystyle \frac{g'}{n'^{ 2} a'}\sim \left(\frac{m_2}{m_1}\right)\left(\frac{a}{a'}\right)^{ 2} = \frac{1}{81.3 (389.2)^{ 2}}= 8.1\times 10^{-8}.$">|; 

$key = q/displaystylefrac{g}{n^{,2},a}simleft(frac{n'}{n}right)^2left(frac{a}{a'}right)=frac{left(7.48times10^{-2}right)^{,2}}{389.2}=1.4times10^{-5}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.80ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3027.png"
 ALT="$\displaystyle \frac{g}{n^{ 2} a}\sim \left(\frac{n'}{n}\right)^2\left(\frac{a...
...\right)= \frac{\left(7.48\times 10^{-2}\right)^{ 2}}{389.2}=1.4\times 10^{-5}.$">|; 

$key = q/displaystylefrac{m_1,m_2}{m_1+m_2},frac{d^{,2}{bfr}}{dt^{,2}}=-frac{G,m_1,m_2}{r^{,3}},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img851.png"
 ALT="$\displaystyle \frac{m_1 m_2}{m_1+m_2}  \frac{d^{ 2}{\bf r}}{dt^{ 2}} =-
\frac{G m_1 m_2}{r^{ 3}}  {\bf r},$">|; 

$key = q/displaystylefrac{m_2}{m_1+m_2}<0.0385.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2308.png"
 ALT="$\displaystyle \frac{m_2}{m_1+ m_2} &lt; 0.0385.$">|; 

$key = q/displaystylefrac{mbox{boldmathOmega}}{mitOmega}simeql,{bfe}_{x'}+m,{bfe}_{y'}+{bfe}_{z'},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4451.png"
 ALT="$\displaystyle \frac{\mbox{\boldmath$\Omega$}}{\mit\Omega} \simeq l {\bf e}_{x'} + m {\bf e}_{y'}+{\bf e}_{z'},$">|; 

$key = q/displaystylefrac{mu_2}{3,mu_1}=frac{rho_2^{,3},(1+rho_2+rho_2^{,2}slash3)}{(1+rho_2)^2,(1-rho_2^{,3})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2199.png"
 ALT="$\displaystyle \frac{\mu_2}{3 \mu_1} = \frac{\rho_2^{ 3} (1+\rho_2+\rho_2^{ 2}/3)}{(1+\rho_2)^2 (1-\rho_2^{ 3})}.$">|; 

$key = q/displaystylefrac{mu_2}{3,mu_1}=frac{rho_2^{,3},(1-rho_2+rho_2^{,2}slash3)}{(1+rho_2+rho_2^{,2}),(1-rho_2)^3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.44ex; " SRC="|."$dir".q|img2191.png"
 ALT="$\displaystyle \frac{\mu_2}{3 \mu_1} = \frac{\rho_2^{ 3} (1-\rho_2+\rho_2^{ 2}/3)}{(1+\rho_2+\rho_2^{ 2}) (1-\rho_2)^3}.$">|; 

$key = q/displaystylefrac{mu_2}{mu_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2208.png"
 ALT="$\displaystyle \frac{\mu_2}{\mu_1}$">|; 

$key = q/displaystylefrac{mu_2}{mu_1}=frac{(1-rho_1^{,3}),(1+rho_1)^2}{rho_1^{,3},(rho_1^{,2}+3,rho_1+3)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2206.png"
 ALT="$\displaystyle \frac{\mu_2}{\mu_1} = \frac{(1-\rho_1^{ 3}) (1+\rho_1)^2}{\rho_1^{ 3} (\rho_1^{ 2}+3 \rho_1+3)}.$">|; 

$key = q/displaystylefrac{mu}{h},skew{3}dot{e}_Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img5144.png"
 ALT="$\displaystyle \frac{\mu}{h} \skew{3}\dot{e}_Z$">|; 

$key = q/displaystylefrac{partial(X,dot{X})}{partial(p,q)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4729.png"
 ALT="$\displaystyle \frac{\partial(X,\dot{X})}{\partial (p,q)}$">|; 

$key = q/displaystylefrac{partial(Y,dot{Y})}{partial(p,q)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4732.png"
 ALT="$\displaystyle \frac{\partial(Y,\dot{Y})}{\partial (p,q)}$">|; 

$key = q/displaystylefrac{partial(x,dot{x})}{partial(a,e)}+frac{partial(y,dot{y})}{partial(a,e)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4787.png"
 ALT="$\displaystyle \frac{\partial(x,\dot{x})}{\partial(a,e)}+\frac{\partial(y,\dot{y})}{\partial(a,e)}$">|; 

$key = q/displaystylefrac{partial(x,dot{x})}{partial(e,skew{5}bar{lambda}_0-varpi)}+frac{partial(y,dot{y})}{partial(e,skew{5}bar{lambda}_0-varpi)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img4788.png"
 ALT="$\displaystyle \frac{\partial(x,\dot{x})}{\partial(e,\skew{5}\bar{\lambda}_0-\varpi)}+\frac{\partial(y,\dot{y})}{\partial(e,\skew{5}\bar{\lambda}_0-\varpi)}$">|; 

$key = q/displaystylefrac{partial(x,dot{x})}{partial(skew{5}bar{lambda}_0-varpi,a)}+frac{partial(y,dot{y})}{partial(skew{5}bar{lambda}_0-varpi,a)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img4789.png"
 ALT="$\displaystyle \frac{\partial(x,\dot{x})}{\partial(\skew{5}\bar{\lambda}_0-\varpi,a)}+\frac{\partial(y,\dot{y})}{\partial(\skew{5}\bar{\lambda}_0-\varpi,a)}$">|; 

$key = q/displaystylefrac{partialH}{partiala};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4803.png"
 ALT="$\displaystyle \frac{\partial H}{\partial a}$">|; 

$key = q/displaystylefrac{partialH}{partiale};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4805.png"
 ALT="$\displaystyle \frac{\partial H}{\partial e}$">|; 

$key = q/displaystylefrac{partialL}{partiala};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4801.png"
 ALT="$\displaystyle \frac{\partial L}{\partial a}$">|; 

$key = q/displaystylefrac{partialU}{partialrho_1}=frac{partialU}{partialrho_2}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2212.png"
 ALT="$\displaystyle \frac{\partial U}{\partial \rho_1} = \frac{\partial U}{\partial \rho_2} = 0,$">|; 

$key = q/displaystylefrac{partialU}{partialx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2182.png"
 ALT="$\displaystyle \frac{\partial U}{\partial x}$">|; 

$key = q/displaystylefrac{partialU}{partialx}=frac{partialU}{partialy}=frac{partialU}{partialz}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2177.png"
 ALT="$\displaystyle \frac{\partial U}{\partial x} = \frac{\partial U}{\partial y}= \frac{\partial U}{\partial z}=0.$">|; 

$key = q/displaystylefrac{partialU}{partialy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2184.png"
 ALT="$\displaystyle \frac{\partial U}{\partial y}$">|; 

$key = q/displaystylefrac{partialU}{partialz}=left(frac{mu_1}{rho_1^{,3}}+frac{mu_2}{rho_2^{,3}}right)z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2178.png"
 ALT="$\displaystyle \frac{\partial U}{\partial z} = \left(\frac{\mu_1}{\rho_1^{ 3}}+ \frac{\mu_2}{\rho_2^{ 3}}\right) z.$">|; 

$key = q/displaystylefrac{partialU}{partial{bfr}_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2967.png"
 ALT="$\displaystyle \frac{\partial U}{\partial {\bf r}_1}$">|; 

$key = q/displaystylefrac{partialU}{partial{bfr}_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2969.png"
 ALT="$\displaystyle \frac{\partial U}{\partial {\bf r}_2}$">|; 

$key = q/displaystylefrac{partialU}{partial{bfr}_3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img2971.png"
 ALT="$\displaystyle \frac{\partial U}{\partial {\bf r}_3}$">|; 

$key = q/displaystylefrac{partialV}{partialx}=A_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3951.png"
 ALT="$\displaystyle \frac{\partial V}{\partial x} = A_x,$">|; 

$key = q/displaystylefrac{partialX}{partialp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4713.png"
 ALT="$\displaystyle \frac{\partial X}{\partial p}$">|; 

$key = q/displaystylefrac{partialY}{partialp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4715.png"
 ALT="$\displaystyle \frac{\partial Y}{\partial p}$">|; 

$key = q/displaystylefrac{partial^{,2}f_1}{partialt^{,2}}+mu,frac{f_1}{r^{,3}}+sum_{k=1,6}frac{partialg_1}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4664.png"
 ALT="$\displaystyle \frac{\partial^{ 2} f_1}{\partial t^{ 2}} +\mu \frac{f_1}{r^{ 3}} +\sum_{k=1,6} \frac{\partial g_1}{\partial c_k} \frac{d c_k}{dt}$">|; 

$key = q/displaystylefrac{partial^{,2}f_2}{partialt^{,2}}+mu,frac{f_2}{r^{,3}}+sum_{k=1,6}frac{partialg_2}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4665.png"
 ALT="$\displaystyle \frac{\partial^{ 2} f_2}{\partial t^{ 2}}+\mu \frac{f_2}{r^{ 3}}+\sum_{k=1,6} \frac{\partial g_2}{\partial c_k} \frac{d c_k}{dt}$">|; 

$key = q/displaystylefrac{partial^{,2}f_3}{partialt^{,2}}+mu,frac{f_3}{r^{,3}}+sum_{k=1,6}frac{partialg_3}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4666.png"
 ALT="$\displaystyle \frac{\partial^{ 2} f_3}{\partial t^{ 2}}+\mu \frac{f_3}{r^{ 3}}+\sum_{k=1,6} \frac{\partial g_3}{\partial c_k} \frac{d c_k}{dt}$">|; 

$key = q/displaystylefrac{partialdot{X}}{partialp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4717.png"
 ALT="$\displaystyle \frac{\partial \dot{X}}{\partial p}$">|; 

$key = q/displaystylefrac{partialdot{Y}}{partialp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4719.png"
 ALT="$\displaystyle \frac{\partial \dot{Y}}{\partial p}$">|; 

$key = q/displaystylefrac{partialdot{x}}{partial(skew{5}bar{lambda}_0-varpi)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img4775.png"
 ALT="$\displaystyle \frac{\partial\dot{x}}{\partial(\skew{5}\bar{\lambda}_0-\varpi)}$">|; 

$key = q/displaystylefrac{partialdot{y}}{partiala};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4777.png"
 ALT="$\displaystyle \frac{\partial\dot{y}}{\partial a}$">|; 

$key = q/displaystylefrac{partialdot{y}}{partiale};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4779.png"
 ALT="$\displaystyle \frac{\partial\dot{y}}{\partial e}$">|; 

$key = q/displaystylefrac{partialsigma_{ij}}{partialx_j}=rho,frac{partial{mitPhi}}{partialx_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4265.png"
 ALT="$\displaystyle \frac{\partial\sigma_{ij}}{\partial x_j}=\rho \frac{\partial{\mit\Phi}}{\partial x_i}.$">|; 

$key = q/displaystylefrac{partialskew{3}dot{x}_j}{partialskew{3}dot{q}_i}=frac{partialx_j}{partialq_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img1399.png"
 ALT="$\displaystyle \frac{\partial \skew{3}\dot{x}_j}{\partial\skew{3}\dot{q}_i} = \frac{\partial x_j}{\partial q_i},$">|; 

$key = q/displaystylefrac{partialx}{partiala};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4769.png"
 ALT="$\displaystyle \frac{\partial x}{\partial a}$">|; 

$key = q/displaystylefrac{partialx}{partiale};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4771.png"
 ALT="$\displaystyle \frac{\partial x}{\partial e}$">|; 

$key = q/displaystylefrac{partialy}{partial(skew{5}bar{lambda}_0-varpi)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.14ex; " SRC="|."$dir".q|img4773.png"
 ALT="$\displaystyle \frac{\partial y}{\partial (\skew{5}\bar{\lambda}_0-\varpi)}$">|; 

$key = q/displaystylefrac{partial{calG}}{partialI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4811.png"
 ALT="$\displaystyle \frac{\partial {\cal G}}{\partial I}$">|; 

$key = q/displaystylefrac{partial{calG}}{partiala};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4807.png"
 ALT="$\displaystyle \frac{\partial {\cal G}}{\partial a}$">|; 

$key = q/displaystylefrac{partial{calG}}{partiale};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4809.png"
 ALT="$\displaystyle \frac{\partial {\cal G}}{\partial e}$">|; 

$key = q/displaystylefrac{partial{calL}}{partialdot{r}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1419.png"
 ALT="$\displaystyle \frac{\partial {\cal L}}{\partial\dot{r}}$">|; 

$key = q/displaystylefrac{partial{calL}}{partialr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1421.png"
 ALT="$\displaystyle \frac{\partial {\cal L}}{\partial r}$">|; 

$key = q/displaystylefrac{partial{calL}}{partialskew{5}dot{theta}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.85ex; " SRC="|."$dir".q|img1423.png"
 ALT="$\displaystyle \frac{\partial {\cal L}}{\partial \skew{5}\dot{\theta}}$">|; 

$key = q/displaystylefrac{partial{calL}}{partialtheta}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1729.png"
 ALT="$\displaystyle \frac{\partial {\cal L}}{\partial\theta} = 0.$">|; 

$key = q/displaystylefrac{partial{calR}}{partiala};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4847.png"
 ALT="$\displaystyle \frac{\partial {\cal R}}{\partial a}$">|; 

$key = q/displaystylefrac{partial{calR}}{partialr}=-mu',r'left[frac{rslashr'-beta}{(r^{,2}+r'^{,2}-2,r,r',beta)^{3slash2}}+frac{beta}{r'^{,3}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4189.png"
 ALT="$\displaystyle \frac{\partial{\cal R}}{\partial r} =- \mu' r'\left[\frac{r/r'-\beta}{(r^{ 2} + r'^{ 2}-2 r r' \beta)^{3/2}} + \frac{\beta}{r'^{ 3}}\right],$">|; 

$key = q/displaystylefrac{partial{calR}}{partialskew{5}bar{lambda}_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.10ex; " SRC="|."$dir".q|img4845.png"
 ALT="$\displaystyle \frac{\partial {\cal R}}{\partial \skew{5}\bar{\lambda}_0}$">|; 

$key = q/displaystylefrac{partial}{partialx_i}(r,xi_r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4286.png"
 ALT="$\displaystyle \frac{\partial}{\partial x_i}(r \xi_r)$">|; 

$key = q/displaystylefrac{r'}{a'}simeq1-e',cos(n',t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3061.png"
 ALT="$\displaystyle \frac{r'}{a'} \simeq 1 - e' \cos(n' t).$">|; 

$key = q/displaystylefrac{r'}{r_{13}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3000.png"
 ALT="$\displaystyle \frac{r'}{r_{13}}$">|; 

$key = q/displaystylefrac{r'}{r_{23}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img3003.png"
 ALT="$\displaystyle \frac{r'}{r_{23}}$">|; 

$key = q/displaystylefrac{r,f'}{f}simeq-2left(1+frac{3,h^{,2}}{c^{,2},r^{,2}}+cdotsright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1022.png"
 ALT="$\displaystyle \frac{r f'}{f} \simeq - 2\left(1+ \frac{3 h^{ 2}}{c^{ 2} r^{ 2}}+ \cdots\right),$">|; 

$key = q/displaystylefrac{r_1}{r_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2094.png"
 ALT="$\displaystyle \frac{r_1}{r_2}$">|; 

$key = q/displaystylefrac{r_1}{r_2}=frac{(x^{,2}+y^{,2})^{1slash2}}{d-x}=frac{r}{d-r,costheta}=e,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img4000.png"
 ALT="$\displaystyle \frac{r_1}{r_2} = \frac{(x^{ 2}+y^{ 2})^{1/2}}{d-x}= \frac{r}{d-r \cos\theta}=e,$">|; 

$key = q/displaystylefrac{rho}{bar{rho}}=1+frac{1}{3},frac{a}{bar{rho}},frac{dbar{rho}}{da}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4361.png"
 ALT="$\displaystyle \frac{\rho}{\bar{\rho}} =1 +\frac{1}{3} \frac{a}{\bar{\rho}} \frac{d\bar{\rho}}{da}.$">|; 

$key = q/displaystylefrac{r}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img789.png"
 ALT="$\displaystyle \frac{r}{a}$">|; 

$key = q/displaystylefrac{r}{a}=1-e,cosE,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4058.png"
 ALT="$\displaystyle \frac{r}{a} = 1-e \cos E,$">|; 

$key = q/displaystylefrac{skew{3}dot{a}}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2753.png"
 ALT="$\displaystyle \frac{\skew{3}\dot{a}}{a}$">|; 

$key = q/displaystylefrac{skew{3}dot{a}}{a}=frac{2,h}{mu,(1-e^{,2})}left[e,sintheta,F_r+(1+e,costheta),F_thetaright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img5095.png"
 ALT="$\displaystyle \frac{\skew{3}\dot{a}}{a} = \frac{2 h}{\mu (1-e^{ 2})}\left[e \sin\theta F_r + (1+e \cos\theta) F_\theta\right].$">|; 

$key = q/displaystylefrac{skew{3}dot{omega}}{omega}=-frac{3}{2},frac{skew{3}dot{a}}{a}simeq-6.5times10^{-18},{rms}^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1305.png"
 ALT="$\displaystyle \frac{\skew{3}\dot{\omega}}{\omega} = -\frac{3}{2} \frac{\skew{3}\dot{a}}{a} \simeq -6.5\times 10^{-18} {\rm s}^{-1}.$">|; 

$key = q/displaystylefrac{skew{3}hat{nu}_y}{skew{3}hat{nu}_x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2062.png"
 ALT="$\displaystyle \frac{\skew{3}\hat{\nu}_y}{\skew{3}\hat{\nu}_x}$">|; 

$key = q/displaystylefrac{skew{3}hat{nu}_y}{skew{3}hat{nu}_x}=frac{s^{,2}-4,tau}{(1-tau),s}=frac{(1-sigma),s}{s^{,2}-sigma}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2027.png"
 ALT="$\displaystyle \frac{\skew{3}\hat{\nu}_y}{\skew{3}\hat{\nu}_x}= \frac{s^{ 2}-4 \tau}{(1-\tau) s}=\frac{(1-\sigma) s}{s^{ 2}-\sigma}.$">|; 

$key = q/displaystylefrac{skew{5}dot{{mitOmega}}}{{mitOmega}}simeq-8.7times10^{-18},{rms}^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1295.png"
 ALT="$\displaystyle \frac{\skew{5}\dot{{\mit\Omega}}}{{\mit\Omega}} \simeq -8.7\times 10^{-18} {\rm s}^{-1}.$">|; 

$key = q/displaystylefrac{tau}{T}=frac{m}{C_D,2pi,R,A,rho_0},frac{H}{R}left[expleft(frac{h}{H}right)-1right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2919.png"
 ALT="$\displaystyle \frac{\tau}{T} = \frac{m}{C_D 2\pi R A \rho_0} \frac{H}{R}\left[\exp\left(\frac{h}{H}\right)-1\right],
$">|; 

$key = q/displaystylefrac{varv_t}{varv_c}=sqrt{1+e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img659.png"
 ALT="$\displaystyle \frac{\varv_t}{\varv_c} = \sqrt{1+e}.$">|; 

$key = q/displaystylefrac{varv_t}{varv_c}=sqrt{1-e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img662.png"
 ALT="$\displaystyle \frac{\varv_t}{\varv_c} = \sqrt{1-e},$">|; 

$key = q/displaystylefrac{x'}{a'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3030.png"
 ALT="$\displaystyle \frac{x'}{a'}$">|; 

$key = q/displaystylefrac{x^{,2}}{a^{,2}}+frac{y^{,2}}{b^{,2}}=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3985.png"
 ALT="$\displaystyle \frac{x^{ 2}}{a^{ 2}} + \frac{y^{ 2}}{b^{ 2}} = 1,$">|; 

$key = q/displaystylefrac{x^{,2}}{a^{,2}}-frac{y^{,2}}{b^{,2}}=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3991.png"
 ALT="$\displaystyle \frac{x^{ 2}}{a^{ 2}} - \frac{y^{ 2}}{b^{ 2}} = 1,$">|; 

$key = q/displaystylefrac{x_1'}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3056.png"
 ALT="$\displaystyle \frac{x_1'}{a}$">|; 

$key = q/displaystylefrac{y'}{a'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3032.png"
 ALT="$\displaystyle \frac{y'}{a'}$">|; 

$key = q/displaystylefrac{y_1'}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3058.png"
 ALT="$\displaystyle \frac{y_1'}{a}$">|; 

$key = q/displaystylefrac{y_1}{x_1}=-2left(1+frac{3}{4},m^{,2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3566.png"
 ALT="$\displaystyle \frac{y_1}{x_1} =-2\left(1+\frac{3}{4} m^{ 2}\right).$">|; 

$key = q/displaystylefrac{z'}{a'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3034.png"
 ALT="$\displaystyle \frac{z'}{a'}$">|; 

$key = q/displaystylefrac{z_1'}{a'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3060.png"
 ALT="$\displaystyle \frac{z_1'}{a'}$">|; 

$key = q/displaystylefrac{{calI}_parallel}{M,R^{,2}}=frac{J_2}{skew{3}tilde{epsilon}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4604.png"
 ALT="$\displaystyle \frac{{\cal I}_\parallel}{M R^{ 2}}=\frac{J_2}{\skew{3}\tilde{\epsilon}},$">|; 

$key = q/displaystylefrac{{calI}_{yy}-{calI}_{xx}}{{calI}_{zz}}=0.129,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1940.png"
 ALT="$\displaystyle \frac{{\cal I}_{yy}-{\cal I}_{xx}}{{\cal I}_{zz}} = 0.129,$">|; 

$key = q/displaystylefrac{{calI}_{yy}-{calI}_{xx}}{{calI}_{zz}}=2.279times10^{-4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1929.png"
 ALT="$\displaystyle \frac{{\cal I}_{yy}-{\cal I}_{xx}}{{\cal I}_{zz}}= 2.279\times 10^{-4},$">|; 

$key = q/displaystylefrac{{mitDelta}R}{R}=frac{3}{2},frac{m'}{m}left(frac{R}{a}right)^3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1347.png"
 ALT="$\displaystyle \frac{{\mit\Delta} R}{R} = \frac{3}{2} \frac{m'}{m}\left(\frac{R}{a}\right)^3,
$">|; 

$key = q/displaystylefsimeq-frac{G,M}{r^{,2}}-frac{3,G,M,h^{,2}}{c^{,2},r^{,4}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1021.png"
 ALT="$\displaystyle f \simeq -\frac{G M}{r^{ 2}}-\frac{3 G M h^{ 2}}{c^{ 2} r^{ 4}},$">|; 

$key = q/displaystyleg'simeqg-{mitOmega}^{,2},R,cos^2lambdasimeq9.82-0.0338,cos^2lambda,,,{rmm,s}^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1113.png"
 ALT="$\displaystyle g' \simeq g - {\mit\Omega}^{ 2} R \cos^2\lambda \simeq 9.82 - 0.0338 \cos^2\lambda    {\rm m s}^{-2}.$">|; 

$key = q/displaystyleg=frac{3}{4}-frac{9}{32},m+{calO}(m^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3606.png"
 ALT="$\displaystyle g = \frac{3}{4}-\frac{9}{32} m+{\cal O}(m^{ 2}).$">|; 

$key = q/displaystyleg=frac{4pi}{3},G,rho,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4255.png"
 ALT="$\displaystyle g = \frac{4\pi}{3} G \rho a$">|; 

$key = q/displaystyleg_k=frac{partialf_k}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4644.png"
 ALT="$\displaystyle g_k = \frac{\partial f_k}{\partial t},$">|; 

$key = q/displaystyleg_x=G,m',frac{partial}{partialx}!left(frac{1}{|{bfr}'-{bfr}|}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img353.png"
 ALT="$\displaystyle g_x = G m' \frac{\partial}{\partial x}\!\left(\frac{1}{\vert{\bf r}'-{\bf r}\vert}\right),$">|; 

$key = q/displaystyleg_x=G,m',frac{x'-x}{[(x'-x)^2+(y'-y)^2+(z'-z)^2]^{,3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img349.png"
 ALT="$\displaystyle g_x = G m' \frac{x'-x}{[(x'-x)^2+(y'-y)^2+(z'-z)^2]^{ 3/2}},$">|; 

$key = q/displaystyleg_{rmeff}=frac{G,m}{R^{,2}}left(1-2,frac{m'}{m},frac{R^{,3}}{a^{,3}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1325.png"
 ALT="$\displaystyle g_{\rm eff} = \frac{G m}{R^{ 2}}\left(1- 2 \frac{m'}{m} \frac{R^{ 3}}{a^{ 3}}\right).$">|; 

$key = q/displaystylegamma'=g,m=frac{3}{4},m-frac{9}{32},m^{,2}+{calO}(m^{,3}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3654.png"
 ALT="$\displaystyle \gamma' = g m = \frac{3}{4} m - \frac{9}{32} m^{ 2} + {\cal O}(m^{ 3}).$">|; 

$key = q/displaystylegamma(theta,theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4176.png"
 ALT="$\displaystyle \gamma(\theta,\theta')$">|; 

$key = q/displaystylegamma=-gamma_0,sin(n_0,t-varphi_0)-2,e,frac{alpha^{,2}}{1-alpha^{,2}},sin{calM}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1922.png"
 ALT="$\displaystyle \gamma =- \gamma_0 \sin(n_0 t-\varphi_0) - 2 e \frac{\alpha^{ 2}}{1-\alpha^{ 2}} \sin {\cal M}.$">|; 

$key = q/displaystylegamma=-gamma_0,sin(n_0,t-varphi_0)-2,e,frac{n_0^{,2}}{n^{,2}-n_0^{,2}},sin{calM},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img1919.png"
 ALT="$\displaystyle \gamma = -\gamma_0 \sin(n_0 t-\varphi_0) - 2 e \frac{n_0^{ 2}}{n^{ 2}-n_0^{ 2}} \sin {\cal M},$">|; 

$key = q/displaystylegamma=gamma_0-g,m^{,2},T=gamma_0-g,m,n',t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3431.png"
 ALT="$\displaystyle \gamma = \gamma_0 - g m^{ 2} T=\gamma_0-g m n' t,$">|; 

$key = q/displaystylegamma=gamma_0-gamma',n',t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3653.png"
 ALT="$\displaystyle \gamma = \gamma_0 - \gamma' n' t,$">|; 

$key = q/displaystylegamma=phi-p,{calM}=phi-p,n,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1876.png"
 ALT="$\displaystyle \gamma = \phi - p {\cal M}=\phi-p n t,$">|; 

$key = q/displaystylegamma^{,4}+(4+U_{xx}+U_{yy}),gamma^{,2}+(U_{xx},U_{yy}-U_{xy}^{,2})=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img2268.png"
 ALT="$\displaystyle \gamma^{ 4} + (4+U_{xx}+U_{yy}) \gamma^{ 2} + (U_{xx} U_{yy}-U_{xy}^{ 2}) = 0.$">|; 

$key = q/displaystylegamma^{,4}+gamma^{,2}+frac{27}{4},mu_2,(1-mu_2)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2381.png"
 ALT="$\displaystyle \gamma^{ 4} + \gamma^{ 2} + \frac{27}{4} \mu_2 (1-\mu_2)= 0.
$">|; 

$key = q/displaystylegsimeqfrac{G,M}{R^{,2}}+frac{1}{6},{mitOmega}^{,2},R-frac{5}{4},{mitOmega}^{,2},R,cos^2lambda.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1345.png"
 ALT="$\displaystyle g\simeq \frac{G M}{R^{ 2}} + \frac{1}{6} {\mit\Omega}^{ 2} R - \frac{5}{4} {\mit\Omega}^{ 2} R \cos^2\lambda.
$">|; 

$key = q/displaystyleh(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2655.png"
 ALT="$\displaystyle h(t)$">|; 

$key = q/displaystyleh;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2744.png"
 ALT="$\displaystyle h$">|; 

$key = q/displaystyleh=r^{,2},skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img607.png"
 ALT="$\displaystyle h = r^{ 2} \skew{5}\dot{\theta}$">|; 

$key = q/displaystyleh^{,2}=a,(1-e^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2130.png"
 ALT="$\displaystyle h^{ 2} = a (1-e^{ 2}).$">|; 

$key = q/displaystyleh_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4518.png"
 ALT="$\displaystyle h_2$">|; 

$key = q/displaystyleh_2=0.60.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4524.png"
 ALT="$\displaystyle h_2=0.60.$">|; 

$key = q/displaystyleh_2=frac{5slash2}{1+(19slash2),(muslashrho,g,a)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4308.png"
 ALT="$\displaystyle h_2 = \frac{5/2}{1+(19/2)  (\mu/\rho g a)}.$">|; 

$key = q/displaystyleh_2=frac{5slash2}{1+(38pislash3),(mu,R^{,4}slashG,M^{,2})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4513.png"
 ALT="$\displaystyle h_2 = \frac{5/2}{1+(38\pi/3) (\mu R^{ 4}/G M^{ 2})}.$">|; 

$key = q/displaystyleh_X,skew{4}dot{h}_Y-h_Y,skew{3}dot{h}_X=h^{,2},sin^2I,skew{5}dot{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5138.png"
 ALT="$\displaystyle h_X \skew{4}\dot{h}_Y - h_Y \skew{3}\dot{h}_X = h^{ 2} \sin^2 I \skew{5}\dot{\mit\Omega},$">|; 

$key = q/displaystyleh_X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5122.png"
 ALT="$\displaystyle h_X$">|; 

$key = q/displaystyleh_Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5124.png"
 ALT="$\displaystyle h_Y$">|; 

$key = q/displaystyleh_Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5126.png"
 ALT="$\displaystyle h_Z$">|; 

$key = q/displaystyleh_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2579.png"
 ALT="$\displaystyle h_i$">|; 

$key = q/displaystyleh_{rmforced};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2663.png"
 ALT="$\displaystyle h_{\rm forced}$">|; 

$key = q/displaystylehequivr^{,2},skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img646.png"
 ALT="$\displaystyle h\equiv r^{ 2} \skew{5}\dot{\theta}$">|; 

$key = q/displaystylehequivr^{,2},skew{5}dot{theta}=(1-e^{,2})^{1slash2},(mu,a)^{1slash2};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5088.png"
 ALT="$\displaystyle h \equiv r^{ 2} \skew{5}\dot{\theta} = (1-e^{ 2})^{1/2} (\mu a)^{1/2};$">|; 

$key = q/displaystyleindex{force!gravitational}index{gravity}{bff}_{12}=G,m_1,m_2,frac{{bfr}_2-{bfr}_1}{|{bfr}_2-{bfr}_1|^{,3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img341.png"
 ALT="$\displaystyle \index{force!gravitational}\index{gravity}
{\bf f}_{12} = G m_1 m_2 \frac{{\bf r}_2-{\bf r}_1}{\vert{\bf r}_2-{\bf r}_1\vert^{ 3}}.$">|; 

$key = q/displaystyleindex{gravitationalpotential!ofcollectionofpointmasses}{mitPhi}({bfr})=-Gsum_{i=1,N}frac{m_i}{|{bfr}_i-{bfr}|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img359.png"
 ALT="$\displaystyle \index{gravitational potential!of collection of point masses}
{\mit\Phi}({\bf r}) = - G\sum_{i=1,N} \frac{m_i}{\vert{\bf r}_i-{\bf r}\vert}.$">|; 

$key = q/displaystyleindex{orbitalparameter!angularmomentum}{bfh}={bfr}times{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img578.png"
 ALT="$\displaystyle \index{orbital parameter!angular momentum}
{\bf h} = {\bf r}\times {\bf v},$">|; 

$key = q/displaystyleindex{orbitalparameter!apheliondistance}index{aphelion}r_a=frac{r_c}{1-e}=a,(1+e).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img637.png"
 ALT="$\displaystyle \index{orbital parameter!aphelion distance}\index{aphelion}
r_a = \frac{r_c}{1-e} = a (1+e).$">|; 

$key = q/displaystyleindex{orbitalparameter!energy}{calE}=frac{u_c^{,2},h^{,2}}{2},(e^{,2}-1)=frac{G,M}{2,r_p},(e-1).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.58ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img656.png"
 ALT="$\displaystyle \index{orbital parameter!energy}
{\cal E} = \frac{u_c^{ 2} h^{ 2}}{2}  (e^{ 2} -1) = \frac{G M}{2 r_p} (e-1).$">|; 

$key = q/displaystyleint_0^E(1-e,cosE),dE=left(frac{G,M}{a^{,3}}right)^{1slash2}(t-tau),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img689.png"
 ALT="$\displaystyle \int_0^E (1-e \cos E) dE = \left(\frac{G M}{a^{ 3}}\right)^{1/2} (t-\tau),$">|; 

$key = q/displaystyleint_0^Rbar{rho}(a),a^{,4},da=frac{1}{5},bar{rho}(R),R^{,5},(1+eta_0)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4398.png"
 ALT="$\displaystyle \int_0^R\bar{\rho}(a) a^{ 4} da = \frac{1}{5} \bar{\rho}(R) R^{ 5} (1+\eta_0)^{1/2},$">|; 

$key = q/displaystyleint_0^piointY_l^{,m},Y_{l'}^{,m'ast},sintheta,dtheta,dphi=delta_{ll'},delta_{mm'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4117.png"
 ALT="$\displaystyle \int_0^\pi\oint Y_l^{ m} Y_{l'}^{ m'\ast} \sin\theta d\theta d\phi = \delta_{ll'} \delta_{mm'}.$">|; 

$key = q/displaystyleint_P^QnablaUcdotd{bfr}equiv{mitDelta}U=U(Q)-U(P),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle \int_P^Q \nabla U\cdot d{\bf r} \equiv {\mit\Delta} U = U(Q) - U(P),$">|; 

$key = q/displaystyleint_P^Q{bfA}cdotd{bfr}=V(Q),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.05ex; " SRC="|."$dir".q|img3947.png"
 ALT="$\displaystyle \int_P^Q {\bf A}\cdot d{\bf r} = V(Q),$">|; 

$key = q/displaystyleint_{-1}^1P_n(x),P_m(x),dx=int_0^piP_n(costheta),P_m(costheta),sintheta,dtheta=frac{delta_{nm}}{n+1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img427.png"
 ALT="$\displaystyle \int_{-1}^1 P_n(x) P_m(x) dx = \int_0^\pi P_n(\cos\theta) P_m(\cos\theta) \sin\theta d\theta = \frac{\delta_{nm}}{n+1/2}$">|; 

$key = q/displaystyleint_{r_p}^rfrac{r,dr}{[2,r+(e-1),r^{,2}slashr_p-(e+1),r_p]^{1slash2}}=sqrt{G,M},,(t-tau).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.50ex; " SRC="|."$dir".q|img680.png"
 ALT="$\displaystyle \int_{r_p}^r\frac{r dr}{[2 r + (e-1) r^{ 2}/r_p - (e+1) r_p]^{1/2}} =
\sqrt{G M}  (t-\tau).$">|; 

$key = q/displaystyleiota=1.59^circ.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2071.png"
 ALT="$\displaystyle \iota = 1.59^\circ.$">|; 

$key = q/displaystyleiota=frac{3,tau,I}{2,gslashn-3,tau},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2068.png"
 ALT="$\displaystyle \iota = \frac{3 \tau I}{2 g/n-3 \tau},$">|; 

$key = q/displaystylek(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2657.png"
 ALT="$\displaystyle k(t)$">|; 

$key = q/displaystylek;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4859.png"
 ALT="$\displaystyle k$">|; 

$key = q/displaystylek_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2581.png"
 ALT="$\displaystyle k_i$">|; 

$key = q/displaystylek_{rmforced};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2665.png"
 ALT="$\displaystyle k_{\rm forced}$">|; 

$key = q/displaystylel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4505.png"
 ALT="$\displaystyle l$">|; 

$key = q/displaystylel_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3332.png"
 ALT="$\displaystyle l_1$">|; 

$key = q/displaystylel_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3334.png"
 ALT="$\displaystyle l_2$">|; 

$key = q/displaystylel_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3336.png"
 ALT="$\displaystyle l_3$">|; 

$key = q/displaystylel_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3338.png"
 ALT="$\displaystyle l_4$">|; 

$key = q/displaystylel_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3340.png"
 ALT="$\displaystyle l_5$">|; 

$key = q/displaystylel_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3342.png"
 ALT="$\displaystyle l_6$">|; 

$key = q/displaystylel_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3344.png"
 ALT="$\displaystyle l_7$">|; 

$key = q/displaystylel_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3346.png"
 ALT="$\displaystyle l_8$">|; 

$key = q/displaystylel_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3348.png"
 ALT="$\displaystyle l_9$">|; 

$key = q/displaystylel_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3350.png"
 ALT="$\displaystyle l_{10}$">|; 

$key = q/displaystylel_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3352.png"
 ALT="$\displaystyle l_{11}$">|; 

$key = q/displaystylel_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3354.png"
 ALT="$\displaystyle l_{12}$">|; 

$key = q/displaystylelambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img782.png"
 ALT="$\displaystyle \lambda$">|; 

$key = q/displaystylelangleF^{,2}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img410.png"
 ALT="$\displaystyle \langle F^{ 2}\rangle$">|; 

$key = q/displaystylelangleFrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img408.png"
 ALT="$\displaystyle \langle F\rangle$">|; 

$key = q/displaystylelangleKrangle=frac{mu}{2,a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2909.png"
 ALT="$\displaystyle \langle K\rangle = \frac{\mu}{2 a},
$">|; 

$key = q/displaystylelangleKrangle=frac{mu}{2,a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2783.png"
 ALT="$\displaystyle \langle K\rangle =\frac{\mu}{2 a}.$">|; 

$key = q/displaystylelangleUrangle=-frac{mu}{a},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2910.png"
 ALT="$\displaystyle \langle U\rangle = -\frac{\mu}{a},
$">|; 

$key = q/displaystylelanglecdotsrangleequivfrac{1}{T}int_0^T(cdots),dt=(1-e^{,2})^{-1slash2}oint(cdots)left(frac{r}{a}right)^2,frac{dtheta}{2pi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2824.png"
 ALT="$\displaystyle \langle\cdots\rangle \equiv \frac{1}{T}\int_0^T (\cdots) dt = (1-e^{ 2})^{-1/2}\oint (\cdots)\left(\frac{r}{a}\right)^2 \frac{d\theta}{2\pi}.$">|; 

$key = q/displaystylelanglecdotsrangleequivfrac{1}{T}int_0^T(cdots),dt=oint(cdots),(1-e,cosE),frac{dE}{2pi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2772.png"
 ALT="$\displaystyle \langle\cdots\rangle \equiv \frac{1}{T}\int_0^T (\cdots) dt = \oint (\cdots) (1-e \cos E) \frac{dE}{2\pi}.$">|; 

$key = q/displaystylelangledot{I}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2829.png"
 ALT="$\displaystyle \langle\dot{I}\rangle$">|; 

$key = q/displaystylelangledot{varpi}rangle=ointointdot{varpi},frac{d{calM}}{2pi},frac{d{calM}'}{2pi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4193.png"
 ALT="$\displaystyle \langle \dot{\varpi}\rangle = \oint\oint \dot{\varpi} \frac{d{\cal M}}{2\pi} \frac{d{\cal M}'}{2\pi},$">|; 

$key = q/displaystylelangleskew{3}dot{e}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2776.png"
 ALT="$\displaystyle \langle \skew{3}\dot{e}\rangle$">|; 

$key = q/displaystylelangleskew{3}dot{omega}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2779.png"
 ALT="$\displaystyle \langle \skew{3}\dot{\omega} \rangle$">|; 

$key = q/displaystylelangleskew{5}dot{calM}_0rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2778.png"
 ALT="$\displaystyle \langle\skew{5}\dot{\cal M}_0 \rangle$">|; 

$key = q/displaystylelangleskew{5}dot{mitOmega}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2830.png"
 ALT="$\displaystyle \langle\skew{5}\dot{\mit\Omega}\rangle$">|; 

$key = q/displaystyleleft(1-{mitOmega}_1^{,2}+3,m^{,2}slash2right)z_1=c_1,m^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3432.png"
 ALT="$\displaystyle \left(1-{\mit\Omega}_1^{ 2}+3 m^{ 2}/2\right)z_1 = c_1 m^{ 3},$">|; 

$key = q/displaystyleleft(a,frac{depsilon}{da}+2,epsilonright)_{a=R}=frac{15}{2},zeta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4368.png"
 ALT="$\displaystyle \left(a \frac{d\epsilon}{da} +2 \epsilon\right)_{a=R} = \frac{15}{2} \zeta.$">|; 

$key = q/displaystyleleft(a,frac{depsilon}{da}+2,epsilonright)bar{rho}(a)-3int_a^inftyrho(a'),frac{depsilon}{da'},da'=frac{15,{mitOmega}^{,2}}{8pi,G},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4358.png"
 ALT="$\displaystyle \left(a \frac{d\epsilon}{da}+2 \epsilon\right)\bar{\rho}(a) -3\...
...y \rho(a') \frac{d\epsilon}{da'} da' =\frac{15 {\mit\Omega}^{ 2}}{8\pi G},$">|; 

$key = q/displaystyleleft(frac{a}{r}right)^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1853.png"
 ALT="$\displaystyle \left(\frac{a}{r}\right)^3$">|; 

$key = q/displaystyleleft(frac{dE}{d{calM}}right)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4066.png"
 ALT="$\displaystyle \left(\frac{dE}{d{\cal M}}\right)^2$">|; 

$key = q/displaystyleleft(frac{partial^{,2}U}{partialz^{,2}}right)_{z=0}=frac{mu_1}{rho_1^{,3}}+frac{mu_2}{rho_2^{,3}}>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2248.png"
 ALT="$\displaystyle \left(\frac{\partial^{ 2} U}{\partial z^{ 2}}\right)_{z=0} = \frac{\mu_1}{\rho_1^{ 3}} + \frac{\mu_2}{\rho_2^{ 3}}&gt;0.$">|; 

$key = q/displaystyleleft(omega_1^{,2}+3+3,m^{,2}slash2right)x_1+2,omega_1,y_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img3393.png"
 ALT="$\displaystyle \left(\omega_1^{ 2}+3+3 m^{ 2}/2\right)x_1+2 \omega_1 y_1$">|; 

$key = q/displaystyleleft(p_2,frac{x_i}{r}-frac{mu}{r}left[r,frac{partialxi_i}{partialr}-xi_i+frac{partial(r,xi_r)}{partialx_i}right]right)_{r=a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img4279.png"
 ALT="$\displaystyle \left(p_2 \frac{x_i}{r} - \frac{\mu}{r}\left[r \frac{\partial \...
...rtial r} - \xi_i +\frac{\partial (r \xi_r)}{\partial x_i}\right] \right)_{r=a}$">|; 

$key = q/displaystyleleft({array}{c}XYZ{array}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.58ex; vertical-align: -3.25ex; " SRC="|."$dir".q|img739.png"
 ALT="$\displaystyle \left(\begin{array}{c}X\ Y\ Z\end{array}\right)$">|; 

$key = q/displaystyleleft({mitOmega}_1^{,2}-1-frac{3}{2},m^{,2}+frac{9}{16},m^{,3}right)z_1=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3603.png"
 ALT="$\displaystyle \left({\mit\Omega}_1^{ 2} -1 -\frac{3}{2} m^{ 2} + \frac{9}{16} m^{ 3}\right)z_1=0.$">|; 

$key = q/displaystyleleft.frac{df}{dx}right|_{x_0}<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.15ex; " SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle \left.\frac{df}{dx}\right\vert _{x_0} &lt;0$">|; 

$key = q/displaystyleleft.frac{df}{dx}right|_{x_0}>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.15ex; " SRC="|."$dir".q|img211.png"
 ALT="$\displaystyle \left.\frac{df}{dx}\right\vert _{x_0} &gt;0$">|; 

$key = q/displaystyleleft.phantom{=}-frac{a^{,2}}{5}int_a^inftyrho(a'),d[epsilon(a')]right}+frac{{mitOmega}^{,2},a^{,2}}{3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4354.png"
 ALT="$\displaystyle \left.\phantom{=}-\frac{a^{ 2}}{5}\int_a^\infty
\rho(a') d[\epsilon(a')]\right\} +\frac{{\mit\Omega}^{ 2} a^{ 2}}{3}.$">|; 

$key = q/displaystyleleft.phantom{=}-frac{a^{,2}}{5}int_a^inftyrho(a'),d[epsilon(a')]right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4351.png"
 ALT="$\displaystyle \left.\phantom{=}-\frac{a^{ 2}}{5}\int_a^\infty
\rho(a') d[\epsilon(a')]\right\}.$">|; 

$key = q/displaystyleleft[(2,A+B),r^{,2},p_2+2,phi_2right]_{r=a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.40ex; vertical-align: -1.22ex; " SRC="|."$dir".q|img4290.png"
 ALT="$\displaystyle \left[(2 A+B) r^{ 2} p_2 + 2 \phi_2\right]_{r=a}$">|; 

$key = q/displaystyleleft[(4,A+B),a^{,2},p_2+2,phi_2right]_{r=a}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.40ex; vertical-align: -1.22ex; " SRC="|."$dir".q|img4295.png"
 ALT="$\displaystyle \left[(4 A+B) a^{ 2} p_2 + 2 \phi_2\right]_{r=a} = 0.$">|; 

$key = q/displaystyleleft[1-4,(A+B),muright]left(p_2,x_iright)_{r=a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img4292.png"
 ALT="$\displaystyle \left[1-4 (A+B) \mu\right]\left(p_2 x_i\right)_{r=a}$">|; 

$key = q/displaystyleleft[4,tau-(1+gslashn)^{,2}right]skew{3}hat{nu}_x+(1-tau),(1+gslashn),skew{3}hat{nu}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2058.png"
 ALT="$\displaystyle \left[4 \tau-(1+g/n)^{ 2}\right]\skew{3}\hat{\nu}_x + (1-\tau) (1+g/n) \skew{3}\hat{\nu}_y$">|; 

$key = q/displaystyleleftlanglefrac{skew{0}dot{r_a}}{r_a}rightrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2913.png"
 ALT="$\displaystyle \left\langle\frac{\skew{0}\dot{r_a}}{r_a}\right\rangle$">|; 

$key = q/displaystyleleftlanglefrac{skew{0}dot{r_p}}{r_p}rightrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img2911.png"
 ALT="$\displaystyle \left\langle\frac{\skew{0}\dot{r_p}}{r_p}\right\rangle$">|; 

$key = q/displaystyleleftlanglefrac{skew{3}dot{a}}{a}rightrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2774.png"
 ALT="$\displaystyle \left\langle\frac{\skew{3}\dot{a}}{a}\right\rangle$">|; 

$key = q/displaystyleleftlangle|{bfr}'-{bfr}|^{-1}rightrangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img413.png"
 ALT="$\displaystyle \left\langle \vert{\bf r}'-{\bf r}\vert^{-1}\right\rangle$">|; 

$key = q/displaystyleleftlangle|{bfr}'-{bfr}|^{-1}rightrangle=frac{1}{r'}sum_{n=0,infty}left(frac{r}{r'}right)^nP_n(costheta),P_n(costheta').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img437.png"
 ALT="$\displaystyle \left\langle\vert{\bf r}'-{\bf r}\vert^{-1}\right\rangle = \frac{...
...sum_{n=0,\infty}
\left(\frac{r}{r'}\right)^n P_n(\cos\theta) P_n(\cos\theta').$">|; 

$key = q/displaystyleleftlangle|{bfr}'-{bfr}|^{-1}rightrangle=frac{1}{r}sum_{n=0,infty}left(frac{r'}{r}right)^nP_n(costheta),P_n(costheta').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.08ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img434.png"
 ALT="$\displaystyle \left\langle\vert{\bf r}'-{\bf r}\vert^{-1}\right\rangle = \frac{...
...sum_{n=0,\infty}
\left(\frac{r'}{r}\right)^n P_n(\cos\theta) P_n(\cos\theta').$">|; 

$key = q/displaystyleln(1+x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3810.png"
 ALT="$\displaystyle \ln(1+x)$">|; 

$key = q/displaystylem',ddot{bfR}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2408.png"
 ALT="$\displaystyle m' \ddot{\bf R}'$">|; 

$key = q/displaystylem,ddot{bfR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2406.png"
 ALT="$\displaystyle m \ddot{\bf R}$">|; 

$key = q/displaystylem,frac{d^{,2}x}{dt^{,2}}=f(x).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle m \frac{d^{ 2} x}{d t^{ 2}} = f(x).$">|; 

$key = q/displaystylem,frac{d^{,2}x}{dt^{,2}}simeqf(0)+frac{df(0)}{dx},x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img252.png"
 ALT="$\displaystyle m \frac{d^{ 2} x}{d t^{ 2}} \simeq f(0)+ \frac{df(0)}{dx} x,$">|; 

$key = q/displaystylem,frac{d{bfv}}{dt}={bff}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle m \frac{d{\bf v}}{dt} = {\bf f}.$">|; 

$key = q/displaystylem,{bfa}'={bff}-m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1085.png"
 ALT="$\displaystyle m {\bf a}' = {\bf f} - m $">|; 

$key = q/displaystylem,{bfa}={bff}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1084.png"
 ALT="$\displaystyle m {\bf a} = {\bf f}.$">|; 

$key = q/displaystylem,{bfv}!cdot!frac{d{bfv}}{dt}=frac{m}{2}frac{d({bfv}cdot{bfv})}{dt}=frac{m}{2}frac{dvarv^{,2}}{dt}={bff}cdot{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle m {\bf v}\!\cdot\!\frac{d {\bf v}}{dt} =
\frac{m}{2}\frac{d({\bf v}\cdot{\bf v})}{dt}=\frac{m}{2}\frac{d \varv^{ 2}}{dt} =
{\bf f}\cdot{\bf v}.$">|; 

$key = q/displaystylem;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4507.png"
 ALT="$\displaystyle m$">|; 

$key = q/displaystylem=frac{n'}{n}=0.07480;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img3113.png"
 ALT="$\displaystyle m= \frac{n'}{n}= 0.07480$">|; 

$key = q/displaystylem_1,frac{d^{,2}{bfr}_1}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img260.png"
 ALT="$\displaystyle m_1 \frac{d^{ 2}{\bf r}_1}{dt^{ 2}}$">|; 

$key = q/displaystylem_2,frac{d^{,2}{bfr}_2}{dt^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle m_2 \frac{d^{ 2}{\bf r}_2}{dt^{ 2}}$">|; 

$key = q/displaystylem_i,ddot{bfr}_i=-frac{partialU}{partial{bfr}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img2954.png"
 ALT="$\displaystyle m_i \ddot{\bf r}_i=-\frac{\partial U}{\partial {\bf r}_i},$">|; 

$key = q/displaystylem_i,ddot{bfr}_i=-frac{partialU}{partial{bfr}_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img545.png"
 ALT="$\displaystyle m_i \ddot{\bf r}_i = -\frac{\partial U}{\partial {\bf r}_i}.
$">|; 

$key = q/displaystylem_i,ddot{bfr}_i=sum_{j=1,N}^{jneqi}G,m_i,m_j,frac{{bfr}_j-{bfr}_i}{|{bfr}_j-{bfr}_i|^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img534.png"
 ALT="$\displaystyle m_i \ddot{\bf r}_i = \sum_{j=1,N}^{j\neq i} G m_i m_j \frac{{\bf r}_j-{\bf r}_i}{\vert{\bf r}_j-{\bf r}_i\vert^{ 3}},
$">|; 

$key = q/displaystylem_i,frac{d^{,2}{bfr}_i}{dt^{,2}}=sum_{j=1,N}^{jneqi}!{bff}_{ij}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle m_i \frac{d^{ 2} {\bf r}_i}{dt^{ 2}} = \sum_{j=1,N}^{j\neq i}\! {\bf f}_{ij}.$">|; 

$key = q/displaystylem_i,frac{d^{,2}{bfr}_i}{dt^{,2}}=sum_{j=1,N}^{jneqi}{bff}_{ij}+{bfF}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img1485.png"
 ALT="$\displaystyle m_i \frac{d^{ 2}{\bf r}_i}{dt^{ 2}} = \sum_{j=1,N}^{j\neq i}
{\bf f}_{ij} + {\bf F}_i.$">|; 

$key = q/displaystylem_i,frac{d^{,2}{bfr}_i}{dt^{,2}}={bff}_i=sum_{j=1,N}^{jneqi}{bff}_{ij}+{bfF}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle m_i \frac{d^{ 2}{\bf r}_i}{dt^{ 2}} = {\bf f}_i = \sum_{j=1,N}^{j\neq i} {\bf f}_{ij} + {\bf F}_i.$">|; 

$key = q/displaystylem_i,{bfr}_itimesfrac{d^{,2}{bfr}_i}{dt^{,2}}=frac{d}{dt}!left(m_i,{bfr}_itimesfrac{d{bfr}_i}{dt}right)=frac{d{bfl}_i}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle m_i {\bf r}_i\times \frac{d^{ 2}{\bf r}_i }{dt^{ 2}}= \frac{d}...
...eft( m_i {\bf r}_i\times
\frac{d{\bf r}_i}{dt}\right) = \frac{d{\bf l}_i}{dt},$">|; 

$key = q/displaystylem_i,{bfr}_itimesfrac{d^{,2}{bfr}_i}{dt^{,2}}=sum_{j=1,N}^{jneqi}{bfr}_itimes{bff}_{ij}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img169.png"
 ALT="$\displaystyle m_i {\bf r}_i\times \frac{d^{ 2}{\bf r}_i }{dt^{ 2}}= \sum_{j=1,N}^{j\neq i} {\bf r}_i\times {\bf f}_{ij}.$">|; 

$key = q/displaystylem_j,skew{3}ddot{x}_j=f_j,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1392.png"
 ALT="$\displaystyle m_j \skew{3}\ddot{x}_j = f_j,$">|; 

$key = q/displaystylembox{boldmath{{Omega{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1065.png"
 ALT="$\displaystyle \mbox{\boldmath$\Omega$}$">|; 

$key = q/displaystylembox{boldmath{{nu{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1960.png"
 ALT="$\displaystyle \mbox{\boldmath$\nu$}$">|; 

$key = q/displaystylembox{boldmath{{omega{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1492.png"
 ALT="$\displaystyle \mbox{\boldmath$\omega$}$">|; 

$key = q/displaystylembox{boldmath{{tau{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img189.png"
 ALT="$\displaystyle \mbox{\boldmath$\tau$}$">|; 

$key = q/displaystylembox{boldmath{{xi{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4260.png"
 ALT="$\displaystyle \mbox{\boldmath$\xi$}$">|; 

$key = q/displaystylemu,frac{d^{,2}{bfr}}{dt^{,2}}={bff},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img272.png"
 ALT="$\displaystyle \mu \frac{d^{ 2}{\bf r}}{d t^{ 2}} = {\bf f},$">|; 

$key = q/displaystylemu,nabla^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4266.png"
 ALT="$\displaystyle \mu \nabla^{ 2}$">|; 

$key = q/displaystylemu=frac{m_1,m_2}{m_1+m_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.35ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img273.png"
 ALT="$\displaystyle \mu = \frac{m_1 m_2}{m_1+ m_2}$">|; 

$key = q/displaystylemu_1,rho_1^{,2}+mu_2,rho_2^{,2}=x^{,2}+y^{,2}+mu_1,mu_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2179.png"
 ALT="$\displaystyle \mu_1 \rho_1^{ 2} + \mu_2 \rho_2^{ 2} = x^{ 2}+y^{ 2}+\mu_1 \mu_2,$">|; 

$key = q/displaystylemu_2<frac{1}{2}left(1-sqrt{frac{23}{27}}right)=0.0385.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img2307.png"
 ALT="$\displaystyle \mu_2 &lt; \frac{1}{2}\left(1-\sqrt{\frac{23}{27}}\right) = 0.0385.$">|; 

$key = q/displaystylemu_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2673.png"
 ALT="$\displaystyle \mu_l$">|; 

$key = q/displaystylemu_m=frac{M_m}{M_E+M_m},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4587.png"
 ALT="$\displaystyle \mu_m = \frac{M_m}{M_E+M_m},$">|; 

$key = q/displaystylemu_m=frac{M_m}{M}=0.0123;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1770.png"
 ALT="$\displaystyle \mu_m=\frac{M_m}{M} = 0.0123$">|; 

$key = q/displaystylen(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4905.png"
 ALT="$\displaystyle n(t)$">|; 

$key = q/displaystylen;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img791.png"
 ALT="$\displaystyle n$">|; 

$key = q/displaystylen=frac{sqrt{G,M}}{a^{,3slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img859.png"
 ALT="$\displaystyle n= \frac{\sqrt{G M}}{a^{ 3/2}}.$">|; 

$key = q/displaystylen=left(frac{mu}{a^{,3}}right)^{1slash2};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img5085.png"
 ALT="$\displaystyle n= \left(\frac{\mu}{a^{ 3}}\right)^{1/2};$">|; 

$key = q/displaystylen>-3.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img971.png"
 ALT="$\displaystyle n &gt; -3.$">|; 

$key = q/displaystylen^{-1},dot{w}_x+sigma,w_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1988.png"
 ALT="$\displaystyle n^{-1} \dot{w}_x + \sigma w_y$">|; 

$key = q/displaystylen^{-1},dot{w}_y-tau,w_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1990.png"
 ALT="$\displaystyle n^{-1} \dot{w}_y -\tau w_x$">|; 

$key = q/displaystylen^{-2},skew{3}ddot{nu}_x-(1-tau),n^{-1},skew{3}dot{nu}_y+4,tau,nu_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2019.png"
 ALT="$\displaystyle n^{-2} \skew{3}\ddot{\nu}_x - (1-\tau) n^{-1} \skew{3}\dot{\nu}_y + 4 \tau \nu_x$">|; 

$key = q/displaystylen^{-2},skew{3}ddot{nu}_x-(1-tau),n^{-1},skew{3}dot{nu}_y+tau,nu_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1997.png"
 ALT="$\displaystyle n^{-2} \skew{3}\ddot{\nu}_x -(1-\tau) n^{-1} \skew{3}\dot{\nu}_y+\tau \nu_x$">|; 

$key = q/displaystylen^{-2},skew{3}ddot{nu}_y+(1-sigma),n^{-1},skew{3}dot{nu}_x+sigma,nu_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1999.png"
 ALT="$\displaystyle n^{-2} \skew{3}\ddot{\nu}_y+(1-\sigma) n^{-1} \skew{3}\dot{\nu}_x+\sigma \nu_y$">|; 

$key = q/displaystylen_0=alpha,n.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1869.png"
 ALT="$\displaystyle n_0 = \alpha n.$">|; 

$key = q/displaystylen_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2560.png"
 ALT="$\displaystyle n_i$">|; 

$key = q/displaystylen_m=frac{dlambda_m}{dt}simeqleft(frac{G,M}{a_m^{,3}}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1753.png"
 ALT="$\displaystyle n_m = \frac{d\lambda_m}{dt}\simeq \left(\frac{G M}{a_m^{ 3}}\right)^{1/2}$">|; 

$key = q/displaystylen_s=frac{dlambda_s}{dt}=left(frac{G,M_s}{a_s^{,3}}right)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1718.png"
 ALT="$\displaystyle n_s =\frac{d\lambda_s}{dt}= \left(\frac{G M_s}{a_s^{ 3}}\right)^{1/2}$">|; 

$key = q/displaystylenabla(phi,psi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3940.png"
 ALT="$\displaystyle \nabla(\phi \psi)$">|; 

$key = q/displaystylenablaV=frac{partialV}{partialr},{bfe}_r+frac{1}{r}frac{partialV}{partialtheta},{bfe}_theta+frac{partialV}{partialz},{bfe}_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.80ex; " SRC="|."$dir".q|img3973.png"
 ALT="$\displaystyle \nabla V = \frac{\partial V}{\partial r} {\bf e}_r
+ \frac{1}{r}...
... V}{\partial\theta} {\bf e}_\theta
+ \frac{\partial V}{\partial z} {\bf e}_z.$">|; 

$key = q/displaystylenabla^{,2}(r^{,m},{calR}_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4223.png"
 ALT="$\displaystyle \nabla^{ 2}(r^{ m} {\cal R}_n)$">|; 

$key = q/displaystylenabla^{,2}(x_i,{calR}_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4221.png"
 ALT="$\displaystyle \nabla^{ 2}(x_i {\cal R}_n)$">|; 

$key = q/displaystylenabla^{,2}{calR}_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4214.png"
 ALT="$\displaystyle \nabla^{ 2} {\cal R}_n = 0$">|; 

$key = q/displaystylenabla^{,2}{mitPhi}=4pi,G,rho,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4232.png"
 ALT="$\displaystyle \nabla^{ 2}{\mit\Phi} = 4\pi G \rho,$">|; 

$key = q/displaystylenabla^{,2}{mitPhi}_2=4pi,G,rho,delta_2,delta(r-a).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4235.png"
 ALT="$\displaystyle \nabla^{ 2}{\mit\Phi}_2 = 4\pi G \rho \delta_2 \delta(r-a).$">|; 

$key = q/displaystylenablacdot;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4259.png"
 ALT="$\displaystyle \nabla\cdot$">|; 

$key = q/displaystylenablap=-rho,nablaU,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4322.png"
 ALT="$\displaystyle \nabla p =- \rho \nabla U,$">|; 

$key = q/displaystylenablaphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3938.png"
 ALT="$\displaystyle \nabla\phi$">|; 

$key = q/displaystylenabla{calR}=F_r,{bfe}_r+F_theta,{bfe}_theta+F_z,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4154.png"
 ALT="$\displaystyle \nabla{\cal R}= F_r {\bf e}_r + F_\theta {\bf e}_\theta+ F_z {\bf e}_z,$">|; 

$key = q/displaystylenu_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2671.png"
 ALT="$\displaystyle \nu_l$">|; 

$key = q/displaystylenu_x(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2021.png"
 ALT="$\displaystyle \nu_x(t)$">|; 

$key = q/displaystylenu_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2013.png"
 ALT="$\displaystyle \nu_x$">|; 

$key = q/displaystylenu_y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2023.png"
 ALT="$\displaystyle \nu_y(t)$">|; 

$key = q/displaystylenu_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2015.png"
 ALT="$\displaystyle \nu_y$">|; 

$key = q/displaystyleointY_l^{,m},Y_{l'}^{,-m'},d{mitOmega}=(-1)^m,delta_{ll'},delta_{mm'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4493.png"
 ALT="$\displaystyle \oint Y_l^{ m}  Y_{l'}^{ -m'} d{\mit\Omega} = (-1)^m \delta_{ll'} \delta_{mm'}.$">|; 

$key = q/displaystyleomega,sinalpha=sintheta,skew{5}dot{phi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1642.png"
 ALT="$\displaystyle \omega \sin\alpha = \sin\theta \skew{5}\dot{\phi}.$">|; 

$key = q/displaystyleomega,sintheta,,skew{5}dot{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4548.png"
 ALT="$\displaystyle \omega \sin\theta  \skew{5}\dot{\phi}$">|; 

$key = q/displaystyleomega,sintheta,,skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4551.png"
 ALT="$\displaystyle \omega \sin\theta  \skew{5}\dot{\theta}$">|; 

$key = q/displaystyleomega=costheta,,skew{5}dot{phi}+skew{5}dot{psi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1721.png"
 ALT="$\displaystyle \omega = \cos\theta  \skew{5}\dot{\phi} + \skew{5}\dot{\psi},$">|; 

$key = q/displaystyleomega=costheta,skew{5}dot{phi}+skew{5}dot{psi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4544.png"
 ALT="$\displaystyle \omega =\cos\theta \skew{5}\dot{\phi}+\skew{5}\dot{\psi}.$">|; 

$key = q/displaystyleomega=frac{(G,M)^{,1slash2}}{a^{,3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1275.png"
 ALT="$\displaystyle \omega =\frac{(G M)^{ 1/2}}{a^{ 3/2}},$">|; 

$key = q/displaystyleomega=left(frac{5-alpha}{5-2,alpha},frac{G,M}{R^{,3}}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img571.png"
 ALT="$\displaystyle \omega = \left(\frac{5-\alpha}{5-2 \alpha} \frac{G M}{R^{ 3}}\right)^{1/2},
$">|; 

$key = q/displaystyleomega=left(frac{|U_0|}{{calI}_0}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img567.png"
 ALT="$\displaystyle \omega = \left(\frac{\vert U_0\vert}{{\cal I}_0}\right)^{1/2},
$">|; 

$key = q/displaystyleomega=left[frac{{calI}_parallel-(1+3,h_2,zetaslash2),{calI}_perp}{(1+3,h_2,zetaslash2),{calI}_perp}right]{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4504.png"
 ALT="$\displaystyle \omega =\left[\frac{{\cal I}_\parallel-(1+3 h_2 \zeta/2) {\cal I}_\perp}{(1+3 h_2 \zeta/2) {\cal I}_\perp}\right]{\mit\Omega}.$">|; 

$key = q/displaystyleomega^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2092.png"
 ALT="$\displaystyle \omega^{ 2}$">|; 

$key = q/displaystyleomega^{,2}=frac{G,M}{a^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1208.png"
 ALT="$\displaystyle \omega^{ 2} = \frac{G M}{a^{ 3}},$">|; 

$key = q/displaystyleomega_+simeqleft(1-frac{27}{8},mu_2right)omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2386.png"
 ALT="$\displaystyle \omega_+ \simeq \left(1-\frac{27}{8} \mu_2\right)\omega,
$">|; 

$key = q/displaystyleomega_-simeqfrac{3}{2}sqrt{3,mu_2},omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2391.png"
 ALT="$\displaystyle \omega_- \simeq \frac{3}{2}\sqrt{3 \mu_2} \omega,
$">|; 

$key = q/displaystyleomega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3404.png"
 ALT="$\displaystyle \omega_1$">|; 

$key = q/displaystyleomega_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3406.png"
 ALT="$\displaystyle \omega_2$">|; 

$key = q/displaystyleomega_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3408.png"
 ALT="$\displaystyle \omega_3$">|; 

$key = q/displaystyleomega_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3410.png"
 ALT="$\displaystyle \omega_4$">|; 

$key = q/displaystyleomega_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3412.png"
 ALT="$\displaystyle \omega_5$">|; 

$key = q/displaystyleomega_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3414.png"
 ALT="$\displaystyle \omega_6$">|; 

$key = q/displaystyleomega_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3416.png"
 ALT="$\displaystyle \omega_7$">|; 

$key = q/displaystyleomega_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3418.png"
 ALT="$\displaystyle \omega_8$">|; 

$key = q/displaystyleomega_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3420.png"
 ALT="$\displaystyle \omega_9$">|; 

$key = q/displaystyleomega_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3422.png"
 ALT="$\displaystyle \omega_{10}$">|; 

$key = q/displaystyleomega_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3424.png"
 ALT="$\displaystyle \omega_{11}$">|; 

$key = q/displaystyleomega_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3426.png"
 ALT="$\displaystyle \omega_{12}$">|; 

$key = q/displaystyleomega_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1580.png"
 ALT="$\displaystyle \omega_{x'}$">|; 

$key = q/displaystyleomega_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1582.png"
 ALT="$\displaystyle \omega_{y'}$">|; 

$key = q/displaystyleomega_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1590.png"
 ALT="$\displaystyle \omega_{z'}$">|; 

$key = q/displaystyleoverline{U};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4538.png"
 ALT="$\displaystyle \overline{U}$">|; 

$key = q/displaystyleoverline{U}=(1-e^{,2})^{-1slash2}ointleft(frac{r}{a}right)^2U,frac{df}{2pi}=ointfrac{r}{a},U,frac{dE}{2pi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img4537.png"
 ALT="$\displaystyle \overline{U} = (1-e^{ 2})^{-1/2}\oint\left(\frac{r}{a}\right)^2 U \frac{df}{2\pi}=\oint \frac{r}{a} U \frac{dE}{2\pi}.$">|; 

$key = q/displaystyleoverline{calR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img2712.png"
 ALT="$\displaystyle \overline{\cal R}$">|; 

$key = q/displaystyleoverline{calR}=-frac{3,J_3}{2},frac{mu,R^{,3}}{a^{,4}},frac{e}{(1-e^{,2})^{,5slash2}}left(frac{5}{4},sin^2I-1right)sinI,sinomega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2897.png"
 ALT="$\displaystyle \overline{\cal R}= -\frac{3 J_3}{2} \frac{\mu R^{ 3}}{a^{ 4}...
...e}{(1-e^{ 2})^{ 5/2}}\left(\frac{5}{4} \sin^2 I-1\right)\sin I \sin\omega.
$">|; 

$key = q/displaystyleoverline{calR}=frac{J_2}{2},frac{mu,R^{,2}}{a^{,3}},(1-e^{,2})^{-3slash2}left(1-frac{3}{2},sin^2Iright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2714.png"
 ALT="$\displaystyle \overline{\cal R} = \frac{J_2}{2} \frac{\mu R^{ 2}}{a^{ 3}} (1-e^{ 2})^{-3/2}\left(1-\frac{3}{2} \sin^2 I\right).$">|; 

$key = q/displaystyleoverline{calR}=frac{mu,h^{,2}}{c^{,2},a^{,3},(1-e^{,2})^{,3slash2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2890.png"
 ALT="$\displaystyle \overline{\cal R}= \frac{\mu h^{ 2}}{c^{ 2} a^{ 3} (1-e^{ 2})^{ 3/2}},
$">|; 

$key = q/displaystylep(r,theta,phi)=p_0(r)-rho,mitPhi_2(r,theta,phi)+p_2(r,theta,phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4268.png"
 ALT="$\displaystyle p(r,\theta,\phi) = p_0(r) -\rho \mit\Phi_2(r,\theta,\phi) + p_2(r,\theta,\phi),$">|; 

$key = q/displaystylep(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2659.png"
 ALT="$\displaystyle p(t)$">|; 

$key = q/displaystylep;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4861.png"
 ALT="$\displaystyle p$">|; 

$key = q/displaystylep=frac{partialK}{partialskew{3}dot{x}}=frac{partial{calL}}{partialskew{3}dot{x}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1439.png"
 ALT="$\displaystyle p = \frac{\partial K}{\partial \skew{3}\dot{x}}= \frac{\partial {\cal L}}{\partial\skew{3}\dot{x}},$">|; 

$key = q/displaystylep_0(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4278.png"
 ALT="$\displaystyle p_0(a)$">|; 

$key = q/displaystylep_0(r)=frac{rho,g}{2,a},(3,a^{,2}-r^{,2}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4282.png"
 ALT="$\displaystyle p_0(r) = \frac{\rho g}{2 a} (3 a^{ 2}-r^{ 2}).$">|; 

$key = q/displaystylep_0=frac{2pi}{3},G,gamma^{,2},R^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img497.png"
 ALT="$\displaystyle p_0 = \frac{2\pi}{3} G \gamma^{ 2} R^{ 2}.$">|; 

$key = q/displaystylep_0=int_0^R,gamma,g(r),dr,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img493.png"
 ALT="$\displaystyle p_0 = \int_0^R \gamma g(r) dr,$">|; 

$key = q/displaystylep_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2583.png"
 ALT="$\displaystyle p_i$">|; 

$key = q/displaystylep_i=frac{partial{calL}}{partialskew{3}dot{q}_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img1442.png"
 ALT="$\displaystyle p_i = \frac{\partial {\cal L}}{\partial\skew{3}\dot{q}_i},$">|; 

$key = q/displaystylep_k={rmconst.};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1447.png"
 ALT="$\displaystyle p_k = {\rm const.}$">|; 

$key = q/displaystylep_psi=frac{partial{calL}}{partialskew{5}dot{psi}}={calI}_parallel,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1723.png"
 ALT="$\displaystyle p_\psi = \frac{\partial{\cal L}}{\partial\skew{5}\dot{\psi}} = {\cal I}_\parallel  \omega$">|; 

$key = q/displaystylep_theta=frac{partial{calL}}{partialskew{5}dot{theta}}=m,r^{,2},skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.85ex; " SRC="|."$dir".q|img1448.png"
 ALT="$\displaystyle p_\theta = \frac{\partial {\cal L}}{\partial\skew{5}\dot{\theta}} = m r^{ 2} \skew{5}\dot{\theta}$">|; 

$key = q/displaystylep_{rmforced};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2667.png"
 ALT="$\displaystyle p_{\rm forced}$">|; 

$key = q/displaystylephantom{12}frac{partial{calL}}{partialtheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1425.png"
 ALT="$\displaystyle \phantom{12}
\frac{\partial {\cal L}}{\partial\theta}$">|; 

$key = q/displaystylephantom{=}+(-A_1,D_2-B_1,C_2+A_2,D_1+B_2,C_1),sin{mitOmega},cos{mitOmega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4731.png"
 ALT="$\displaystyle \phantom{=}+ (-A_1 D_2-B_1 C_2+A_2 D_1+B_2 C_1) \sin{\mit\Omega} \cos{\mit\Omega},$">|; 

$key = q/displaystylephantom{=}+(A_1,D_2+B_1,C_2-A_2,D_1-B_2,C_1),sin{mitOmega},cos{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4734.png"
 ALT="$\displaystyle \phantom{=} + (A_1 D_2+B_1 C_2-A_2 D_1-B_2 C_1) \sin{\mit\Omega} \cos{\mit\Omega}.$">|; 

$key = q/displaystylephantom{=}+2,skew{3}tilde{epsilon},beta_m,cos(2,theta),cos(alpha_n-phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1777.png"
 ALT="$\displaystyle \phantom{=}+ 2 \skew{3}\tilde{\epsilon} \beta_m \cos(2 \theta) \cos(\alpha_n-\phi),$">|; 

$key = q/displaystylephantom{=}+3,e,e',cos(2,skew{5}bar{lambda}-varpi'-varpi)-frac{e'^{,2}}{8},cos(skew{5}bar{lambda}'+skew{5}bar{lambda}-2,varpi');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img5058.png"
 ALT="$\displaystyle \phantom{=}+3 e e' \cos(2 \skew{5}\bar{\lambda}-\varpi'-\varp...
...rac{e'^{ 2}}{8} \cos(\skew{5}\bar{\lambda}'+\skew{5}\bar{\lambda}-2 \varpi')$">|; 

$key = q/displaystylephantom{=}+a_4,m^{,2},cos(2,D)+a_5,m^{,4},cos(4,D)+a_6,m^{,2},e,cos(2,D-{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3219.png"
 ALT="$\displaystyle \phantom{=} +a_4 m^{ 2} \cos(2 D) + a_5 m^{ 4} \cos(4 D) + a_6 m^{ 2} e \cos(2 D-{\cal M})$">|; 

$key = q/displaystylephantom{=}+a_7,m^{,2},e,cos(2,D+{calM})+a_8,m^{,2},e',cos{calM}'+a_9,m^{,2},e',cos(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3220.png"
 ALT="$\displaystyle \phantom{=}+a_7 m^{ 2} e \cos(2 D+{\cal M})+a_8 m^{ 2} e' \cos {\cal M}' + a_9 m^{ 2} e' \cos(2 D-{\cal M}')$">|; 

$key = q/displaystylephantom{=}+a_{10},m^{,2},e',cos(2,D+{calM}')+a_{11},m^{,2},zeta,cosD+a_{12},m^{,2},zeta,cos(3,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3221.png"
 ALT="$\displaystyle \phantom{=}+a_{10} m^{ 2} e' \cos(2 D+{\cal M}')+a_{11} m^{ 2} \zeta \cos D + a_{12} m^{ 2} \zeta \cos(3 D),$">|; 

$key = q/displaystylephantom{=}+alpha,sin^2I,sin(2,theta),cos[2,({mitOmega}-phi)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4550.png"
 ALT="$\displaystyle \phantom{=}+ \alpha \sin^2 I \sin(2 \theta) \cos[2 ({\mit\Omega}-\phi)],$">|; 

$key = q/displaystylephantom{=}+b_4,m^{,2},sin(2,D)+b_5,m^{,4},sin(4,D)+b_6,m^{,2},e,sin(2,D-{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3223.png"
 ALT="$\displaystyle \phantom{=} +b_4 m^{ 2} \sin(2 D) + b_5 m^{ 4} \sin(4 D) + b_6 m^{ 2} e \sin(2 D-{\cal M})$">|; 

$key = q/displaystylephantom{=}+b_7,m^{,2},e,sin(2,D+{calM})+b_8,m^{,2},e',sin{calM}'+b_9,m^{,2},e',sin(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3224.png"
 ALT="$\displaystyle \phantom{=}+b_7 m^{ 2} e \sin(2 D+{\cal M})+b_8 m^{ 2} e' \sin {\cal M}' + b_9 m^{ 2} e' \sin(2 D-{\cal M}')$">|; 

$key = q/displaystylephantom{=}+b_{10},m^{,2},e',sin(2,D+{calM}')+b_{11},m^{,2},zeta,sinD+b_{12},m^{,2},zeta,sin(3,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3225.png"
 ALT="$\displaystyle \phantom{=}+b_{10} m^{ 2} e' \sin(2 D+{\cal M}')+b_{11} m^{ 2} \zeta \sin D + b_{12} m^{ 2} \zeta \sin(3 D),$">|; 

$key = q/displaystylephantom{=}+c_5,m^{,2},I,sin(2,D+F),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3227.png"
 ALT="$\displaystyle \phantom{=} +c_5 m^{ 2} I \sin(2 D+F),$">|; 

$key = q/displaystylephantom{=}+cos(omega+theta),sin(omega'+theta'),sinI,sinI'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4187.png"
 ALT="$\displaystyle \phantom{=}+\cos(\omega+\theta) \sin(\omega'+\theta') \sin I \sin I'.$">|; 

$key = q/displaystylephantom{=}+cos({mitOmega}-{mitOmega}'),cos(omega+theta),sin(omega'+theta'),cosI,cosI';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4186.png"
 ALT="$\displaystyle \phantom{=}+\cos({\mit\Omega}-{\mit\Omega}') \cos(\omega+\theta) \sin(\omega'+\theta') \cos I \cos I'$">|; 

$key = q/displaystylephantom{=}+cos({mitOmega}-{mitOmega}'),sin(omega+theta),sin(omega'+theta'),cosI,cosI';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4181.png"
 ALT="$\displaystyle \phantom{=}+\cos({\mit\Omega}-{\mit\Omega}') \sin(\omega+\theta) \sin(\omega'+\theta') \cos I \cos I'$">|; 

$key = q/displaystylephantom{=}+d_5,m^{,2},I,sin(2,D+F).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3237.png"
 ALT="$\displaystyle \phantom{=} +d_5 m^{ 2} I \sin(2 D+F).$">|; 

$key = q/displaystylephantom{=}+delta,alpha,F^{,3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img4967.png"
 ALT="$\displaystyle \phantom{=}+ \delta \alpha F^{ 3}.$">|; 

$key = q/displaystylephantom{=}+e'^{,2}left(frac{5,j}{8}+frac{j^{,2}}{2}right)cos[j,skew{5}bar{lambda}-(2+j),skew{5}bar{lambda}'+2,varpi'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5034.png"
 ALT="$\displaystyle \phantom{=}+ e'^{ 2}\left(\frac{5 j}{8} +\frac{j^{ 2}}{2}\right)\cos[j \skew{5}\bar{\lambda}-(2+j) \skew{5}\bar{\lambda}'+2 \varpi']$">|; 

$key = q/displaystylephantom{=}+e'^{,2}left(frac{j^{,2}}{2}-frac{5,j}{8}right)cos[j,skew{5}bar{lambda}+(2-j),skew{5}bar{lambda}'-2,varpi'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5033.png"
 ALT="$\displaystyle \phantom{=}+ e'^{ 2}\left(\frac{j^{ 2}}{2} -\frac{5 j}{8}\right)\cos[j \skew{5}\bar{\lambda}+(2-j) \skew{5}\bar{\lambda}'-2 \varpi']$">|; 

$key = q/displaystylephantom{=}+e,e',cos(varpi-varpi')+2,s,s',cos(skew{5}bar{lambda}-skew{5}bar{lambda}'-{mitOmega}+{mitOmega}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5004.png"
 ALT="$\displaystyle \phantom{=}+ e e' \cos(\varpi-\varpi') + 2 s s' \cos(\skew{5}\bar{\lambda}-\skew{5}\bar{\lambda}'-{\mit\Omega}+{\mit\Omega}')$">|; 

$key = q/displaystylephantom{=}+e^{,2}left(frac{5,j}{8}+frac{j^{,2}}{2}right)cos[(2+j),skew{5}bar{lambda}-j,skew{5}bar{lambda}'-2,varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5030.png"
 ALT="$\displaystyle \phantom{=}+ e^{ 2}\left(\frac{5 j}{8} +\frac{j^{ 2}}{2}\right)\cos[(2+j) \skew{5}\bar{\lambda}-j \skew{5}\bar{\lambda}'-2 \varpi]$">|; 

$key = q/displaystylephantom{=}+e^{,2}left(frac{5,j}{8}+frac{j^{,2}}{2}right)sin[(2+j),skew{5}bar{lambda}-2,varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5026.png"
 ALT="$\displaystyle \phantom{=}+ e^{ 2}\left(\frac{5 j}{8} + \frac{j^{ 2}}{2}\right)\sin[(2+j) \skew{5}\bar{\lambda}-2 \varpi]$">|; 

$key = q/displaystylephantom{=}+e^{,2}left(frac{j^{,2}}{2}+frac{5,j}{8}right)cos[(2+j),skew{5}bar{lambda}-2,varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5021.png"
 ALT="$\displaystyle \phantom{=}+ e^{ 2}\left(\frac{j^{ 2}}{2} + \frac{5 j}{8}\right)\cos[(2+j) \skew{5}\bar{\lambda}-2 \varpi]$">|; 

$key = q/displaystylephantom{=}+e^{,2}left(frac{j^{,2}}{2}-frac{5,j}{8}right)cos[(2-j),skew{5}bar{lambda}+j,skew{5}bar{lambda}'-2,varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5031.png"
 ALT="$\displaystyle \phantom{=}+ e^{ 2}\left(\frac{j^{ 2}}{2} -\frac{5 j}{8}\right)\cos[(2-j) \skew{5}\bar{\lambda}+j \skew{5}\bar{\lambda}'-2 \varpi]$">|; 

$key = q/displaystylephantom{=}+e^{,4}left(frac{103}{96},sin4{calM}-frac{11}{24},sin2{calM}right)+{calO}(e^5).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4070.png"
 ALT="$\displaystyle \phantom{=}+e^{ 4}\left(\frac{103}{96} \sin 4{\cal M} - \frac{11}{24} \sin 2{\cal M}\right)+{\cal O}(e^5).$">|; 

$key = q/displaystylephantom{=}+frac{13,e^{,3}}{4},cos3{calM}+frac{103,e^{,4}}{24},cos4{calM}+{calO}(e^5),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4068.png"
 ALT="$\displaystyle \phantom{=}+\frac{13 e^{ 3}}{4} \cos 3{\cal M} + \frac{103 e^{ 4}}{24} \cos 4{\cal M} +{\cal O}(e^5),$">|; 

$key = q/displaystylephantom{=}+frac{1}{4},(k,k'+h,h'),alpha,(2-2,alpha,D-alpha^{,2},D^{,2}),b_{1slash2}^{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2497.png"
 ALT="$\displaystyle \phantom{=}+\frac{1}{4} (k k'+h h') \alpha (2-2 \alpha D - \alpha^{ 2} D^{ 2}) b_{1/2}^{(1)}$">|; 

$key = q/displaystylephantom{=}+frac{1}{4},(p,p'+q,q'),alpha^{,2},b_{3slash2}^{(1)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2498.png"
 ALT="$\displaystyle \phantom{=}+\frac{1}{4} (p p'+q q') \alpha^{ 2} b_{3/2}^{(1)}.$">|; 

$key = q/displaystylephantom{=}+frac{3,e^{,2}}{8},cos3{calM}+frac{e^{,3}}{3},cos4{calM}+{calO}(e^{,4}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4055.png"
 ALT="$\displaystyle \phantom{=}
+\frac{3 e^{ 2}}{8} \cos 3{\cal M}+ \frac{e^{ 3}}{3} \cos 4{\cal M}+ {\cal O}(e^{ 4}).$">|; 

$key = q/displaystylephantom{=}+frac{3}{2},m^{,2},cos[2,(1-m),T],deltaX-frac{3}{2},m^{,2},sin[2,(1-m),T],deltaY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3158.png"
 ALT="$\displaystyle \phantom{=}+ \frac{3}{2} m^{ 2} \cos[2 (1-m) T] \delta X -\frac{3}{2} m^{ 2} \sin[2 (1-m) T] \delta Y$">|; 

$key = q/displaystylephantom{=}+frac{3}{2},m^{,2},e',cos(m,T)+frac{21}{4},m^{,2},e',cos[(2-3,m),T]-frac{3}{4},m^{,2},e',cos[(2-m),T];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3156.png"
 ALT="$\displaystyle \phantom{=} +\frac{3}{2} m^{ 2} e' \cos(m T) + \frac{21}{4} m^{ 2} e' \cos[(2-3 m) T]-\frac{3}{4} m^{ 2} e' \cos[(2-m) T]$">|; 

$key = q/displaystylephantom{=}+frac{3}{2},m^{,2},e',cos{calM}'-frac{7}{2},m^{,2},e',cos(2,D-{calM}')+frac{1}{2},m^{,2},e',cos(2,D+{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3638.png"
 ALT="$\displaystyle \phantom{=}+\frac{3}{2} m^{ 2} e' \cos{\cal M}' -\frac{7}{2} m^{ 2} e' \cos(2 D-{\cal M}')+\frac{1}{2} m^{ 2} e' \cos(2 D+{\cal M}')$">|; 

$key = q/displaystylephantom{=}+frac{3}{4},m^{,2},e',sin(2,D+{calM}')-frac{3}{8},m^{,2},zeta,sinD-frac{15}{8},m^{,2},zeta,sin(3,D);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3200.png"
 ALT="$\displaystyle \phantom{=}+
\frac{3}{4} m^{ 2} e' \sin(2 D+{\cal M}') - \frac{3}{8} m^{ 2} \zeta \sin D - \frac{15}{8} m^{ 2} \zeta \sin(3 D)$">|; 

$key = q/displaystylephantom{=}+frac{4,e^{,4}}{3},cos4{calM}+{calO}(e^5).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4065.png"
 ALT="$\displaystyle \phantom{=}+\frac{4 e^{ 4}}{3} \cos 4{\cal M} + {\cal O}(e^5).$">|; 

$key = q/displaystylephantom{=}+frac{66702631253}{7077888},m^{,7}+frac{29726828924189}{679477248},m^{,8}+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img3663.png"
 ALT="$\displaystyle \phantom{=}+\frac{66702631253}{7077888} m^{ 7}
+\frac{29726828924189}{679477248} m^{ 8}+\cdots,$">|; 

$key = q/displaystylephantom{=}+frac{9}{8},m^{,2},zeta,cos[(1-m),T]+frac{15}{8},m^{,2},zeta,cos[3,(1-m),T];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3157.png"
 ALT="$\displaystyle \phantom{=} +\frac{9}{8} m^{ 2} \zeta \cos[(1-m) T] + \frac{15}{8} m^{ 2} \zeta \cos[3 (1-m) T]$">|; 

$key = q/displaystylephantom{=}+frac{cosI}{n,a^{,2},(1-e^{,2})^{1slash2}},frac{partial{calR}}{partialq},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4873.png"
 ALT="$\displaystyle \phantom{=}+ \frac{\cos I}{n a^{ 2} (1-e^{ 2})^{1/2}} \frac{\partial {\cal R}}{\partial q},$">|; 

$key = q/displaystylephantom{=}+frac{e'}{2},(-1+2,j+alpha,D),b_{1slash2}^{(j-1)},cos[j,skew{5}bar{lambda}'+(1-j),skew{5}bar{lambda}-varpi'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img5047.png"
 ALT="$\displaystyle \phantom{=}+\frac{e'}{2} (-1+2 j+\alpha D) b_{1/2}^{(j-1)} \cos[j \skew{5}\bar{\lambda}'+(1-j) \skew{5}\bar{\lambda}-\varpi']$">|; 

$key = q/displaystylephantom{=}+frac{e,sinomega,cosI,cos(omega+theta),F_z}{1+e,costheta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img5146.png"
 ALT="$\displaystyle \phantom{=} + \frac{e \sin\omega \cos I \cos(\omega+\theta) F_z}{1+e \cos\theta}$">|; 

$key = q/displaystylephantom{=}+frac{e^{,2}}{8}left[-8,cos(omega+{calM})-cos(omega-{calM})+9,cos(omega+3{calM})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4985.png"
 ALT="$\displaystyle \phantom{=}+ \frac{e^{ 2}}{8}\left[-8 \cos(\omega+{\cal M})- \cos(\omega-{\cal M}) + 9 \cos(\omega+3{\cal M})\right],$">|; 

$key = q/displaystylephantom{=}+frac{e^{,2}}{8}left[-8,sin(omega+{calM})+sin(omega-{calM})+9,sin(omega+3{calM})right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4989.png"
 ALT="$\displaystyle \phantom{=}+ \frac{e^{ 2}}{8}\left[-8 \sin(\omega+{\cal M})+ \sin(\omega-{\cal M}) + 9 \sin(\omega+3{\cal M})\right].$">|; 

$key = q/displaystylephantom{=}+frac{e^{,2}}{8}left[9,cos(omega+{mitOmega}+3{calM})-cos(omega+{mitOmega}-{calM})-8,cos(omega+{mitOmega}+{calM})right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4992.png"
 ALT="$\displaystyle \phantom{=}+ \frac{e^{ 2}}{8}\left[9 \cos(\omega+{\mit\Omega}+3...
...os(\omega+{\mit\Omega}-{\cal M}) - 8 \cos(\omega+{\mit\Omega}+{\cal M})\right]$">|; 

$key = q/displaystylephantom{=}+frac{e^{,2}}{8}left[9,sin(omega+{mitOmega}+3{calM})-sin(omega+{mitOmega}-{calM})-8,sin(omega+{mitOmega}+{calM})right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4996.png"
 ALT="$\displaystyle \phantom{=}+ \frac{e^{ 2}}{8}\left[9 \sin(\omega+{\mit\Omega}+3...
...in(\omega+{\mit\Omega}-{\cal M}) - 8 \sin(\omega+{\mit\Omega}+{\cal M})\right]$">|; 

$key = q/displaystylephantom{=}+frac{e^{,3}}{3},sin4{calM}+{calO}(e^{,4}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4053.png"
 ALT="$\displaystyle \phantom{=}+ \frac{e^{ 3}}{3} \sin 4{\cal M} + {\cal O}(e^{ 4}),$">|; 

$key = q/displaystylephantom{=}+frac{e^{,4}}{6}left(2,sin4{calM}-sin2{calM}right)+{calO}(e^5).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4057.png"
 ALT="$\displaystyle \phantom{=}+\frac{e^{ 4}}{6}\left(2 \sin 4{\cal M}-\sin 2{\cal M}\right) + {\cal O}(e^5).$">|; 

$key = q/displaystylephantom{=}+frac{e}{2},left(-2,j-alpha,Dright),b^{(j)}_{1slash2},cos[j,skew{5}bar{lambda}'+(1-j),skew{5}bar{lambda}-varpi];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.01ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img5046.png"
 ALT="$\displaystyle \phantom{=}+\frac{e}{2} \left(-2 j-\alpha D\right) b^{(j)}_{1/2} \cos[j \skew{5}\bar{\lambda}'+(1-j) \skew{5}\bar{\lambda}-\varpi]$">|; 

$key = q/displaystylephantom{=}+frac{n,epsilon'alpha,cosI}{(1-e^{,2})^{1slash2}},frac{partial{calS}}{partialq},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.08ex; " SRC="|."$dir".q|img4895.png"
 ALT="$\displaystyle \phantom{=}+ \frac{n \epsilon'\alpha \cos I}{(1-e^{ 2})^{1/2}} \frac{\partial {\cal S}}{\partial q},$">|; 

$key = q/displaystylephantom{=}+frac{s'^{,2}}{2},alpha,b_{3slash2}^{(j-1)},cos[j,skew{5}bar{lambda}'+(2-j),skew{5}bar{lambda}-2,{mitOmega}'].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img5053.png"
 ALT="$\displaystyle \phantom{=}+\frac{s'^{ 2}}{2} \alpha b_{3/2}^{(j-1)} \cos[j \skew{5}\bar{\lambda}'+(2-j) \skew{5}\bar{\lambda}-2 {\mit\Omega}'].$">|; 

$key = q/displaystylephantom{=}+frac{s^{,2}}{2},alpha,b^{(j-1)}_{3slash2},cos[j,skew{5}bar{lambda}'+(2-j),skew{5}bar{lambda}-2,{mitOmega}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img5051.png"
 ALT="$\displaystyle \phantom{=}+\frac{s^{ 2}}{2} \alpha b^{(j-1)}_{3/2} \cos[j \skew{5}\bar{\lambda}'+(2-j) \skew{5}\bar{\lambda}-2 {\mit\Omega}]$">|; 

$key = q/displaystylephantom{=}+frac{tan(Islash2)}{n,a^{,2},(1-e^{,2})^{1slash2}},frac{partial{calR}}{partialI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4838.png"
 ALT="$\displaystyle \phantom{=} + \frac{\tan(I/2)}{n a^{ 2} (1-e^{ 2})^{1/2}} \frac{\partial {\cal R}}{\partial I},$">|; 

$key = q/displaystylephantom{=}+h,(-2,j-alpha,D),b^{(j)}_{1slash2},sin[(1-j),skew{5}bar{lambda}+j,skew{5}bar{lambda}'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2457.png"
 ALT="$\displaystyle \phantom{=}+ h (-2 j-\alpha D) b^{(j)}_{1/2}
 \sin[(1-j) \skew{5}\bar{\lambda}+j \skew{5}\bar{\lambda}' ]$">|; 

$key = q/displaystylephantom{=}+h,(-2,j-alpha,D),b^{(j)}_{1slash2},sin[j,skew{5}bar{lambda}'+(1-j),skew{5}bar{lambda}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2490.png"
 ALT="$\displaystyle \phantom{=}+ h (-2 j-\alpha D) b^{(j)}_{1/2}
 \sin[j \skew{5}\bar{\lambda}' +(1-j) \skew{5}\bar{\lambda}]$">|; 

$key = q/displaystylephantom{=}+j,e,sin[(1-j),skew{5}bar{lambda}-varpi]+j,e,sin[(1+j),skew{5}bar{lambda}-varpi].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5027.png"
 ALT="$\displaystyle \phantom{=}
+ j e \sin[(1-j) \skew{5}\bar{\lambda}-\varpi] + j e \sin[(1+j) \skew{5}\bar{\lambda}-\varpi].$">|; 

$key = q/displaystylephantom{=}+j^{,2},e,e',cos[(1+j),skew{5}bar{lambda}-(1+j),skew{5}bar{lambda}'-varpi+varpi'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5038.png"
 ALT="$\displaystyle \phantom{=}+ j^{ 2} e e' \cos[(1+j) \skew{5}\bar{\lambda}-(1+j) \skew{5}\bar{\lambda}'-\varpi+\varpi']$">|; 

$key = q/displaystylephantom{=}+j^{,2},e,e',cos[(1-j),skew{5}bar{lambda}-(1-j),skew{5}bar{lambda}'-varpi+varpi'].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5039.png"
 ALT="$\displaystyle \phantom{=}+ j^{ 2} e e' \cos[(1-j) \skew{5}\bar{\lambda}-(1-j) \skew{5}\bar{\lambda}'-\varpi+\varpi'].$">|; 

$key = q/displaystylephantom{=}+k',(-1+2,j+alpha,D),b^{(j-1)}_{1slash2},cos[(1-j),skew{5}bar{lambda}+j,skew{5}bar{lambda}'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2458.png"
 ALT="$\displaystyle \phantom{=}+k' (-1+2 j+\alpha D) b^{(j-1)}_{1/2}
 \cos[ (1-j) \skew{5}\bar{\lambda}+j \skew{5}\bar{\lambda}' ]$">|; 

$key = q/displaystylephantom{=}+k',(-1+2,j+alpha,D),b^{(j-1)}_{1slash2},cos[j,skew{5}bar{lambda}'+(1-j),skew{5}bar{lambda}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2491.png"
 ALT="$\displaystyle \phantom{=}+k' (-1+2 j+\alpha D) b^{(j-1)}_{1/2}
 \cos[ j \skew{5}\bar{\lambda}'+(1-j) \skew{5}\bar{\lambda}]$">|; 

$key = q/displaystylephantom{=}+l_4,m^{,2},sin(2,D)+l_5,m^{,4},sin(4,D)+l_6,m,e,sin(2,D-{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3233.png"
 ALT="$\displaystyle \phantom{=} +l_4 m^{ 2} \sin(2 D) + l_5 m^{ 4} \sin(4 D) + l_6 m e \sin(2 D-{\cal M})$">|; 

$key = q/displaystylephantom{=}+l_7,m^{,2},e,sin(2,D+{calM})+l_8,m,e',sin{calM}'+l_9,m^{,2},e',sin(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3234.png"
 ALT="$\displaystyle \phantom{=}+l_7 m^{ 2} e \sin(2 D+{\cal M})+l_8 m e' \sin {\cal M}' + l_9 m^{ 2} e' \sin(2 D-{\cal M}')$">|; 

$key = q/displaystylephantom{=}+l_{10},m^{,2},e',sin(2,D+{calM}')+l_{11},m,zeta,sinD+l_{12},m^{,2},zeta,sin(3,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3235.png"
 ALT="$\displaystyle \phantom{=}+l_{10} m^{ 2} e' \sin(2 D+{\cal M}')+l_{11} m \zeta \sin D + l_{12} m^{ 2} \zeta \sin(3 D),$">|; 

$key = q/displaystylephantom{=}+left(-frac{9}{8},sin[(1-m),T]+frac{15}{8},sin[3,(1-m),T]right)Y^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3130.png"
 ALT="$\displaystyle \phantom{=} + \left(-\frac{9}{8} \sin[(1-m) T]+\frac{15}{8} \sin[3 (1-m) T]\right)Y^{ 2}$">|; 

$key = q/displaystylephantom{=}+left(frac{11}{8},m^{,2}+frac{59}{12},m^{,3}+frac{893}{72},m^{,4}right)sin(2,D)+frac{201}{256},m^{,4},sin(4,D);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3642.png"
 ALT="$\displaystyle \phantom{=}+\left(\frac{11}{8} m^{ 2}+\frac{59}{12} m^{ 3}+\frac{893}{72} m^{ 4}\right)\sin(2 D)+\frac{201}{256} m^{ 4} \sin(4 D)$">|; 

$key = q/displaystylephantom{=}+left(frac{15}{4},m,e+frac{263}{16},m^{,2},eright)sin(2,D-{calM})+frac{17}{8},m^{,2},e,cos(2,D+{calM}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3589.png"
 ALT="$\displaystyle \phantom{=}+\left(\frac{15}{4} m e +\frac{263}{16} m^{ 2} e\right)\sin (2 D-{\cal M}) +\frac{17}{8} m^{ 2} e \cos(2 D+{\cal M})
,$">|; 

$key = q/displaystylephantom{=}+left(frac{15}{4},m,e+frac{263}{16},m^{,2},eright)sin(2,D-{calM})+frac{17}{8},m^{,2},e,cos(2,D+{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3641.png"
 ALT="$\displaystyle \phantom{=}+\left(\frac{15}{4} m e +\frac{263}{16} m^{ 2} e\right)\sin (2 D-{\cal M}) +\frac{17}{8} m^{ 2} e \cos(2 D+{\cal M})$">|; 

$key = q/displaystylephantom{=}+left(frac{3}{8},cos[(1-m),T]-frac{15}{8},cos[3,(1-m),T]right)Y^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3127.png"
 ALT="$\displaystyle \phantom{=} + \left(\frac{3}{8} \cos[(1-m) T]-\frac{15}{8} \cos[3 (1-m) T]\right)Y^{ 2}$">|; 

$key = q/displaystylephantom{=}+left(frac{3}{8},m,I+frac{25}{32},m^{,2},Iright)sin(2,D-F)+frac{11}{16},m^{,2},I,sin(2,D+F).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3646.png"
 ALT="$\displaystyle \phantom{=}+\left(\frac{3}{8} m I +\frac{25}{32} m^{ 2} I\right)\sin(2 D-F) + \frac{11}{16} m^{ 2} I \sin(2 D+F).$">|; 

$key = q/displaystylephantom{=}+r_4,m^{,2},cos(2,D)+r_5,m^{,4},cos(4,D)+r_6,m,e,cos(2,D-{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3229.png"
 ALT="$\displaystyle \phantom{=} +r_4 m^{ 2} \cos(2 D) + r_5 m^{ 4} \cos(4 D) + r_6 m e \cos(2 D-{\cal M})$">|; 

$key = q/displaystylephantom{=}+r_7,m^{,2},e,cos(2,D+{calM})+r_8,m,e',cos{calM}'+r_9,m^{,2},e',cos(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3230.png"
 ALT="$\displaystyle \phantom{=}+r_7 m^{ 2} e \cos(2 D+{\cal M})+r_8 m e' \cos {\cal M}' + r_9 m^{ 2} e' \cos(2 D-{\cal M}')$">|; 

$key = q/displaystylephantom{=}+r_{10},m^{,2},e',cos(2,D+{calM}')+r_{11},m,zeta,cosD+r_{12},m^{,2},zeta,cos(3,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3231.png"
 ALT="$\displaystyle \phantom{=}+r_{10} m^{ 2} e' \cos(2 D+{\cal M}')+r_{11} m \zeta \cos D + r_{12} m^{ 2} \zeta \cos(3 D),$">|; 

$key = q/displaystylephantom{=}+s,s',alpha,b_{3slash2}^{(j+1)},cos(j,skew{5}bar{lambda}'-j,skew{5}bar{lambda}+{mitOmega}'-{mitOmega});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img5045.png"
 ALT="$\displaystyle \phantom{=}+ s s' \alpha b_{3/2}^{(j+1)} \cos(j \skew{5}\bar{\lambda}'-j \skew{5}\bar{\lambda}+{\mit\Omega}'-{\mit\Omega})$">|; 

$key = q/displaystylephantom{=}+s^{,2}left[cos(omega-{mitOmega}+{calM})-cos(omega+{mitOmega}+{calM})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4993.png"
 ALT="$\displaystyle \phantom{=}+s^{ 2}\left[\cos(\omega-{\mit\Omega}+{\cal M}) - \cos(\omega+{\mit\Omega}+{\cal M})\right],$">|; 

$key = q/displaystylephantom{=}+sin(omega+theta),sin(omega'+theta'),sinI,sinI',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4182.png"
 ALT="$\displaystyle \phantom{=}+\sin(\omega+\theta) \sin(\omega'+\theta') \sin I \sin I',$">|; 

$key = q/displaystylephantom{=}+sin(tilde{omega}+f)left[cosI,sintheta,cos({mitOmega}-phi)+sinI,costhetaright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img4536.png"
 ALT="$\displaystyle \phantom{=}+ \sin(\tilde{\omega}+f)\left[\cos I \sin\theta \cos({\mit\Omega}-\phi)+\sin I \cos\theta\right],$">|; 

$key = q/displaystylephantom{=}+sin({mitOmega}-{mitOmega}'),cos(omega+theta),sin(omega'+theta'),cosI';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4180.png"
 ALT="$\displaystyle \phantom{=}+\sin({\mit\Omega}-{\mit\Omega}') \cos(\omega+\theta) \sin(\omega'+\theta') \cos I'$">|; 

$key = q/displaystylephantom{=}+x_4,m^{,2},cos(2,D)+x_5,m^{,4},cos(4,D)+x_6,m,e,cos(2,D-{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3207.png"
 ALT="$\displaystyle \phantom{=} +x_4 m^{ 2} \cos(2 D) + x_5 m^{ 4} \cos(4 D) + x_6 m e \cos(2 D-{\cal M})$">|; 

$key = q/displaystylephantom{=}+x_7,m^{,2},e,cos(2,D+{calM})+x_8,m,e',cos{calM}'+x_9,m^{,2},e',cos(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3208.png"
 ALT="$\displaystyle \phantom{=}+x_7 m^{ 2} e \cos(2 D+{\cal M})+x_8 m e' \cos {\cal M}' + x_9 m^{ 2} e' \cos(2 D-{\cal M}')$">|; 

$key = q/displaystylephantom{=}+x_{10},m^{,2},e',cos(2,D+{calM}')+x_{11},m,zeta,cosD+x_{12},m^{,2},zeta,cos(3,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3209.png"
 ALT="$\displaystyle \phantom{=}+x_{10} m^{ 2} e' \cos(2 D+{\cal M}')+x_{11} m \zeta \cos D + x_{12} m^{ 2} \zeta \cos(3 D),$">|; 

$key = q/displaystylephantom{=}+y_4,m^{,2},sin(2,D)+y_5,m^{,4},sin(4,D)+y_6,m,e,sin(2,D-{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3212.png"
 ALT="$\displaystyle \phantom{=} +y_4 m^{ 2} \sin(2 D) + y_5 m^{ 4} \sin(4 D) + y_6 m e \sin(2 D-{\cal M})$">|; 

$key = q/displaystylephantom{=}+y_7,m^{,2},e,sin(2,D+{calM})+y_8,m,e',sin{calM}'+y_9,m^{,2},e',sin(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3213.png"
 ALT="$\displaystyle \phantom{=}+y_7 m^{ 2} e \sin(2 D+{\cal M})+y_8 m e' \sin {\cal M}' + y_9 m^{ 2} e' \sin(2 D-{\cal M}')$">|; 

$key = q/displaystylephantom{=}+y_{10},m^{,2},e',sin(2,D+{calM}')+y_{11},m,zeta,sinD+y_{12},m^{,2},zeta,sin(3,D),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3214.png"
 ALT="$\displaystyle \phantom{=}+y_{10} m^{ 2} e' \sin(2 D+{\cal M}')+y_{11} m \zeta \sin D + y_{12} m^{ 2} \zeta \sin(3 D),$">|; 

$key = q/displaystylephantom{=}+z_5,m^{,2},I,sin(2,D+F),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3217.png"
 ALT="$\displaystyle \phantom{=} +z_5 m^{ 2} I \sin(2 D+F),$">|; 

$key = q/displaystylephantom{=}-2,s,s',cos(skew{5}bar{lambda}+skew{5}bar{lambda}'-{mitOmega}-{mitOmega}').;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5010.png"
 ALT="$\displaystyle \phantom{=}-2 s s' \cos(\skew{5}\bar{\lambda}+\skew{5}\bar{\lambda}'-{\mit\Omega}-{\mit\Omega}').$">|; 

$key = q/displaystylephantom{=}-2pi,G,r^{,n}int_r^inftyint_0^pir'^{,1-n},rho(r',theta'),P_n(costheta'),sintheta',dtheta',dr'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img441.png"
 ALT="$\displaystyle \phantom{=}-2\pi G r^{ n}\int_r^\infty \int_0^\pi r'^{ 1-n} 
\rho(r',\theta') P_n(\cos\theta') \sin\theta' d\theta' dr'.$">|; 

$key = q/displaystylephantom{=}-3,deltaX^{,2}+frac{3}{2}left(deltaY^{,2}+deltaZ^{,2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3159.png"
 ALT="$\displaystyle \phantom{=}-3 \delta X^{ 2}+\frac{3}{2}\left(\delta Y^{ 2}+\delta Z^{ 2}\right),$">|; 

$key = q/displaystylephantom{=}-3,m,e',sin{calM}'+frac{77}{16},m^{,2},e',sin(2,D-{calM}')-frac{11}{16},m^{,2},e',sin(2,D+{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3643.png"
 ALT="$\displaystyle \phantom{=}-3 m e' \sin{\cal M}'+\frac{77}{16} m^{ 2} e' \sin(2 D-{\cal M}') -\frac{11}{16} m^{ 2} e' \sin(2 D + {\cal M}')$">|; 

$key = q/displaystylephantom{=}-cosomega,sinIleft[costheta,F_r-left(frac{2+e,costheta}{1+e,costheta}right)sintheta,F_thetaright];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5148.png"
 ALT="$\displaystyle \phantom{=}-\cos\omega \sin I\left[\cos\theta F_r-\left(\frac{2+e \cos\theta}{1+e \cos\theta}\right)\sin\theta F_\theta \right]$">|; 

$key = q/displaystylephantom{=}-e,e',cos(2,skew{5}bar{lambda}-varpi-varpi')-e,e',cos(2,skew{5}bar{lambda}'-varpi-varpi');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5008.png"
 ALT="$\displaystyle \phantom{=}-e e' \cos(2 \skew{5}\bar{\lambda}-\varpi-\varpi')-e e' \cos(2 \skew{5}\bar{\lambda}'-\varpi-\varpi')$">|; 

$key = q/displaystylephantom{=}-frac{1}{4},(k,k'+h,h'),alpha,b_{3slash2}^{(2)}+frac{1}{4},(p,p'+q,q'),alpha,b_{3slash2}^{(1)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2506.png"
 ALT="$\displaystyle \phantom{=}-\frac{1}{4} (k k'+h h') \alpha b_{3/2}^{(2)}+\frac{1}{4} (p p'+q q') \alpha b_{3/2}^{(1)},$">|; 

$key = q/displaystylephantom{=}-frac{1}{4},(k,k'+h,h'),alpha^{,2},b_{3slash2}^{(2)}+frac{1}{4},(p,p'+q,q'),alpha^{,2},b_{3slash2}^{(1)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2533.png"
 ALT="$\displaystyle \phantom{=}-\frac{1}{4} (k k'+h h') \alpha^{ 2} b_{3/2}^{(2)}+\frac{1}{4} (p p'+q q') \alpha^{ 2} b_{3/2}^{(1)}.$">|; 

$key = q/displaystylephantom{=}-frac{1}{8},(p^{,2}+q^{,2}+p'^{,2}+q'^{,2}),alpha,b_{3slash2}^{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img5073.png"
 ALT="$\displaystyle \phantom{=} - \frac{1}{8} (p^{ 2}+q^{ 2}+p'^{ 2}+q'^{ 2}) \alpha b_{3/2}^{(1)}$">|; 

$key = q/displaystylephantom{=}-frac{1}{8},(p^{,2}+q^{,2}+p'^{,2}+q'^{,2}),alpha^{,2},b_{3slash2}^{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img5081.png"
 ALT="$\displaystyle \phantom{=}- \frac{1}{8} (p^{ 2}+q^{ 2}+p'^{ 2}+q'^{ 2}) \alpha^{ 2} b_{3/2}^{(1)}$">|; 

$key = q/displaystylephantom{=}-frac{21}{4},m^{,2},e',sin[(2-3,m),T]+frac{3}{4},m^{,2},e',sin[(2-m),T];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3162.png"
 ALT="$\displaystyle \phantom{=} - \frac{21}{4} m^{ 2} e' \sin[(2-3 m) T]+\frac{3}{4} m^{ 2} e' \sin[(2-m) T]$">|; 

$key = q/displaystylephantom{=}-frac{3}{2},m^{,2},sin(2,D),deltaX-frac{3}{2},m^{,2},cos(2,D),deltaY+3,deltaX,deltaY,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3201.png"
 ALT="$\displaystyle \phantom{=} -\frac{3}{2} m^{ 2} \sin(2 D) \delta X -\frac{3}{2} m^{ 2} \cos(2 D) \delta Y +3 \delta X \delta Y,$">|; 

$key = q/displaystylephantom{=}-frac{3}{2},m^{,2},sin[2,(1-m),T],deltaX-frac{3}{2},m^{,2},cos[2,(1-m),T],deltaY+3,deltaX,deltaY,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3164.png"
 ALT="$\displaystyle \phantom{=}-\frac{3}{2} m^{ 2} \sin[2 (1-m) T] \delta X -\frac{3}{2} m^{ 2} \cos[2 (1-m) T] \delta Y+3 \delta X \delta Y,$">|; 

$key = q/displaystylephantom{=}-frac{3}{4},m^{,2},e',cos(2,D+{calM}')+frac{9}{8},m^{,2},zeta,cosD+frac{15}{8},m^{,2},zeta,cos(3,D);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3197.png"
 ALT="$\displaystyle \phantom{=} -
\frac{3}{4} m^{ 2} e' \cos(2 D+{\cal M}') + \frac{9}{8} m^{ 2} \zeta \cos D + \frac{15}{8} m^{ 2} \zeta \cos(3 D)$">|; 

$key = q/displaystylephantom{=}-frac{3}{8},m^{,2},zeta,sin[(1-m),T]-frac{15}{8},m^{,2},zeta,sin[3,(1-m),T],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3163.png"
 ALT="$\displaystyle \phantom{=} -\frac{3}{8} m^{ 2} \zeta \sin[(1-m) T] - \frac{15}{8} m^{ 2} \zeta \sin[3 (1-m) T],$">|; 

$key = q/displaystylephantom{=}-frac{cosI}{n,a^{,2},(1-e^{,2})^{1slash2}},frac{partial{calR}}{partialp}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4875.png"
 ALT="$\displaystyle \phantom{=}- \frac{\cos I}{n a^{ 2} (1-e^{ 2})^{1/2}} \frac{\partial {\cal R}}{\partial p}.$">|; 

$key = q/displaystylephantom{=}-frac{e,cosI,sintheta,F_z}{1+e,costheta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img5149.png"
 ALT="$\displaystyle \phantom{=}- \frac{e \cos I \sin\theta F_z}{1+e \cos\theta}.$">|; 

$key = q/displaystylephantom{=}-frac{e^{,4}}{3}left(cos4{calM}-cos2{calM}right)+{calO}(e^5).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4060.png"
 ALT="$\displaystyle \phantom{=}
- \frac{e^{ 4}}{3}\left(\cos 4{\cal M}-\cos 2{\cal M}\right)+{\cal O}(e^5).$">|; 

$key = q/displaystylephantom{=}-frac{n,epsilon'alpha,cosI}{(1-e^{,2})^{1slash2}},frac{partial{calS}}{partialp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4897.png"
 ALT="$\displaystyle \phantom{=}- \frac{n \epsilon'\alpha \cos I}{(1-e^{ 2})^{1/2}} \frac{\partial {\cal S}}{\partial p},$">|; 

$key = q/displaystylephantom{=}-j,e,cos[(1-j),skew{5}bar{lambda}-varpi]+j,e,cos[(1+j),skew{5}bar{lambda}-varpi)],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5022.png"
 ALT="$\displaystyle \phantom{=}
- j e \cos[(1-j) \skew{5}\bar{\lambda}-\varpi] + j e \cos[(1+j) \skew{5}\bar{\lambda}-\varpi)],$">|; 

$key = q/displaystylephantom{=}-j^{,2},e,e',cos[(1+j),skew{5}bar{lambda}+(1-j),skew{5}bar{lambda}'-varpi-varpi'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5036.png"
 ALT="$\displaystyle \phantom{=}-j^{ 2} e e' \cos[(1+j) \skew{5}\bar{\lambda}+ (1-j) \skew{5}\bar{\lambda}'-\varpi-\varpi']$">|; 

$key = q/displaystylephantom{=}-j^{,2},e,e',cos[(1-j),skew{5}bar{lambda}+(1+j),skew{5}bar{lambda}'-varpi-varpi'];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5037.png"
 ALT="$\displaystyle \phantom{=}-j^{ 2} e e' \cos[(1-j) \skew{5}\bar{\lambda}+(1+j) \skew{5}\bar{\lambda}'-\varpi-\varpi']$">|; 

$key = q/displaystylephantom{=}-left(frac{15}{8},m,e+frac{155}{32},m^{,2},eright)cos(2,D-{calM})-frac{17}{16},m^{,2},e,cos(2,D+{calM}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3587.png"
 ALT="$\displaystyle \phantom{=}-\left(\frac{15}{8} m e +\frac{155}{32} m^{ 2} e\right)\cos (2 D-{\cal M}) -\frac{17}{16} m^{ 2} e \cos(2 D+{\cal M}),$">|; 

$key = q/displaystylephantom{=}-left(frac{15}{8},m,e+frac{155}{32},m^{,2},eright)cos(2,D-{calM})-frac{17}{16},m^{,2},e,cos(2,D+{calM});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3636.png"
 ALT="$\displaystyle \phantom{=}-\left(\frac{15}{8} m e +\frac{155}{32} m^{ 2} e\right)\cos (2 D-{\cal M}) -\frac{17}{16} m^{ 2} e \cos(2 D+{\cal M})$">|; 

$key = q/displaystylephantom{=}-s,s',alpha,b_{3slash2}^{(j-1)},cos[j,skew{5}bar{lambda}'+(2-j),skew{5}bar{lambda}-{mitOmega}'-{mitOmega}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img5052.png"
 ALT="$\displaystyle \phantom{=}- s s' \alpha b_{3/2}^{(j-1)} \cos[j \skew{5}\bar{\lambda}'+(2-j) \skew{5}\bar{\lambda}-{\mit\Omega}'-{\mit\Omega}]$">|; 

$key = q/displaystylephantom{=}-s^{,2}left[sin(omega-{mitOmega}+{calM})+sin(omega+{mitOmega}+{calM})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4997.png"
 ALT="$\displaystyle \phantom{=}-s^{ 2}\left[\sin(\omega-{\mit\Omega}+{\cal M}) +\sin(\omega+{\mit\Omega}+{\cal M})\right],$">|; 

$key = q/displaystylephantom{=}-sin({mitOmega}-{mitOmega}'),cos(omega+theta),cos(omega'+theta'),cosI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4184.png"
 ALT="$\displaystyle \phantom{=}-\sin({\mit\Omega}-{\mit\Omega}') \cos(\omega+\theta) \cos(\omega'+\theta') \cos I$">|; 

$key = q/displaystylephantom{=}-sin({mitOmega}-{mitOmega}'),sin(omega+theta),cos(omega'+theta'),cosI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4179.png"
 ALT="$\displaystyle \phantom{=}-\sin({\mit\Omega}-{\mit\Omega}') \sin(\omega+\theta) \cos(\omega'+\theta') \cos I$">|; 

$key = q/displaystylephantom{=}-sin({mitOmega}-{mitOmega}'),sin(omega+theta),sin(omega'+theta'),cosI';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4185.png"
 ALT="$\displaystyle \phantom{=}-\sin({\mit\Omega}-{\mit\Omega}') \sin(\omega+\theta) \sin(\omega'+\theta') \cos I'$">|; 

$key = q/displaystylephantom{=}=0.090'',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4614.png"
 ALT="$\displaystyle \phantom{=}=0.090'',$">|; 

$key = q/displaystylephantom{=}=0.21''.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4619.png"
 ALT="$\displaystyle \phantom{=}= 0.21''.$">|; 

$key = q/displaystylephantom{=}=17.2'',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4616.png"
 ALT="$\displaystyle \phantom{=}= 17.2'',$">|; 

$key = q/displaystylephantom{=}=9.2'',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4612.png"
 ALT="$\displaystyle \phantom{=} = 9.2'',$">|; 

$key = q/displaystylephantom{=}left.+3,I_m,sin(2,theta),sin(lambda_m-phi),sin(lambda_m-alpha_n)-1right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img1760.png"
 ALT="$\displaystyle \phantom{=}\left.
+ 3 I_m \sin(2 \theta) \sin(\lambda_m-\phi) \sin(\lambda_m-\alpha_n)-1\right]$">|; 

$key = q/displaystylephantom{=}left.+frac{21}{4},e',cos[(2-3,m),T]right}X+m^{,2}left{-frac{3}{2},sin[2,(1-m),T]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3120.png"
 ALT="$\displaystyle \phantom{=}\left.+\frac{21}{4} e' \cos[(2-3 m) T]\right\}X+m^{ 2}\left\{-\frac{3}{2} \sin[2 (1-m) T]\right.$">|; 

$key = q/displaystylephantom{=}left.+frac{3}{4},e',sin[(2-m),T]-frac{21}{4},e',sin[(2-3,m),T]right}X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3124.png"
 ALT="$\displaystyle \phantom{=}\left.+\frac{3}{4} e' \sin[(2-m) T] -\frac{21}{4} e' \sin[(2-3 m) T]\right\}X,$">|; 

$key = q/displaystylephantom{=}left.+frac{3}{4},e',sin[(2-m),T]-frac{21}{4},e',sin[(2-3,m),T]right}Y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3121.png"
 ALT="$\displaystyle \phantom{=}\left. +\frac{3}{4} e' \sin[(2-m) T]-\frac{21}{4} e' \sin[(2-3 m) T]\right\}Y,$">|; 

$key = q/displaystylephantom{=}left.+frac{7,e}{2},sin(2,phi-3,{calM})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1864.png"
 ALT="$\displaystyle \phantom{=}\left.+ \frac{7 e}{2} \sin(2 \phi-3 {\cal M})\right],$">|; 

$key = q/displaystylephantom{=}left.+frac{alpha,cosI}{(1-e^{,2})^{1slash2}},frac{partial{calS}}{partialq}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4917.png"
 ALT="$\displaystyle \phantom{=}\left.+ \frac{\alpha \cos I}{(1-e^{ 2})^{1/2}} \frac{\partial {\cal S}}{\partial q}\right],$">|; 

$key = q/displaystylephantom{=}left.+h',(-1+2,j+alpha,D),b^{(j-1)}_{1slash2},sin[(1-j),skew{5}bar{lambda}+j,skew{5}bar{lambda}']right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2459.png"
 ALT="$\displaystyle \phantom{=}\left. +h' (-1+2 j+\alpha D) b^{(j-1)}_{1/2}
 \sin[ (1-j) \skew{5}\bar{\lambda}+j \skew{5}\bar{\lambda}' ]\right\}$">|; 

$key = q/displaystylephantom{=}left.+h',(-1+2,j+alpha,D),b^{(j-1)}_{1slash2},sin[j,skew{5}bar{lambda}'+(1-j),skew{5}bar{lambda}]right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2492.png"
 ALT="$\displaystyle \phantom{=}\left. +h' (-1+2 j+\alpha D) b^{(j-1)}_{1/2}
 \sin[ j \skew{5}\bar{\lambda}' +(1-j) \skew{5}\bar{\lambda}]\right\}$">|; 

$key = q/displaystylephantom{=}left.+left(-frac{e}{2},sin[(2,p-1),n,t]+sin[2,(p-1),n,t]+frac{7,e}{2},sin[(2,p-3),n,t]right)cos2gammaright].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1881.png"
 ALT="$\displaystyle \phantom{=}\left.+\left(-\frac{e}{2} \sin[(2 p-1) n t]
+\sin[2 (p-1) n t]+\frac{7 e}{2} \sin[(2 p-3) n t]\right)\cos 2\gamma\right].$">|; 

$key = q/displaystylephantom{=}left.+left(frac{3}{4},cos[(1-m),T]-frac{15}{4},cos[3,(1-m),T]right)X,Y+left(frac{3}{2},sin[(1-m),T]right)Z^{,2}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3131.png"
 ALT="$\displaystyle \phantom{=} \left.+ \left(\frac{3}{4} \cos[(1-m) T]-\frac{15}{4...
...,(1-m) T]\right)X Y +\left(\frac{3}{2} \sin[(1-m) T]\right)Z^{ 2}\right\},$">|; 

$key = q/displaystylephantom{=}left.+sin(2,I),sin(2,theta),cos({mitOmega}-phi)-sin^2I,sin^2theta,cos[2,({mitOmega}-phi)]right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4540.png"
 ALT="$\displaystyle \phantom{=}\left. + \sin(2 I) \sin(2 \theta) \cos ({\mit\Omega}-\phi)
-\sin^2 I  \sin^2\theta \cos[2 ({\mit\Omega}-\phi)]\right\},$">|; 

$key = q/displaystylephantom{=}left.-4,k',cos(skew{5}bar{lambda}-2,skew{5}bar{lambda}')+4,h',sin(skew{5}bar{lambda}-2,skew{5}bar{lambda}')right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2461.png"
 ALT="$\displaystyle \phantom{=}\left.-4 k' \cos(\skew{5}\bar{\lambda}-2 \skew{5}\b...
...lambda}')+4 h' \sin(\skew{5}\bar{\lambda}-2 \skew{5}\bar{\lambda}')\right\},$">|; 

$key = q/displaystylephantom{=}left.-frac{21}{4},e',cos[(2-3,m),T]right}Y+m^{,2}left{-frac{3}{2},sin[2,(1-m),T]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3123.png"
 ALT="$\displaystyle \phantom{=}\left.-\frac{21}{4} e' \cos[(2-3 m) T]\right\}Y+m^{ 2}\left\{-\frac{3}{2} \sin[2 (1-m) T]\right.$">|; 

$key = q/displaystylephantom{=}left.-frac{alpha,cosI}{(1-e^{,2})^{1slash2}},frac{partial{calS}}{partialp}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4919.png"
 ALT="$\displaystyle \phantom{=}\left.- \frac{\alpha \cos I}{(1-e^{ 2})^{1/2}} \frac{\partial {\cal S}}{\partial p}\right],$">|; 

$key = q/displaystylephantom{=}left.-left(frac{3}{4},sin[(1-m),T]+frac{15}{4},sin[3,(1-m),T]right)X,Y-left(frac{3}{2},cos[(1-m),T]right)Z^{,2}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3128.png"
 ALT="$\displaystyle \phantom{=} \left.- \left(\frac{3}{4} \sin[(1-m) T]+\frac{15}{4...
...,(1-m) T]\right)X Y -\left(\frac{3}{2} \cos[(1-m) T]\right)Z^{ 2}\right\},$">|; 

$key = q/displaystylephantom{simeq}+left(frac{m_1}{m_1+m_2}right)^3left(frac{r}{r'}right)^3P_3(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3005.png"
 ALT="$\displaystyle \phantom{\simeq}
+\left(\frac{m_1}{m_1+m_2}\right)^3\left(\frac{r}{r'}\right)^3 P_3(\cos\theta),$">|; 

$key = q/displaystylephantom{simeq}-left(frac{m_2}{m_1+m_2}right)^3left(frac{r}{r'}right)^3P_3(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3002.png"
 ALT="$\displaystyle \phantom{\simeq}
-\left(\frac{m_2}{m_1+m_2}\right)^3\left(\frac{r}{r'}\right)^3 P_3(\cos\theta),$">|; 

$key = q/displaystylephi(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1781.png"
 ALT="$\displaystyle \phi(t)$">|; 

$key = q/displaystylephi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4554.png"
 ALT="$\displaystyle \phi$">|; 

$key = q/displaystylephi=tan^{-1}left(frac{b}{a}right)=tan^{-1}left(sqrt{e^{,2}-1},right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4021.png"
 ALT="$\displaystyle \phi = \tan^{-1}\left(\frac{b}{a}\right) = \tan^{-1}\left(\sqrt{e^{ 2}-1} \right)$">|; 

$key = q/displaystylephisimeq-{mitOmega}_phi,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1733.png"
 ALT="$\displaystyle \phi \simeq- {\mit\Omega}_\phi t,$">|; 

$key = q/displaystylepileft(1-frac{3}{2},frac{M_0}{M}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1057.png"
 ALT="$\displaystyle \pi \left(1- \frac{3}{2} \frac{M_0}{M}\right),
$">|; 

$key = q/displaystylepileft(frac{m,a^{,3}}{8,c}right)^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img294.png"
 ALT="$\displaystyle \pi\left(\frac{m a^{ 3}}{8 c}\right)^{1/2}.
$">|; 

$key = q/displaystylepsi(eta)=frac{1+etaslash2-eta^{,2}slash10}{(1+eta)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4388.png"
 ALT="$\displaystyle \psi(\eta) =\frac{1+\eta/2-\eta^{ 2}/10}{(1+\eta)^{1/2}}.$">|; 

$key = q/displaystylepsi=(n+g),t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2018.png"
 ALT="$\displaystyle \psi = (n+g) t,$">|; 

$key = q/displaystylepsi=frac{T}{2},skew{5}dot{theta}=pileft[3+r_c,frac{f'(r_c)}{f(r_c)}right]^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img981.png"
 ALT="$\displaystyle \psi = \frac{T}{2}  \skew{5}\dot{\theta} = \pi \left[3+r_c \frac{f'(r_c)}{f(r_c)}\right]^{-1/2}$">|; 

$key = q/displaystylepsi=frac{pi}{(3+n)^{1slash2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img983.png"
 ALT="$\displaystyle \psi = \frac{\pi}{(3+n)^{1/2}}.$">|; 

$key = q/displaystylepsisimeqpileft(1+frac{3,h^{,2}}{c^{,2},r^{,2}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1024.png"
 ALT="$\displaystyle \psi \simeq \pi\left(1+ \frac{3 h^{ 2}}{c^{ 2} r^{ 2}}\right).$">|; 

$key = q/displaystyleq(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2661.png"
 ALT="$\displaystyle q(t)$">|; 

$key = q/displaystyleq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img4863.png"
 ALT="$\displaystyle q$">|; 

$key = q/displaystyleq_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2585.png"
 ALT="$\displaystyle q_i$">|; 

$key = q/displaystyleq_{rmforced};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2669.png"
 ALT="$\displaystyle q_{\rm forced}$">|; 

$key = q/displaystyler'(theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4170.png"
 ALT="$\displaystyle r'(\theta')$">|; 

$key = q/displaystyler(a,theta)=a+delta(a,theta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4345.png"
 ALT="$\displaystyle r(a,\theta)= a + \delta(a,\theta),$">|; 

$key = q/displaystyler(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4169.png"
 ALT="$\displaystyle r (\theta)$">|; 

$key = q/displaystyler(theta)=frac{r_c}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img625.png"
 ALT="$\displaystyle r(\theta) = \frac{r_c}{1 + e \cos\theta},$">|; 

$key = q/displaystyler,costheta=a,(cosE-e).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img701.png"
 ALT="$\displaystyle r \cos\theta = a (\cos E-e).$">|; 

$key = q/displaystyler,frac{partialxi_i}{partialr}-xi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4288.png"
 ALT="$\displaystyle r \frac{\partial\xi_i}{\partial r}-\xi_i$">|; 

$key = q/displaystyler,skew{5}ddot{theta}+2,skew{3}dot{r},skew{5}dot{theta}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img604.png"
 ALT="$\displaystyle r \skew{5}\ddot{\theta} + 2 \skew{3}\dot{r} \skew{5}\dot{\theta} = 0.$">|; 

$key = q/displaystyler,xi_r=(2,A+B),r^{,2},p_2+2,phi_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4285.png"
 ALT="$\displaystyle r \xi_r = (2 A+B) r^{ 2} p_2 + 2 \phi_2,$">|; 

$key = q/displaystyler;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img644.png"
 ALT="$\displaystyle r$">|; 

$key = q/displaystyler=R'(theta)=Rleft[1-frac{2}{3},epsilon',P_2(costheta)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1266.png"
 ALT="$\displaystyle r = R'(\theta) = R\left[1-\frac{2}{3} \epsilon' P_2(\cos\theta)\right].$">|; 

$key = q/displaystyler=R+delta(theta,phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4440.png"
 ALT="$\displaystyle r = R + \delta(\theta,\phi),$">|; 

$key = q/displaystyler=R_theta(theta)=Rleft[1-frac{2}{3},epsilon,P_2(costheta)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img463.png"
 ALT="$\displaystyle r = R_\theta(\theta) = R\left[1-\frac{2}{3} \epsilon P_2(\cos\theta)\right],$">|; 

$key = q/displaystyler=a+delta_2(theta,phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4228.png"
 ALT="$\displaystyle r = a + \delta_2(\theta,\phi),$">|; 

$key = q/displaystyler=aleft[1-frac{2}{3},epsilon(a),P_2(costheta)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4328.png"
 ALT="$\displaystyle r = a\left[1-\frac{2}{3} \epsilon(a) P_2(\cos\theta)\right].$">|; 

$key = q/displaystyler=frac{a,(1-e^{,2})}{1+e,cos(alpha,theta)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img1043.png"
 ALT="$\displaystyle r = \frac{a  (1-e^{ 2} )}{1+e \cos(\alpha \theta)} ,
$">|; 

$key = q/displaystyler=frac{a,(1-e^{,2})}{1+e,cosf}=a,(1-e,cosE).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4531.png"
 ALT="$\displaystyle r = \frac{a (1-e^{ 2})}{1+e \cos f} = a (1-e \cos E).$">|; 

$key = q/displaystyler=frac{a,(1-e^{,2})}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img855.png"
 ALT="$\displaystyle r = \frac{a (1-e^{ 2})}{1+e \cos\theta},$">|; 

$key = q/displaystyler=frac{r_c}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img4001.png"
 ALT="$\displaystyle r = \frac{r_c}{1+e \cos\theta},$">|; 

$key = q/displaystyler=frac{r_p,(1+e)}{1+e,costheta},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img675.png"
 ALT="$\displaystyle r = \frac{r_p (1+e)}{1+e \cos\theta},$">|; 

$key = q/displaystyler=frac{r_p}{1-e},(1-e,cosE),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.24ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img682.png"
 ALT="$\displaystyle r = \frac{r_p}{1-e} (1-e \cos E),$">|; 

$key = q/displaystyler=frac{varv}{2,{mitOmega},sinlambda},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1337.png"
 ALT="$\displaystyle r = \frac{\varv}{2 {\mit\Omega} \sin\lambda},
$">|; 

$key = q/displaystyler=r_0,theta^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img950.png"
 ALT="$\displaystyle r = r_0 \theta^{ 2}.$">|; 

$key = q/displaystyler^{,2},nabla^{,2}Y_l^{,m}+l,(l+1),Y_l^{,m}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img4109.png"
 ALT="$\displaystyle r^{ 2} \nabla^{ 2} Y_l^{ m} + l (l+1) Y_l^{ m} = 0$">|; 

$key = q/displaystyler^{,2},nabla^{,2}{calS}_n+n,(n+1),{calS}_n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4209.png"
 ALT="$\displaystyle r^{ 2} \nabla^{ 2} {\cal S}_n + n (n+1) {\cal S}_n = 0$">|; 

$key = q/displaystyler^{,2},skew{5}ddot{theta}+2,r,skew{3}dot{r},skew{5}dot{theta}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img605.png"
 ALT="$\displaystyle r^{ 2} \skew{5}\ddot{\theta} + 2 r \skew{3}\dot{r} \skew{5}\dot{\theta} = 0.$">|; 

$key = q/displaystyler^{,2},skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1434.png"
 ALT="$\displaystyle r^{ 2} \skew{5}\dot{\theta}$">|; 

$key = q/displaystyler^{,2}=A,t^{,2}+B,t+C,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1032.png"
 ALT="$\displaystyle r^{ 2} = A t^{ 2}+B t+C,
$">|; 

$key = q/displaystyler_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3309.png"
 ALT="$\displaystyle r_1$">|; 

$key = q/displaystyler_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3311.png"
 ALT="$\displaystyle r_2$">|; 

$key = q/displaystyler_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3313.png"
 ALT="$\displaystyle r_3$">|; 

$key = q/displaystyler_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3315.png"
 ALT="$\displaystyle r_4$">|; 

$key = q/displaystyler_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3317.png"
 ALT="$\displaystyle r_5$">|; 

$key = q/displaystyler_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3319.png"
 ALT="$\displaystyle r_6$">|; 

$key = q/displaystyler_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3321.png"
 ALT="$\displaystyle r_7$">|; 

$key = q/displaystyler_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3323.png"
 ALT="$\displaystyle r_8$">|; 

$key = q/displaystyler_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3325.png"
 ALT="$\displaystyle r_9$">|; 

$key = q/displaystyler_c=frac{h^{,2}}{G,M}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img626.png"
 ALT="$\displaystyle r_c = \frac{h^{ 2}}{G M}.$">|; 

$key = q/displaystyler_p=frac{2,b}{alpha+sqrt{alpha^{,2}+4}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img931.png"
 ALT="$\displaystyle r_p = \frac{2 b}{\alpha+\sqrt{\alpha^{ 2}+4}},
$">|; 

$key = q/displaystyler_p=frac{r_c}{1+e}=a,(1-e).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img636.png"
 ALT="$\displaystyle r_p = \frac{r_c}{1+e} = a (1-e).$">|; 

$key = q/displaystyler_{01};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3303.png"
 ALT="$\displaystyle r_{01}$">|; 

$key = q/displaystyler_{02};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3305.png"
 ALT="$\displaystyle r_{02}$">|; 

$key = q/displaystyler_{03};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3307.png"
 ALT="$\displaystyle r_{03}$">|; 

$key = q/displaystyler_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3327.png"
 ALT="$\displaystyle r_{10}$">|; 

$key = q/displaystyler_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3329.png"
 ALT="$\displaystyle r_{11}$">|; 

$key = q/displaystyler_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2986.png"
 ALT="$\displaystyle r_{12}$">|; 

$key = q/displaystyler_{13};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2988.png"
 ALT="$\displaystyle r_{13}$">|; 

$key = q/displaystyler_{23};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2990.png"
 ALT="$\displaystyle r_{23}$">|; 

$key = q/displaystyler_{ij}=|{bfr}_i-{bfr}_j|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2956.png"
 ALT="$\displaystyle r_{ij} = \vert{\bf r}_i-{\bf r}_j\vert.$">|; 

$key = q/displaystylerho(a)=rho_0,a^{-alpha},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4411.png"
 ALT="$\displaystyle \rho(a) =\rho_0 a^{-\alpha},$">|; 

$key = q/displaystylerho(r)=left{{array}{lcc}rho_0,r^{-alpha}&mbox{hspace{1cm}}&rleqR[0.5ex]0&&r>R{array}right.,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img556.png"
 ALT="$\displaystyle \rho(r) = \left\{\begin{array}{lcc} \rho_0 r^{-\alpha}&amp;\mbox{\hspace{1cm}}&amp; r \leq R\ [0.5ex]
0&amp;&amp; r&gt;R\end{array}\right.,
$">|; 

$key = q/displaystylerho(r)=rho_0expleft[-frac{(r-R)}{H}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2733.png"
 ALT="$\displaystyle \rho(r) = \rho_0\exp\left[-\frac{(r-R)}{H}\right],$">|; 

$key = q/displaystylerho(r,theta)=sum_{n=0,infty}rho_n(r),P_n(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img4332.png"
 ALT="$\displaystyle \rho(r,\theta)=\sum_{n=0,\infty}\rho_n(r) P_n(\cos\theta),$">|; 

$key = q/displaystylerho(r,theta)=sum_{n=0,infty}rho_n(r),P_n(costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img442.png"
 ALT="$\displaystyle \rho(r,\theta) = \sum_{n=0,\infty} \rho_n(r) P_n(\cos\theta).$">|; 

$key = q/displaystylerho({bfr})=rho_0(r)+gamma,delta(theta,phi),delta(r-R),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4442.png"
 ALT="$\displaystyle \rho({\bf r}) = \rho_0(r)+\gamma \delta(\theta,\phi) \delta(r-R),$">|; 

$key = q/displaystylerho=frac{m'}{M},a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1209.png"
 ALT="$\displaystyle \rho = \frac{m'}{M} a,$">|; 

$key = q/displaystylerho=rho(a),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4327.png"
 ALT="$\displaystyle \rho=\rho(a),$">|; 

$key = q/displaystylerho_0(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4337.png"
 ALT="$\displaystyle \rho_0(r)$">|; 

$key = q/displaystylerho_0(r)=left{{array}{ccc}gamma&mbox{hspace{0.5cm}}&mbox{forrleqR}0&&mbox{forr>R}{array}right.,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img447.png"
 ALT="$\displaystyle \rho_0(r) = \left\{\begin{array}{ccc}
\gamma&amp;\mbox{\hspace{0.5cm}}&amp;\mbox{for $r\leq R$}\\\\
0&amp;&amp;\mbox{for $r&gt;R$}\end{array}\right.,$">|; 

$key = q/displaystylerho_1,skew{3}dot{rho}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2118.png"
 ALT="$\displaystyle \rho_1 \skew{3}\dot{\rho}_1$">|; 

$key = q/displaystylerho_1=rho_2=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2213.png"
 ALT="$\displaystyle \rho_1 = \rho_2 =1,$">|; 

$key = q/displaystylerho_1^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2112.png"
 ALT="$\displaystyle \rho_1^{ 2}$">|; 

$key = q/displaystylerho_2(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4339.png"
 ALT="$\displaystyle \rho_2(r)$">|; 

$key = q/displaystylerho_2,skew{3}dot{rho}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2120.png"
 ALT="$\displaystyle \rho_2 \skew{3}\dot{\rho}_2$">|; 

$key = q/displaystylerho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2202.png"
 ALT="$\displaystyle \rho_2$">|; 

$key = q/displaystylerho_2=alpha-frac{alpha^{,2}}{3}-frac{alpha^{,3}}{9}-frac{23,alpha^{,4}}{81}+{calO}(alpha^{,5}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.67ex; " SRC="|."$dir".q|img2195.png"
 ALT="$\displaystyle \rho_2 = \alpha - \frac{\alpha^{ 2}}{3} - \frac{\alpha^{ 3}}{9} -\frac{23 \alpha^{ 4}}{81}+{\cal O}(\alpha^{ 5}),$">|; 

$key = q/displaystylerho_2^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2114.png"
 ALT="$\displaystyle \rho_2^{ 2}$">|; 

$key = q/displaystylerho_n(r)=(n+1slash2)int_0^pileft[rho(r)+frac{2}{3},r,frac{drho}{dr},epsilon(r),P_2(costheta)right]P_n(costheta),sintheta,dtheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4336.png"
 ALT="$\displaystyle \rho_n(r)= (n+1/2)\int_0^\pi\left[\rho(r)+\frac{2}{3} r \frac{d...
...}{dr} \epsilon(r) P_2(\cos\theta)\right]P_n(\cos\theta) \sin\theta d\theta.$">|; 

$key = q/displaystylerho_n(r)=(n+1slash2)int_0^pirho(a),P_n(costheta),sintheta,dtheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4333.png"
 ALT="$\displaystyle \rho_n(r)=(n+1/2)\int_0^\pi \rho(a) P_n(\cos\theta) \sin\theta d\theta.$">|; 

$key = q/displaystylerho_n(r)=(n+1slash2)int_0^pirho(r,theta),P_n(costheta),sintheta,dtheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img443.png"
 ALT="$\displaystyle \rho_n(r) = (n+1/2)\int_0^\pi\rho(r,\theta) P_n(\cos\theta) \sin\theta d\theta.$">|; 

$key = q/displaystylerightarrow0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4238.png"
 ALT="$\displaystyle \rightarrow 0,$">|; 

$key = q/displaystylerightarrow{mitchi}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4240.png"
 ALT="$\displaystyle \rightarrow {\mit\chi}_2$">|; 

$key = q/displaystylesigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1982.png"
 ALT="$\displaystyle \sigma$">|; 

$key = q/displaystylesigma_{ij}=-p,delta_{ij}+muleft(frac{partialxi_i}{partialx_j}+frac{partialxi_j}{partialx_i}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4258.png"
 ALT="$\displaystyle \sigma_{ij} = -p \delta_{ij} + \mu\left(\frac{\partial \xi_i}{\partial x_j}+\frac{\partial \xi_j}{\partial x_i}\right),$">|; 

$key = q/displaystylesimeq(-iota,sinpsi,,,-iota,cospsi,,,1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2066.png"
 ALT="$\displaystyle \simeq (-\iota \sin\psi,  -\iota \cos\psi,  1),$">|; 

$key = q/displaystylesimeq(1-j^{,2},e^{,2}-j^{,2},e'^{,2}),cos[j,(skew{5}bar{lambda}-skew{5}bar{lambda}')];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5029.png"
 ALT="$\displaystyle \simeq (1-j^{ 2} e^{ 2}-j^{ 2} e'^{ 2})  \cos[j (\skew{5}\bar{\lambda}-\skew{5}\bar{\lambda}')]$">|; 

$key = q/displaystylesimeq(n-n'),t+2,e,sin[(n-n_p),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3711.png"
 ALT="$\displaystyle \simeq (n-n') t + 2 e \sin[(n-n_p) t],$">|; 

$key = q/displaystylesimeq(nu_x,,nu_y,,1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1961.png"
 ALT="$\displaystyle \simeq(\nu_x, \nu_y, 1),$">|; 

$key = q/displaystylesimeq(p_x,,p_y,,1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1963.png"
 ALT="$\displaystyle \simeq (p_x, p_y, 1),$">|; 

$key = q/displaystylesimeq-2,alpha,[1-(3slash2),sin^2I],sin(2,theta)-2,alpha,sin(2,I),cos(2,theta),cos({mitOmega}-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4549.png"
 ALT="$\displaystyle \simeq -2 \alpha [1-(3/2) \sin^2 I] \sin(2 \theta)-2 \alpha \sin(2 I) \cos(2 \theta) \cos({\mit\Omega}-\phi)$">|; 

$key = q/displaystylesimeq-2,e,sin(omega_+,t-phi_+),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2383.png"
 ALT="$\displaystyle \simeq -2 e \sin(\omega_+ t-\phi_+),$">|; 

$key = q/displaystylesimeq-2,{mitOmega},varv_0,sinlambda,costheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1140.png"
 ALT="$\displaystyle \simeq -2 {\mit\Omega} \varv_0 \sin\lambda \cos\theta,$">|; 

$key = q/displaystylesimeq-2,{mitOmega},varv_0,sinlambda,sintheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1138.png"
 ALT="$\displaystyle \simeq -2 {\mit\Omega} \varv_0 \sin\lambda \sin\theta,$">|; 

$key = q/displaystylesimeq-3,tau,e_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1991.png"
 ALT="$\displaystyle \simeq -3 \tau e_z,$">|; 

$key = q/displaystylesimeq-U_{xx},deltax-U_{xy},deltay,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2262.png"
 ALT="$\displaystyle \simeq - U_{xx} \delta x -U_{xy} \delta y,$">|; 

$key = q/displaystylesimeq-U_{xy},deltax-U_{yy},deltay,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2264.png"
 ALT="$\displaystyle \simeq - U_{xy} \delta x -U_{yy} \delta y,$">|; 

$key = q/displaystylesimeq-e,cos(omega_+,t-phi_+),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2385.png"
 ALT="$\displaystyle \simeq -e \cos(\omega_+ t-\phi_+),$">|; 

$key = q/displaystylesimeq-e,cos(skew{5}bar{lambda}-varpi)+frac{e^{,2}}{2},left[1-cos(2,skew{5}bar{lambda}-2,varpi)right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4979.png"
 ALT="$\displaystyle \simeq - e \cos(\skew{5}\bar{\lambda}-\varpi) + \frac{e^{ 2}}{2} \left[1-\cos(2 \skew{5}\bar{\lambda}-2 \varpi)\right]$">|; 

$key = q/displaystylesimeq-frac{1}{6},m^{,2}+frac{1}{18},m^{,4}+deltaX+frac{1}{2},deltaY^{,2}+frac{1}{2},deltaZ^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3202.png"
 ALT="$\displaystyle \simeq -\frac{1}{6} m^{ 2} + \frac{1}{18}  m^{ 4}+\delta X + \frac{1}{2} \delta Y^{ 2}+\frac{1}{2} \delta Z^{ 2}$">|; 

$key = q/displaystylesimeq-frac{2,beta_m,costheta_0}{{calI}_parallel,omega},sin({mitOmega}_n,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1791.png"
 ALT="$\displaystyle \simeq -\frac{2 \beta_m \cos\theta_0}{{\cal I}_\parallel \omega} \sin({\mit\Omega}_n t).$">|; 

$key = q/displaystylesimeq-frac{3}{2},m^{,2},X_0,sin[2,(1-m),T];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3161.png"
 ALT="$\displaystyle \simeq -\frac{3}{2} m^{ 2} X_0 \sin[2 (1-m) T]$">|; 

$key = q/displaystylesimeq-frac{3}{2},m^{,2}left(1-frac{m^{,2}}{6}right)sin(2,D)-frac{21}{4},m^{,2},e',sin(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3199.png"
 ALT="$\displaystyle \simeq - \frac{3}{2} m^{ 2}\left(1-\frac{m^{ 2}}{6}\right)\sin(2 D)
-\frac{21}{4} m^{ 2} e' \sin(2 D-{\cal M}')$">|; 

$key = q/displaystylesimeq-frac{G,M_m,M}{a_m}+frac{G,M_m,({calI}_parallel-{calI}_perp)}{2,a_m^{,3}}left[3,sin^2theta,sin^2(lambda_m-phi)right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.18ex; " SRC="|."$dir".q|img1759.png"
 ALT="$\displaystyle \simeq - \frac{G M_m M}{a_m} + \frac{G M_m ({\cal I}_\paralle...
...al I}_\perp)}{2 a_m^{ 3}}\left[3 \sin^2\theta \sin^2(\lambda_m-\phi)\right.$">|; 

$key = q/displaystylesimeq-frac{n_0^{,2}}{2}left[left(-frac{e}{2},cos[(2,p-1),n,t]+cos[2,(p-1),n,t]+frac{7,e}{2},cos[(2,p-3),n,t]right)sin2gammaright.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1880.png"
 ALT="$\displaystyle \simeq-\frac{n_0^{ 2}}{2}\left[\left(-\frac{e}{2} \cos[(2 p-1)...
...[2 (p-1) n t]+\frac{7 e}{2} \cos[(2 p-3) n t]\right)\sin 2\gamma\right.$">|; 

$key = q/displaystylesimeq-n^{-1},skew{3}dot{nu}_x+nu_y.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1996.png"
 ALT="$\displaystyle \simeq-n^{-1} \skew{3}\dot{\nu}_x+\nu_y.$">|; 

$key = q/displaystylesimeq-sin[(1-m),T]+frac{3}{2},e',sinT-frac{1}{2},e',sin[(1-2,m),T],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3090.png"
 ALT="$\displaystyle \simeq -\sin[(1-m) T] +\frac{3}{2} e' \sin T- \frac{1}{2} e' \sin[(1-2 m) T],$">|; 

$key = q/displaystylesimeq-sin[(n-n'),t]+frac{3}{2},e',sin(n,t)-frac{1}{2},e',sin[(n-2,n'),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3059.png"
 ALT="$\displaystyle \simeq -\sin[(n-n') t]+\frac{3}{2} e' \sin(n t)-\frac{1}{2} e' \sin[(n-2 n') t],$">|; 

$key = q/displaystylesimeq-sqrt{3,mu_2},d,sin(omega_-,t-phi_-),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.64ex; " SRC="|."$dir".q|img2390.png"
 ALT="$\displaystyle \simeq -\sqrt{3 \mu_2} d \sin(\omega_- t-\phi_-),$">|; 

$key = q/displaystylesimeq-varv_0,sin(theta+2,{mitOmega},sinlambda,,t).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1146.png"
 ALT="$\displaystyle \simeq -\varv_0 \sin(\theta+2 {\mit\Omega} \sin\lambda  t).$">|; 

$key = q/displaystylesimeq-varv_0,sintheta-2,{mitOmega},varv_0,sinlambda,costheta,,t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1144.png"
 ALT="$\displaystyle \simeq- \varv_0 \sin\theta - 2 {\mit\Omega} \varv_0 \sin\lambda \cos\theta  t.$">|; 

$key = q/displaystylesimeq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1989.png"
 ALT="$\displaystyle \simeq 0,$">|; 

$key = q/displaystylesimeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2000.png"
 ALT="$\displaystyle \simeq 0.$">|; 

$key = q/displaystylesimeq0^circ+2,e,sinvarpi=1.87^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img812.png"
 ALT="$\displaystyle \simeq 0^\circ+2 e \sin\varpi = 1.87^\circ,$">|; 

$key = q/displaystylesimeq1-e',cos(m,T),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3092.png"
 ALT="$\displaystyle \simeq 1-e' \cos(m T),$">|; 

$key = q/displaystylesimeq1-e,cos(skew{5}bar{lambda}-varpi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img795.png"
 ALT="$\displaystyle \simeq 1 - e \cos(\skew{5}\bar{\lambda}-\varpi),$">|; 

$key = q/displaystylesimeq1-frac{1}{6},m^{,2}+frac{1}{18},m^{,4},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3189.png"
 ALT="$\displaystyle \simeq 1-\frac{1}{6} m^{ 2}+\frac{1}{18} m^{ 4},$">|; 

$key = q/displaystylesimeq1-frac{g}{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2063.png"
 ALT="$\displaystyle \simeq 1-\frac{g}{n},$">|; 

$key = q/displaystylesimeq180^circ-2,e,sinvarpi=178.13^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img816.png"
 ALT="$\displaystyle \simeq 180^\circ -2 e \sin\varpi=178.13^\circ,$">|; 

$key = q/displaystylesimeq2,s,sin(omega+{calM})+2,e,sleft[sin(omega+2{calM})-sinomega)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4999.png"
 ALT="$\displaystyle \simeq 2 s \sin(\omega+{\cal M}) + 2 e s\left[\sin(\omega+2{\cal M})-\sin\omega)\right],$">|; 

$key = q/displaystylesimeq270^circ+2,e,cosvarpi=269.57^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img818.png"
 ALT="$\displaystyle \simeq 270^\circ +2 e \cos\varpi=269.57^\circ,$">|; 

$key = q/displaystylesimeq3+3^{4slash3},mu_2^{,2slash3}-frac{10}{3},mu_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2229.png"
 ALT="$\displaystyle \simeq 3 + 3^{4/3} \mu_2^{ 2/3}-\frac{10}{3} \mu_2,$">|; 

$key = q/displaystylesimeq3+3^{4slash3},mu_2^{,2slash3}-frac{14}{3},mu_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2231.png"
 ALT="$\displaystyle \simeq 3 + 3^{4/3} \mu_2^{ 2/3}-\frac{14}{3} \mu_2,$">|; 

$key = q/displaystylesimeq3+mu_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2233.png"
 ALT="$\displaystyle \simeq 3 + \mu_2,$">|; 

$key = q/displaystylesimeq3,deltaX,deltaZ.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3166.png"
 ALT="$\displaystyle \simeq 3 \delta X \delta Z.$">|; 

$key = q/displaystylesimeq3,tau,I,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2059.png"
 ALT="$\displaystyle \simeq 3 \tau I,$">|; 

$key = q/displaystylesimeq3,tau,I,sin[(n+g),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2020.png"
 ALT="$\displaystyle \simeq 3 \tau I \sin[(n+g) t],$">|; 

$key = q/displaystylesimeq3,tau,e_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1998.png"
 ALT="$\displaystyle \simeq 3 \tau e_z,$">|; 

$key = q/displaystylesimeq3-mu_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2235.png"
 ALT="$\displaystyle \simeq 3 - \mu_2,$">|; 

$key = q/displaystylesimeq3-mu_2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2237.png"
 ALT="$\displaystyle \simeq 3 - \mu_2.$">|; 

$key = q/displaystylesimeq87.70^circ.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img828.png"
 ALT="$\displaystyle \simeq 87.70^\circ.$">|; 

$key = q/displaystylesimeq88.56^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img826.png"
 ALT="$\displaystyle \simeq 88.56^\circ,$">|; 

$key = q/displaystylesimeq90^circ-2,e,cosvarpi=90.43^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img814.png"
 ALT="$\displaystyle \simeq 90^\circ -2 e \cos\varpi=90.43^\circ,$">|; 

$key = q/displaystylesimeq91.44^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img822.png"
 ALT="$\displaystyle \simeq 91.44^\circ,$">|; 

$key = q/displaystylesimeq92.30^circ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img824.png"
 ALT="$\displaystyle \simeq 92.30^\circ,$">|; 

$key = q/displaystylesimeqA_1,sin(omega_1,t-phi_1)+A_2,sin(omega_2,t-phi_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2034.png"
 ALT="$\displaystyle \simeq A_1 \sin(\omega_1 t-\phi_1)+ A_2 \sin(\omega_2 t-\phi_2),$">|; 

$key = q/displaystylesimeqE'+{bfv}cdot{bfp}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2795.png"
 ALT="$\displaystyle \simeq E'+ {\bf v}\cdot{\bf p}',$">|; 

$key = q/displaystylesimeqE,N,A,(c-v_r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2808.png"
 ALT="$\displaystyle \simeq E N A (c-v_r),$">|; 

$key = q/displaystylesimeqE-{bfv}cdot{bfp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2792.png"
 ALT="$\displaystyle \simeq E - {\bf v}\cdot{\bf p},$">|; 

$key = q/displaystylesimeqG,m_3=n'^{,2},a'^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3012.png"
 ALT="$\displaystyle \simeq G m_3=n'^{ 2} a'^{ 3},$">|; 

$key = q/displaystylesimeqI,sin(skew{5}bar{lambda}-{mitOmega}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img797.png"
 ALT="$\displaystyle \simeq I \sin(\skew{5}\bar{\lambda}-{\mit\Omega}).$">|; 

$key = q/displaystylesimeqI,sin(theta+varpi-{mitOmega}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img785.png"
 ALT="$\displaystyle \simeq I \sin(\theta+\varpi-{\mit\Omega}).$">|; 

$key = q/displaystylesimeqI,sin[(n-n_n),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3713.png"
 ALT="$\displaystyle \simeq I \sin[(n-n_n) t],$">|; 

$key = q/displaystylesimeqI_0+frac{J_3}{2,J_2},frac{R}{a},frac{e_0}{1-e_0^{,2}},cosI_0,sinomega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2906.png"
 ALT="$\displaystyle \simeq I_0+\frac{J_3}{2 J_2} \frac{R}{a} \frac{e_0}{1-e_0^{ 2}} \cos I_0 \sin\omega,$">|; 

$key = q/displaystylesimeqIleft(frac{M}{E+M}right)left(frac{a}{a'}right)sinF,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3684.png"
 ALT="$\displaystyle \simeq I\left(\frac{M}{E+M}\right)\left(\frac{a}{a'}\right)\sin F,$">|; 

$key = q/displaystylesimeqK_1,A_1,cos(omega_1,t-phi_1)+K_2,A_2,cos(omega_2,t-phi_2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2035.png"
 ALT="$\displaystyle \simeq K_1 A_1 \cos(\omega_1 t-\phi_1)+ K_2 A_2 \cos(\omega_2 t-\phi_2),$">|; 

$key = q/displaystylesimeqR_X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3191.png"
 ALT="$\displaystyle \simeq R_X,$">|; 

$key = q/displaystylesimeqR_Y,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3193.png"
 ALT="$\displaystyle \simeq R_Y,$">|; 

$key = q/displaystylesimeqR_Z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3195.png"
 ALT="$\displaystyle \simeq R_Z,$">|; 

$key = q/displaystylesimeqX_0+deltaX+frac{1}{2},deltaY^{,2}+frac{1}{2},deltaZ^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3170.png"
 ALT="$\displaystyle \simeq X_0+\delta X +\frac{1}{2} \delta Y^{ 2}+\frac{1}{2} \delta Z^{ 2},$">|; 

$key = q/displaystylesimeqX_0^{,-1},deltaZ-deltaX,deltaZ.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img3172.png"
 ALT="$\displaystyle \simeq X_0^{ -1} \delta Z-\delta X \delta Z.$">|; 

$key = q/displaystylesimeqalpha,sin(2,I),sin(2,theta),sin({mitOmega}-phi)-2,alpha,sin^2I,sin^2theta,sin[2,({mitOmega}-phi)].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4552.png"
 ALT="$\displaystyle \simeq \alpha \sin(2 I) \sin(2 \theta) \sin({\mit\Omega}-\phi)-2 \alpha \sin^2 I \sin^2\theta \sin[2 ({\mit\Omega}-\phi)].$">|; 

$key = q/displaystylesimeqcos(n',t)-frac{3}{2},e'+frac{1}{2},e',cos(2,n',t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3031.png"
 ALT="$\displaystyle \simeq \cos(n' t)-\frac{3}{2} e'+\frac{1}{2} e' \cos(2 n' t),$">|; 

$key = q/displaystylesimeqcos(omega+{calM})+e,left[cos(omega+2{calM})-cosomegaright];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4984.png"
 ALT="$\displaystyle \simeq\cos(\omega+{\cal M}) +e \left[\cos(\omega+2{\cal M})-\cos\omega\right]$">|; 

$key = q/displaystylesimeqcos(omega+{mitOmega}+{calM})+eleft[cos(omega+{mitOmega}+2{calM})-cos(omega+{mitOmega})right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4991.png"
 ALT="$\displaystyle \simeq \cos(\omega+{\mit\Omega}+{\cal M}) + e\left[\cos(\omega+{\mit\Omega}+2{\cal M}) - \cos(\omega+{\mit\Omega})\right]$">|; 

$key = q/displaystylesimeqcos[(1-m),T]-frac{3}{2},e',cosT+frac{1}{2},e',cos[(1-2,m),T],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3089.png"
 ALT="$\displaystyle \simeq \cos[(1-m) T] -\frac{3}{2} e' \cos T + \frac{1}{2} e' \cos[(1-2 m) T],$">|; 

$key = q/displaystylesimeqcos[(n-n'),t]-frac{3}{2},e',cos(n,t)+frac{1}{2},e',cos[(n-2,n'),t],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3057.png"
 ALT="$\displaystyle \simeq \cos[(n-n') t]-\frac{3}{2} e' \cos(n t) +\frac{1}{2} e' \cos[(n-2 n') t],$">|; 

$key = q/displaystylesimeqcos{calM}+e,(cos2{calM}-1)+frac{e^{,2}}{8}left(9,cos3{calM}-9,cos{calM}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4981.png"
 ALT="$\displaystyle \simeq \cos {\cal M} + e (\cos 2{\cal M}-1)+ \frac{e^{ 2}}{8}\left(9 \cos 3{\cal M}
- 9 \cos{\cal M}\right).$">|; 

$key = q/displaystylesimeqd,sin(omega_-,t-phi_-),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2389.png"
 ALT="$\displaystyle \simeq d \sin(\omega_- t-\phi_-),$">|; 

$key = q/displaystylesimeqe_0-frac{J_3}{2,J_2},frac{R}{a},sinI_0,sinomega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img2904.png"
 ALT="$\displaystyle \simeq e_0- \frac{J_3}{2 J_2} \frac{R}{a} \sin I_0 \sin\omega,$">|; 

$key = q/displaystylesimeqfrac{1}{2}sum_{j=-infty,infty}left{left[(1-zeta'+zeta'^{,2})+(zeta-zeta'-2,zeta,zeta'+2,zeta'^{,2}),alpha,Dright.right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img4975.png"
 ALT="$\displaystyle \simeq\frac{1}{2}\sum_{j=-\infty,\infty}\left\{ \left[(1-\zeta'+\...
...}) + (\zeta-\zeta'-2 \zeta \zeta' + 2 \zeta'^{ 2}) \alpha D\right.\right.$">|; 

$key = q/displaystylesimeqfrac{3,tau,I}{3,tau-2,gslashn}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2065.png"
 ALT="$\displaystyle \simeq \frac{3 \tau I}{3 \tau-2 g/n}.$">|; 

$key = q/displaystylesimeqfrac{3}{2},m^{,2},X_0,cos[2,(1-m),T];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3155.png"
 ALT="$\displaystyle \simeq
\frac{3}{2} m^{ 2} X_0 \cos[2 (1-m) T]$">|; 

$key = q/displaystylesimeqfrac{3}{2},m^{,2}left(1-frac{m^{,2}}{6}right)cos(2,D)+frac{3}{2},m^{,2},e',cos{calM}'+frac{21}{4},m^{,2},e',cos(2,D-{calM}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3196.png"
 ALT="$\displaystyle \simeq \frac{3}{2} m^{ 2}\left(1-\frac{m^{ 2}}{6}\right)\cos(2...
...} m^{ 2} e' \cos {\cal M}'
+\frac{21}{4} m^{ 2} e' \cos(2 D-{\cal M}')$">|; 

$key = q/displaystylesimeqfrac{E}{c},N,A,(c-v_r),{bfe}_r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2810.png"
 ALT="$\displaystyle \simeq \frac{E}{c} N A (c-v_r) {\bf e}_r,$">|; 

$key = q/displaystylesimeqleft(-(I+iota),sinpsi,,,-(I+iota),cospsi,,,1right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2067.png"
 ALT="$\displaystyle \simeq \left(-(I+\iota) \sin\psi,  -(I+\iota) \cos\psi,  1\right),$">|; 

$key = q/displaystylesimeqleft(-1+frac{e^{,2}}{2}+frac{e'^{,2}}{2}+s^{,2}+s'^{,2}right)cos(skew{5}bar{lambda}'-skew{5}bar{lambda});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img5054.png"
 ALT="$\displaystyle \simeq
\left(-1+\frac{e^{ 2}}{2}+\frac{e'^{ 2}}{2}+ s^{ 2}+s'^{ 2}\right)\cos(\skew{5}\bar{\lambda}'-\skew{5}\bar{\lambda})$">|; 

$key = q/displaystylesimeqleft(1+frac{m^{,2}}{6}right)deltaY-deltaX,deltaY,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3203.png"
 ALT="$\displaystyle \simeq \left(1+\frac{m^{ 2}}{6}\right)\delta Y-\delta X \delta Y,$">|; 

$key = q/displaystylesimeqleft(1+frac{m^{,2}}{6}right)deltaZ-deltaX,deltaY.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3204.png"
 ALT="$\displaystyle \simeq \left(1+\frac{m^{ 2}}{6}\right)\delta Z -\delta X \delta Y.$">|; 

$key = q/displaystylesimeqleft(frac{M}{E+M}right)left(frac{a}{a'}right)sinD,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img3682.png"
 ALT="$\displaystyle \simeq \left(\frac{M}{E+M}\right)\left(\frac{a}{a'}\right)\sin D,$">|; 

$key = q/displaystylesimeqm^{,2},zetaleft(-3,cos[(1-m),T],X,Z+3,sin[(1-m),T],Y,Zright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3132.png"
 ALT="$\displaystyle \simeq m^{ 2} \zeta \left(-3 \cos[(1-m) T] X Z + 3 \sin[(1-m) T]  Y Z \right).$">|; 

$key = q/displaystylesimeqm^{,2},zetaleft{-left(frac{3}{8},sin[(1-m),T]+frac{15}{8},sin[3,(1-m),T]right)X^{,2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3129.png"
 ALT="$\displaystyle \simeq m^{ 2} \zeta \left\{-\left(\frac{3}{8} \sin[(1-m) T]+\frac{15}{8} \sin[3 (1-m) T]\right)X^{ 2}\right.$">|; 

$key = q/displaystylesimeqm^{,2},zetaleft{left(frac{9}{8},cos[(1-m),T]+frac{15}{8},cos[3,(1-m),T]right)X^{,2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3126.png"
 ALT="$\displaystyle \simeq m^{ 2} \zeta \left\{\left(\frac{9}{8} \cos[(1-m) T]+\frac{15}{8} \cos[3 (1-m) T]\right)X^{ 2}\right.$">|; 

$key = q/displaystylesimeqm^{,2}left[-1-3,e',cos(m,T)right]Z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.60ex; " SRC="|."$dir".q|img3125.png"
 ALT="$\displaystyle \simeq m^{ 2}\left[-1-3 e' \cos(m T)\right]Z.$">|; 

$key = q/displaystylesimeqm^{,2}left{frac{1}{2}+frac{3}{2},cos[2,(1-m),T]+frac{3}{2},e',cos(m,T)-frac{3}{4},e',cos[(2-m),T]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3119.png"
 ALT="$\displaystyle \simeq m^{ 2}\left\{ \frac{1}{2}+\frac{3}{2} \cos[2 (1-m) T]+\frac{3}{2} e' \cos(m T)
-\frac{3}{4} e' \cos[(2-m) T]\right.$">|; 

$key = q/displaystylesimeqm^{,2}left{frac{1}{2}-frac{3}{2},cos[2,(1-m),T]+frac{3}{2},e',cos(m,T)+frac{3}{4},e',cos[(2-m),T]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3122.png"
 ALT="$\displaystyle \simeq m^{ 2}\left\{ \frac{1}{2}-\frac{3}{2} \cos[2 (1-m) T]+\frac{3}{2} e' \cos(m T)
+\frac{3}{4} e' \cos[(2-m) T]\right.$">|; 

$key = q/displaystylesimeqn,t+X_0^{,-1},deltaY-deltaX,deltaY,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img3171.png"
 ALT="$\displaystyle \simeq n t+X_0^{ -1} \delta Y - \delta X \delta Y,$">|; 

$key = q/displaystylesimeqn^{-1}skew{3}dot{nu}_y+nu_x,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1994.png"
 ALT="$\displaystyle \simeq n^{-1}\skew{3}\dot{\nu}_y +\nu_x,$">|; 

$key = q/displaystylesimeqn_s^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img4576.png"
 ALT="$\displaystyle \simeq n_s^{ 2},$">|; 

$key = q/displaystylesimeqr,I,sin(theta+varpi-{mitOmega}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img781.png"
 ALT="$\displaystyle \simeq r I \sin(\theta+\varpi-{\mit\Omega}),$">|; 

$key = q/displaystylesimeqr,cos(theta+varpi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img779.png"
 ALT="$\displaystyle \simeq r \cos(\theta+\varpi),$">|; 

$key = q/displaystylesimeqr,sin(theta+varpi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img780.png"
 ALT="$\displaystyle \simeq r \sin(\theta+\varpi),$">|; 

$key = q/displaystylesimeqs^{,2}left[cos(skew{5}bar{lambda}+skew{5}bar{lambda}'-2,{mitOmega})-cos(skew{5}bar{lambda}-skew{5}bar{lambda}')right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img5014.png"
 ALT="$\displaystyle \simeq s^{ 2}\left[\cos(\skew{5}\bar{\lambda}+\skew{5}\bar{\lambda}'-2 {\mit\Omega}) - \cos(\skew{5}\bar{\lambda}-\skew{5}\bar{\lambda}')\right]$">|; 

$key = q/displaystylesimeqsin(n',t)+frac{1}{2},e',sin(2,n',t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3033.png"
 ALT="$\displaystyle \simeq \sin(n' t)+\frac{1}{2} e' \sin(2 n' t),$">|; 

$key = q/displaystylesimeqsin(omega+{calM})+e,left[sin(omega+2{calM})-sinomegaright];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4988.png"
 ALT="$\displaystyle \simeq\sin(\omega+{\cal M}) +e \left[\sin(\omega+2{\cal M})-\sin\omega\right]$">|; 

$key = q/displaystylesimeqsin(omega+{mitOmega}+{calM})+eleft[sin(omega+{mitOmega}+2{calM})-sin(omega+{mitOmega})right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4995.png"
 ALT="$\displaystyle \simeq \sin(\omega+{\mit\Omega}+{\cal M}) + e\left[\sin(\omega+{\mit\Omega}+2{\cal M}) - \sin(\omega+{\mit\Omega})\right]$">|; 

$key = q/displaystylesimeqsin{calM}+e,sin2{calM}+frac{e^{,2}}{8}left(9,sin3{calM}-7,sin{calM}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img4980.png"
 ALT="$\displaystyle \simeq \sin {\cal M} + e \sin 2{\cal M} + \frac{e^{ 2}}{8}\left(9 \sin 3{\cal M} - 7 \sin {\cal M}\right),$">|; 

$key = q/displaystylesimeqskew{5}bar{lambda}+2,e,sin(skew{5}bar{lambda}-varpi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img796.png"
 ALT="$\displaystyle \simeq \skew{5}\bar{\lambda} + 2 e \sin(\skew{5}\bar{\lambda}-\varpi),$">|; 

$key = q/displaystylesimeqtheta+varpi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img783.png"
 ALT="$\displaystyle \simeq \theta+\varpi,$">|; 

$key = q/displaystylesimeqvarv_0,cos(theta+2,{mitOmega},sinlambda,,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1145.png"
 ALT="$\displaystyle \simeq \varv_0 \cos(\theta +2 {\mit\Omega} \sin\lambda  t),$">|; 

$key = q/displaystylesimeqvarv_0,costheta-2,{mitOmega},varv_0,sinlambda,sintheta,,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1142.png"
 ALT="$\displaystyle \simeq \varv_0 \cos\theta -2 {\mit\Omega} \varv_0 \sin\lambda \sin\theta  t,$">|; 

$key = q/displaystylesimeq{bfp}'+frac{E'}{c^{,2}},{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2796.png"
 ALT="$\displaystyle \simeq {\bf p}' + \frac{E'}{c^{ 2}} {\bf v}.$">|; 

$key = q/displaystylesimeq{bfp}-frac{E}{c^{,2}},{bfv},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2793.png"
 ALT="$\displaystyle \simeq {\bf p} - \frac{E}{c^{ 2}} {\bf v},$">|; 

$key = q/displaystylesin(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3824.png"
 ALT="$\displaystyle \sin(-\alpha)$">|; 

$key = q/displaystylesin(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3858.png"
 ALT="$\displaystyle \sin(2\alpha)$">|; 

$key = q/displaystylesin(3alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3862.png"
 ALT="$\displaystyle \sin(3\alpha)$">|; 

$key = q/displaystylesin(4alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3866.png"
 ALT="$\displaystyle \sin(4\alpha)$">|; 

$key = q/displaystylesin(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3832.png"
 ALT="$\displaystyle \sin(\alpha\pm\beta)$">|; 

$key = q/displaystylesin(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3852.png"
 ALT="$\displaystyle \sin(\alpha/2)$">|; 

$key = q/displaystylesin(etaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img916.png"
 ALT="$\displaystyle \sin(\eta/2)$">|; 

$key = q/displaystylesin(j,vartheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5023.png"
 ALT="$\displaystyle \sin(j \vartheta)$">|; 

$key = q/displaystylesin(omega+theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4986.png"
 ALT="$\displaystyle \sin(\omega+\theta)$">|; 

$key = q/displaystylesin(xislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img918.png"
 ALT="$\displaystyle \sin(\xi/2)$">|; 

$key = q/displaystylesin2theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1858.png"
 ALT="$\displaystyle \sin 2\theta$">|; 

$key = q/displaystylesinE;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img895.png"
 ALT="$\displaystyle \sin E$">|; 

$key = q/displaystylesinE=sum_{n=1,infty}left[frac{J_{n-1}(n,e)+J_{n+1}(n,e)}{n}right]sin(n,{calM}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img4051.png"
 ALT="$\displaystyle \sin E = \sum_{n=1,\infty}\left[\frac{J_{n-1}(n e)+ J_{n+1}(n e)}{n}\right]\sin(n {\cal M}).$">|; 

$key = q/displaystylesin^2alpha+cos^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3830.png"
 ALT="$\displaystyle \sin^2\alpha+\cos^2\alpha$">|; 

$key = q/displaystylesin^2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3870.png"
 ALT="$\displaystyle \sin^2\alpha$">|; 

$key = q/displaystylesin^3alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3874.png"
 ALT="$\displaystyle \sin^3\alpha$">|; 

$key = q/displaystylesin^4alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3878.png"
 ALT="$\displaystyle \sin^4\alpha$">|; 

$key = q/displaystylesinalpha+sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3838.png"
 ALT="$\displaystyle \sin\alpha+\sin\beta$">|; 

$key = q/displaystylesinalpha,cosbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3850.png"
 ALT="$\displaystyle \sin\alpha \cos\beta$">|; 

$key = q/displaystylesinalpha,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3846.png"
 ALT="$\displaystyle \sin\alpha \sin\beta$">|; 

$key = q/displaystylesinalpha-sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3840.png"
 ALT="$\displaystyle \sin\alpha-\sin\beta$">|; 

$key = q/displaystylesinh(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3882.png"
 ALT="$\displaystyle \sinh(-\alpha)$">|; 

$key = q/displaystylesinh(2alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3915.png"
 ALT="$\displaystyle \sinh(2\alpha)$">|; 

$key = q/displaystylesinh(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3889.png"
 ALT="$\displaystyle \sinh(\alpha\pm\beta)$">|; 

$key = q/displaystylesinh(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3909.png"
 ALT="$\displaystyle \sinh(\alpha/2)$">|; 

$key = q/displaystylesinh(etaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img922.png"
 ALT="$\displaystyle \sinh(\eta/2)$">|; 

$key = q/displaystylesinh(xislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img923.png"
 ALT="$\displaystyle \sinh(\xi/2)$">|; 

$key = q/displaystylesinhalpha+sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3895.png"
 ALT="$\displaystyle \sinh\alpha+\sinh\beta$">|; 

$key = q/displaystylesinhalpha,coshbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3907.png"
 ALT="$\displaystyle \sinh\alpha \cosh\beta$">|; 

$key = q/displaystylesinhalpha,sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3903.png"
 ALT="$\displaystyle \sinh\alpha \sinh\beta$">|; 

$key = q/displaystylesinhalpha-sinhbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3897.png"
 ALT="$\displaystyle \sinh\alpha-\sinh\beta$">|; 

$key = q/displaystylesinhu=frac{varv^{,2}}{4,g,a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1478.png"
 ALT="$\displaystyle \sinh u = \frac{\varv^{ 2}}{4 g a}.
$">|; 

$key = q/displaystylesinhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3818.png"
 ALT="$\displaystyle \sinh x$">|; 

$key = q/displaystylesintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img899.png"
 ALT="$\displaystyle \sin \theta$">|; 

$key = q/displaystylesinx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3812.png"
 ALT="$\displaystyle \sin x$">|; 

$key = q/displaystyleskew{1}dot{bfe}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4144.png"
 ALT="$\displaystyle \skew{1}\dot{\bf e} =$">|; 

$key = q/displaystyleskew{2}ddot{bfr}+mu,frac{{bfr}}{r^{,3}}=nabla{calR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4136.png"
 ALT="$\displaystyle \skew{2}\ddot{\bf r} + \mu \frac{{\bf r}}{r^{ 3}} = \nabla{\cal R},$">|; 

$key = q/displaystyleskew{2}dot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4152.png"
 ALT="$\displaystyle \skew{2}\dot{\bf r}$">|; 

$key = q/displaystyleskew{2}dot{r}=frac{r^{,2},e,sintheta,skew{5}dot{theta}}{a,(1-e^{,2})}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img4160.png"
 ALT="$\displaystyle \skew{2}\dot{r} = \frac{r^{ 2} e \sin\theta \skew{5}\dot{\theta}}{a (1-e^{ 2})}.$">|; 

$key = q/displaystyleskew{3}bar{varv}=sqrt{frac{3}{10}},varv_{rmesc},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -1.82ex; " SRC="|."$dir".q|img560.png"
 ALT="$\displaystyle \skew{3}\bar{\varv} = \sqrt{\frac{3}{10}} \varv_{\rm esc},
$">|; 

$key = q/displaystyleskew{3}ddot{eta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2108.png"
 ALT="$\displaystyle \skew{3}\ddot{\eta}$">|; 

$key = q/displaystyleskew{3}ddot{eta}_p+n_0^{,2},eta_p=-n_0^{,2},eta_o.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3740.png"
 ALT="$\displaystyle \skew{3}\ddot{\eta}_p + n_0^{ 2} \eta_p =-n_0^{ 2} \eta_o.
$">|; 

$key = q/displaystyleskew{3}ddot{r}-frac{h^{,2}}{r^{,3}}=-frac{G,M}{r^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img614.png"
 ALT="$\displaystyle \skew{3}\ddot{r} -\frac{h^{ 2}}{r^{ 3}}= - \frac{G M}{r^{ 2}}.$">|; 

$key = q/displaystyleskew{3}ddot{r}-frac{h^{,2}}{r^{,3}}=f(r),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img955.png"
 ALT="$\displaystyle \skew{3}\ddot{r} - \frac{h^{ 2}}{r^{ 3}} = f(r),$">|; 

$key = q/displaystyleskew{3}ddot{r}-r,skew{5}dot{theta}^{,2}=-frac{G,M}{r^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img603.png"
 ALT="$\displaystyle \skew{3}\ddot{r}-r \skew{5}\dot{\theta}^{ 2} = - \frac{G M}{r^{ 2}},$">|; 

$key = q/displaystyleskew{3}ddot{r}=-h,frac{d^{,2}u}{dtheta^{,2}},skew{5}dot{theta}=-u^{,2},h^{,2},frac{d^{,2}u}{dtheta^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img619.png"
 ALT="$\displaystyle \skew{3}\ddot{r} = - h  \frac{d^{ 2} u}{d\theta^{ 2}} \skew{5}\dot{\theta} = - u^{ 2} h^{ 2} \frac{d^{ 2} u}{d\theta^{ 2}}.$">|; 

$key = q/displaystyleskew{3}ddot{xi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2106.png"
 ALT="$\displaystyle \skew{3}\ddot{\xi}$">|; 

$key = q/displaystyleskew{3}ddot{x},skew{3}dot{x}-2,omega,skew{3}dot{x},skew{3}dot{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2165.png"
 ALT="$\displaystyle \skew{3}\ddot{x} \skew{3}\dot{x} - 2 \omega \skew{3}\dot{x} \skew{3}\dot{y}$">|; 

$key = q/displaystyleskew{3}ddot{x}-(l+x),skew{5}dot{theta}^{,2}-g,costheta+frac{k}{m},x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1459.png"
 ALT="$\displaystyle \skew{3}\ddot{x} - (l+x) \skew{5}\dot{\theta}^{ 2} - g \cos\theta + \frac{k}{m} x$">|; 

$key = q/displaystyleskew{3}ddot{x}-2,omega,skew{3}dot{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2155.png"
 ALT="$\displaystyle \skew{3}\ddot{x} - 2 \omega \skew{3}\dot{y}$">|; 

$key = q/displaystyleskew{3}ddot{y}+2,omega,skew{3}dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2157.png"
 ALT="$\displaystyle \skew{3}\ddot{y} + 2 \omega \skew{3}\dot{x}$">|; 

$key = q/displaystyleskew{3}ddot{y},skew{3}dot{y}+2,omega,skew{3}dot{x},skew{3}dot{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2167.png"
 ALT="$\displaystyle \skew{3}\ddot{y} \skew{3}\dot{y} + 2 \omega \skew{3}\dot{x} \skew{3}\dot{y}$">|; 

$key = q/displaystyleskew{3}ddot{zeta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2110.png"
 ALT="$\displaystyle \skew{3}\ddot{\zeta}$">|; 

$key = q/displaystyleskew{3}ddot{z},skew{3}dot{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2169.png"
 ALT="$\displaystyle \skew{3}\ddot{z} \skew{3}\dot{z}$">|; 

$key = q/displaystyleskew{3}ddot{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img2159.png"
 ALT="$\displaystyle \skew{3}\ddot{z}$">|; 

$key = q/displaystyleskew{3}dot{bfx}={bfA},skew{3}dot{mbox{boldmathxi}}-omega,{bfB},mbox{boldmathxi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2324.png"
 ALT="$\displaystyle \skew{3}\dot{\bf x} = {\bf A} \skew{3}\dot{\mbox{\boldmath $\xi$}} - \omega {\bf B} \mbox{\boldmath $\xi$},
$">|; 

$key = q/displaystyleskew{3}dot{calE}={bfF}cdotdot{bfr}=F_r,skew{5}dot{r}+r,skew{5}dot{theta},F_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img5094.png"
 ALT="$\displaystyle \skew{3}\dot{\cal E} = {\bf F}\cdot \dot{\bf r}=F_r \skew{5}\dot{r} + r \skew{5}\dot{\theta} F_\theta,$">|; 

$key = q/displaystyleskew{3}dot{e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2757.png"
 ALT="$\displaystyle \skew{3}\dot{e}$">|; 

$key = q/displaystyleskew{3}dot{e}=frac{{bfe}cdotdot{bfe}}{e}=skew{3}dot{e}_x=frac{h}{mu}left[sintheta,F_r+(costheta+cosE),F_thetaright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img5113.png"
 ALT="$\displaystyle \skew{3}\dot{e} = \frac{{\bf e}\cdot\dot{\bf e}}{e} = \skew{3}\do...
..._x = \frac{h}{\mu}\left[ \sin\theta F_r+(\cos\theta+\cos E) F_\theta \right],$">|; 

$key = q/displaystyleskew{3}dot{e}_Z=sinomega,sinI,skew{3}dot{e}+e,cosomega,sinI,skew{3}dot{omega}+e,sinomega,cosI,dot{I}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5143.png"
 ALT="$\displaystyle \skew{3}\dot{e}_Z = \sin\omega \sin I \skew{3}\dot{e} +e \cos\omega \sin I \skew{3}\dot{\omega} +e \sin\omega \cos I \dot{I}.$">|; 

$key = q/displaystyleskew{3}dot{e}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img5108.png"
 ALT="$\displaystyle \skew{3}\dot{e}_x$">|; 

$key = q/displaystyleskew{3}dot{e}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img5109.png"
 ALT="$\displaystyle \skew{3}\dot{e}_y$">|; 

$key = q/displaystyleskew{3}dot{e}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5111.png"
 ALT="$\displaystyle \skew{3}\dot{e}_z$">|; 

$key = q/displaystyleskew{3}dot{h}=frac{{bfh}cdotdot{bfh}}{h}=skew{3}dot{h}_z=r,F_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img5103.png"
 ALT="$\displaystyle \skew{3}\dot{h} = \frac{{\bf h}\cdot\dot{\bf h}}{h} = \skew{3}\dot{h}_z = r F_\theta,$">|; 

$key = q/displaystyleskew{3}dot{h}_X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5128.png"
 ALT="$\displaystyle \skew{3}\dot{h}_X$">|; 

$key = q/displaystyleskew{3}dot{h}_Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5130.png"
 ALT="$\displaystyle \skew{3}\dot{h}_Y$">|; 

$key = q/displaystyleskew{3}dot{h}_Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img5132.png"
 ALT="$\displaystyle \skew{3}\dot{h}_Z$">|; 

$key = q/displaystyleskew{3}dot{h}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img5097.png"
 ALT="$\displaystyle \skew{3}\dot{h}_x$">|; 

$key = q/displaystyleskew{3}dot{h}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img5099.png"
 ALT="$\displaystyle \skew{3}\dot{h}_y$">|; 

$key = q/displaystyleskew{3}dot{h}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5101.png"
 ALT="$\displaystyle \skew{3}\dot{h}_z$">|; 

$key = q/displaystyleskew{3}dot{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2759.png"
 ALT="$\displaystyle \skew{3}\dot{\omega}$">|; 

$key = q/displaystyleskew{3}dot{omega}=frac{3,mu,h^{,2}}{c^{,2},n,a^{,5},(1-e^{,2})^{,2}}=frac{3,mu^{,3slash2}}{c^{,2},a^{,5slash2},(1-e^{,2})},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2891.png"
 ALT="$\displaystyle \skew{3}\dot{\omega} =\frac{3 \mu h^{ 2}}{c^{ 2} n a^{ 5} (1-e^{ 2})^{ 2}}= \frac{3 \mu^{ 3/2}}{c^{ 2} a^{ 5/2} (1-e^{ 2})},
$">|; 

$key = q/displaystyleskew{3}dot{r}=-frac{skew{3}dot{u}}{u^{,2}}=-r^{,2},frac{du}{dtheta},frac{dtheta}{dt}=-h,frac{du}{dtheta}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img618.png"
 ALT="$\displaystyle \skew{3}\dot{r} = - \frac{\skew{3}\dot{u}}{u^{ 2}} = - r^{ 2} \frac{du}{d\theta} \frac{d\theta}{dt} = - h \frac{du}{d\theta}.$">|; 

$key = q/displaystyleskew{3}dot{r}^{,2}=(e-1),frac{G,M}{r_p}-(e+1),frac{r_p,G,M}{r^{,2}}+frac{2,G,M}{r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img679.png"
 ALT="$\displaystyle \skew{3}\dot{r}^{ 2} = (e-1) \frac{G M}{r_p} - (e+1) \frac{r_p G M}{r^{ 2}}
+ \frac{2 G M}{r}.$">|; 

$key = q/displaystyleskew{3}dot{x}_j=sum_{i=1,{calF}}frac{partialx_j}{partialq_i},skew{3}dot{q}_i+frac{partialx_j}{partialt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.02ex; vertical-align: -2.89ex; " SRC="|."$dir".q|img1397.png"
 ALT="$\displaystyle \skew{3}\dot{x}_j= \sum_{i=1,{\cal F}} \frac{\partial x_j}{\partial q_i} \skew{3}\dot{q}_i
+ \frac{\partial x_j}{\partial t},$">|; 

$key = q/displaystyleskew{3}hat{nu}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2064.png"
 ALT="$\displaystyle \skew{3}\hat{\nu}_x$">|; 

$key = q/displaystyleskew{3}tilde{delta}(theta,phi)=-frac{h_2}{g},deltachi(R,theta,phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4461.png"
 ALT="$\displaystyle \skew{3}\tilde{\delta}(\theta,\phi) = - \frac{h_2}{g} \delta\chi(R,\theta,\phi),$">|; 

$key = q/displaystyleskew{3}tilde{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4516.png"
 ALT="$\displaystyle \skew{3}\tilde{\epsilon}$">|; 

$key = q/displaystyleskew{3}tilde{epsilon}=0.003273.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4603.png"
 ALT="$\displaystyle \skew{3}\tilde{\epsilon} = 0.003273.$">|; 

$key = q/displaystyleskew{3}tilde{epsilon}=3.273times10^{-3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4523.png"
 ALT="$\displaystyle \skew{3}\tilde{\epsilon} = 3.273\times 10^{-3}.$">|; 

$key = q/displaystyleskew{3}tilde{epsilon}=frac{{calI}_parallel-{calI}_perp}{{calI}_parallel};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img4510.png"
 ALT="$\displaystyle \skew{3}\tilde{\epsilon}= \frac{{\cal I}_\parallel-{\cal I}_\perp}{{\cal I}_\parallel}$">|; 

$key = q/displaystyleskew{3}tilde{epsilon}=frac{{calI}_{parallel}-{calI}_perp}{{calI}_parallel}=0.00335;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.30ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1717.png"
 ALT="$\displaystyle \skew{3}\tilde{\epsilon} = \frac{{\cal I}_{\parallel}-{\cal I}_\perp}{{\cal I}_\parallel}=0.00335$">|; 

$key = q/displaystyleskew{5}bar{lambda}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2541.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}'$">|; 

$key = q/displaystyleskew{5}bar{lambda}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4901.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}(t)$">|; 

$key = q/displaystyleskew{5}bar{lambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img793.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}$">|; 

$key = q/displaystyleskew{5}bar{lambda}=skew{5}bar{lambda}_0+n,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img755.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda} = \skew{5}\bar{\lambda}_0 + n t,$">|; 

$key = q/displaystyleskew{5}bar{lambda}=varpi+{calM}=varpi+n,(t-tau).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img753.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda} =\varpi + {\cal M} = \varpi + n (t-\tau).$">|; 

$key = q/displaystyleskew{5}bar{lambda}_{AE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img811.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}_{AE}$">|; 

$key = q/displaystyleskew{5}bar{lambda}_{SS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img817.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}_{SS}$">|; 

$key = q/displaystyleskew{5}bar{lambda}_{VE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img815.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}_{VE}$">|; 

$key = q/displaystyleskew{5}bar{lambda}_{WS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img813.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda}_{WS}$">|; 

$key = q/displaystyleskew{5}bar{lambda}simeqlambda-2,e,sin(lambda-varpi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img810.png"
 ALT="$\displaystyle \skew{5}\bar{\lambda} \simeq \lambda -2 e \sin(\lambda-\varpi),$">|; 

$key = q/displaystyleskew{5}ddot{phi}+cos(theta-phi),skew{5}ddot{theta}-sin(theta-phi),skew{5}dot{theta}^{,2}+frac{g}{l},sinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1458.png"
 ALT="$\displaystyle \skew{5}\ddot{\phi} + \cos(\theta-\phi) \skew{5}\ddot{\theta} -\sin(\theta-\phi) \skew{5}\dot{\theta}^{ 2} + \frac{g}{l} \sin\phi$">|; 

$key = q/displaystyleskew{5}ddot{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1862.png"
 ALT="$\displaystyle \skew{5}\ddot{\phi}$">|; 

$key = q/displaystyleskew{5}ddot{theta}+cos(alpha+theta),frac{skew{3}ddot{s}}{l}+frac{g}{l},sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1464.png"
 ALT="$\displaystyle \skew{5}\ddot{\theta} + \cos(\alpha+\theta) \frac{\skew{3}\ddot{s}}{l} + \frac{g}{l} \sin\theta$">|; 

$key = q/displaystyleskew{5}ddot{theta}+frac{2,skew{3}dot{x},skew{5}dot{theta}}{l+x}+frac{g}{l+x},sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1460.png"
 ALT="$\displaystyle \skew{5}\ddot{\theta} + \frac{2 \skew{3}\dot{x} \skew{5}\dot{\theta}}{l+x}+ \frac{g}{l+x} \sin\theta$">|; 

$key = q/displaystyleskew{5}ddot{theta}+omega^2,sintheta+frac{g}{a},cos(omega,t+theta)=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1465.png"
 ALT="$\displaystyle \skew{5}\ddot{\theta} + \omega^2 \sin\theta + \frac{g}{a} \cos(\omega t+\theta) = 0.
$">|; 

$key = q/displaystyleskew{5}dot{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img5117.png"
 ALT="$\displaystyle \skew{5}\dot{\cal M}$">|; 

$key = q/displaystyleskew{5}dot{calM}=(1-e,cosE),dot{E}-sinE,skew{3}dot{e}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5116.png"
 ALT="$\displaystyle \skew{5}\dot{\cal M} =(1-e \cos E) \dot{E}-\sin E \skew{3}\dot{e}.$">|; 

$key = q/displaystyleskew{5}dot{calM}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2755.png"
 ALT="$\displaystyle \skew{5}\dot{\cal M}_0$">|; 

$key = q/displaystyleskew{5}dot{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2763.png"
 ALT="$\displaystyle \skew{5}\dot{\mit\Omega}$">|; 

$key = q/displaystyleskew{5}dot{mitOmega}=frac{cos{mitOmega},skew{3}dot{h}_X+sin{mitOmega},skew{3}dot{h}_Y}{h,sinI}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img5139.png"
 ALT="$\displaystyle \skew{5}\dot{\mit\Omega}=\frac{\cos{\mit\Omega} \skew{3}\dot{h}_X+\sin{\mit\Omega} \skew{3}\dot{h}_Y }{h \sin I}.$">|; 

$key = q/displaystyleskew{5}dot{mitOmega}=frac{sin(omega+theta),r,F_z}{h,sinI}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img5141.png"
 ALT="$\displaystyle \skew{5}\dot{\mit\Omega} =\frac{\sin(\omega+\theta) r F_z}{h \sin I}.$">|; 

$key = q/displaystyleskew{5}dot{omega}=frac{3,J_2}{4},n,frac{R^{,2}}{a^{,2}},frac{(5,cos^2I-1)}{(1-e^{,2})^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2716.png"
 ALT="$\displaystyle \skew{5}\dot{\omega} = \frac{3 J_2}{4} n \frac{R^{ 2}}{a^{ 2}} \frac{(5 \cos^2 I-1)}{(1-e^{ 2})^{ 2}},$">|; 

$key = q/displaystyleskew{5}dot{omega}_x+sigma,omega_y,omega_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1977.png"
 ALT="$\displaystyle \skew{5}\dot{\omega}_x + \sigma \omega_y \omega_z$">|; 

$key = q/displaystyleskew{5}dot{omega}_y-tau,omega_x,omega_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1979.png"
 ALT="$\displaystyle \skew{5}\dot{\omega}_y -\tau \omega_x \omega_z$">|; 

$key = q/displaystyleskew{5}dot{phi}=1.00328,omega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1658.png"
 ALT="$\displaystyle \skew{5}\dot{\phi} = 1.00328 \omega.$">|; 

$key = q/displaystyleskew{5}dot{phi}=omegaleft[1+left(frac{{calI}_parallel^{,2}}{{calI}_perp^{,2}}-1right)cos^2alpharight]^{1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.58ex; vertical-align: -2.51ex; " SRC="|."$dir".q|img1643.png"
 ALT="$\displaystyle \skew{5}\dot{\phi} = \omega\left[1 + \left(\frac{{\cal I}_\parallel^{ 2}}{{\cal I}_\perp^{ 2}}-1\right)\cos^2\alpha\right]^{1/2}.$">|; 

$key = q/displaystyleskew{5}dot{phi}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1788.png"
 ALT="$\displaystyle \skew{5}\dot{\phi}_1$">|; 

$key = q/displaystyleskew{5}dot{phi}simeq-frac{4,skew{3}tilde{epsilon},alpha_s,costheta}{{calI}_{parallel},omega}=-{mitOmega}_phi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1732.png"
 ALT="$\displaystyle \skew{5}\dot{\phi} \simeq
-\frac{4 \skew{3}\tilde{\epsilon} \alpha_s \cos\theta}{{\cal I}_{\parallel} \omega} = -{\mit\Omega}_\phi,$">|; 

$key = q/displaystyleskew{5}dot{psi}=-{mitOmega}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1645.png"
 ALT="$\displaystyle \skew{5}\dot{\psi}=-{\mit\Omega}.$">|; 

$key = q/displaystyleskew{5}dot{psi}=left(frac{{calI}_perp-{calI}_parallel}{{calI}_parallel}right),costheta,,skew{5}dot{phi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1470.png"
 ALT="$\displaystyle \skew{5}\dot{\psi} = \left(\frac{{\cal I}_\perp-{\cal I}_\parallel}{{\cal I}_\parallel}\right) \cos\theta  \skew{5}\dot{\phi}.
$">|; 

$key = q/displaystyleskew{5}dot{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2742.png"
 ALT="$\displaystyle \skew{5}\dot{r}$">|; 

$key = q/displaystyleskew{5}dot{r}=(1-e,cosE),skew{3}dot{a}-a,cosE,skew{3}dot{e}+a,e,sinE,dot{E}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5114.png"
 ALT="$\displaystyle \skew{5}\dot{r}=(1-e \cos E)  \skew{3}\dot{a}- a \cos E \skew{3}\dot{e} +a e \sin E \dot{E}.$">|; 

$key = q/displaystyleskew{5}dot{theta}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1790.png"
 ALT="$\displaystyle \skew{5}\dot{\theta}_1$">|; 

$key = q/displaystyleskew{5}dot{theta}simeqfrac{h}{r_c^{,2}}=left[-frac{f(r_c)}{r_c}right]^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img979.png"
 ALT="$\displaystyle \skew{5}\dot{\theta} \simeq \frac{h}{r_c^{ 2}} = \left[-\frac{f(r_c)}{r_c}\right]^{1/2},$">|; 

$key = q/displaystyleskew{5}dot{varpi}=frac{27}{8},mu_2,omega.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2388.png"
 ALT="$\displaystyle \skew{5}\dot{\varpi} = \frac{27}{8} \mu_2  \omega.
$">|; 

$key = q/displaystyleskew{5}dot{{mitOmega}}=-frac{3,J_2}{2},n,frac{R^{,2}}{a^{,2}},frac{cosI}{(1-e^{,2})^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img2717.png"
 ALT="$\displaystyle \skew{5}\dot{{\mit\Omega}} = -\frac{3 J_2}{2} n \frac{R^{ 2}}{a^{ 2}} \frac{\cos I}{(1-e^{ 2})^{ 2}},$">|; 

$key = q/displaystylesqrt{2,r_p},cosIsimeqfrac{1}{2,a'}+sqrt{(1-e'^{,2}),a'},cosI',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2311.png"
 ALT="$\displaystyle \sqrt{2 r_p} \cos I \simeq \frac{1}{2 a'} + \sqrt{(1-e'^{ 2}) a'} \cos I',
$">|; 

$key = q/displaystylesum_{i=1,3}m_i,{bfr}_i={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img2957.png"
 ALT="$\displaystyle \sum_{i=1,3} m_i {\bf r}_i={\bf0},$">|; 

$key = q/displaystylesum_{i=1,N}!m_i,frac{d^{,2}{bfr}_i}{dt^{,2}}=sum_{i,j=1,N}^{jneqi}!{bff}_{ij}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle \sum_{i=1,N} \!m_i \frac{d^{ 2} {\bf r}_i}{dt^{ 2}}=\sum_{i,j=1,N}^{j\neq i}\! {\bf f}_{ij}.$">|; 

$key = q/displaystylesum_{i=1,N}2,m_i,r_i^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1686.png"
 ALT="$\displaystyle \sum_{i=1,N}2 m_i r_i^{ 2}$">|; 

$key = q/displaystylesum_{i=1,N}m_i,frac{d^{,2}{bfr}_i}{dt^{,2}}=sum_{i,j=1,N}^{jneqi}{bff}_{ij}+sum_{i=1,N}{bfF}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img184.png"
 ALT="$\displaystyle \sum_{i=1,N} m_i \frac{d^{ 2}{\bf r}_i}{dt^{ 2}} = \sum_{i,j=1,N}^{j\neq i} {\bf f}_{ij} + \sum_{i=1,N}{\bf F}_i,$">|; 

$key = q/displaystylesum_{i=1,N}m_i,r_i^{,2},sin^2psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1691.png"
 ALT="$\displaystyle \sum_{i=1,N} m_i r_i^{ 2} \sin^2\psi$">|; 

$key = q/displaystylesum_{i=1,N}m_i,x_i=sum_{i=1,N}m_i,y_i=sum_{i=1,N}m_i,z_i=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1670.png"
 ALT="$\displaystyle \sum_{i=1,N} m_i x_i = \sum_{i=1,N} m_i y_i =\sum_{i=1,N}m_i z_i = 0.$">|; 

$key = q/displaystylesum_{i=1,N}m_i,y_i,z_i=sum_{i=1,N}m_i,x_i,z_i=sum_{i=1,N}m_i,x_i,y_i=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1671.png"
 ALT="$\displaystyle \sum_{i=1,N}m_i y_i z_i = \sum_{i=1,N}m_i x_i z_i= \sum_{i=1,N}m_i x_i y_i= 0,$">|; 

$key = q/displaystylesum_{i=1,n}x_i,frac{partialf}{partialx_i}=a,f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img541.png"
 ALT="$\displaystyle \sum_{i=1,n} x_i \frac{\partial f}{\partial x_i} = a f
$">|; 

$key = q/displaystylesum_{j=1,8}left(A_{ij}-delta_{ij},g_lright),e_{jl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2587.png"
 ALT="$\displaystyle \sum_{j=1,8}\left (A_{ij}-\delta_{ij} g_l\right) e_{jl}$">|; 

$key = q/displaystylesum_{j=1,8}left(B_{ij}-delta_{ij},f_lright),I_{jl};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img2588.png"
 ALT="$\displaystyle \sum_{j=1,8}\left (B_{ij}-\delta_{ij} f_l\right) I_{jl}$">|; 

$key = q/displaystylesum_{k=1,6}[c_j,c_k],frac{dc_k}{dt}=frac{partial{calR}}{partialc_j},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4689.png"
 ALT="$\displaystyle \sum_{k=1,6}[c_j, c_k] \frac{dc_k}{dt} = \frac{\partial {\cal R}}{\partial c_j},$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialX}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4671.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial X}{\partial c_k}  \frac{dc_k}{dt}$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialY}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4672.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial Y}{\partial c_k}  \frac{dc_k}{dt}$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialZ}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4673.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial Z}{\partial c_k}  \frac{dc_k}{dt}$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialdot{X}}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4674.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial \dot{X}}{\partial c_k}  \frac{dc_k}{dt}$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialdot{Y}}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4675.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial \dot{Y}}{\partial c_k}  \frac{dc_k}{dt}$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialdot{Z}}{partialc_k},frac{dc_k}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4676.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial \dot{Z}}{\partial c_k}  \frac{dc_k}{dt}$">|; 

$key = q/displaystylesum_{k=1,6}frac{partialf_l}{partialc_k}frac{dc_k}{dt}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.85ex; " SRC="|."$dir".q|img4650.png"
 ALT="$\displaystyle \sum_{k=1,6}\frac{\partial f_l}{\partial c_k}\frac{dc_k}{dt} = 0,$">|; 

$key = q/displaystylet=pmleft(frac{m}{2,E}right)^{1slash2}int_{x_0}^xfrac{dx'}{sqrt{1-U(x')slashE}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.30ex; " SRC="|."$dir".q|img218.png"
 ALT="$\displaystyle t=\pm\left(\frac{m}{2 E}\right)^{1/2} \int_{x_0}^x\frac{dx'}{\sqrt{1-U(x')/E}},$">|; 

$key = q/displaystyletan(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3828.png"
 ALT="$\displaystyle \tan(-\alpha)$">|; 

$key = q/displaystyletan(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3836.png"
 ALT="$\displaystyle \tan(\alpha\pm \beta)$">|; 

$key = q/displaystyletan(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3856.png"
 ALT="$\displaystyle \tan(\alpha/2)$">|; 

$key = q/displaystyletan(thetaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img729.png"
 ALT="$\displaystyle \tan(\theta/2)$">|; 

$key = q/displaystyletan(thetaslash2)=left(frac{1+e}{1-e}right)^{1slash2}tan(Eslash2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img721.png"
 ALT="$\displaystyle \tan (\theta/2) = \left(\frac{1+e}{1-e}\right)^{1/2}\tan (E/2).$">|; 

$key = q/displaystyletan^{-1}left[frac{({calI}_parallel-{calI}_perp),tanalpha}{{calI}_parallel+{calI}_perp,tan^2alpha}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.24ex; " SRC="|."$dir".q|img2077.png"
 ALT="$\displaystyle \tan^{-1}\left[\frac{({\cal I}_\parallel-{\cal I}_\perp) \tan\alpha}{{\cal I}_\parallel+{\cal I}_\perp \tan^2\alpha}\right]
$">|; 

$key = q/displaystyletanbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img774.png"
 ALT="$\displaystyle \tan\beta$">|; 

$key = q/displaystyletanh(-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3886.png"
 ALT="$\displaystyle \tanh(-\alpha)$">|; 

$key = q/displaystyletanh(alphapmbeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3893.png"
 ALT="$\displaystyle \tanh(\alpha\pm \beta)$">|; 

$key = q/displaystyletanh(alphaslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3913.png"
 ALT="$\displaystyle \tanh(\alpha/2)$">|; 

$key = q/displaystyletanhx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3822.png"
 ALT="$\displaystyle \tanh x$">|; 

$key = q/displaystyletanlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img772.png"
 ALT="$\displaystyle \tan \lambda$">|; 

$key = q/displaystyletantheta=frac{{calI}_perp}{{calI}_parallel},tanalpha.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.19ex; vertical-align: -2.19ex; " SRC="|."$dir".q|img1599.png"
 ALT="$\displaystyle \tan\theta = \frac{{\cal I}_\perp}{{\cal I}_\parallel} \tan\alpha.$">|; 

$key = q/displaystyletanx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3816.png"
 ALT="$\displaystyle \tan x$">|; 

$key = q/displaystyletau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1984.png"
 ALT="$\displaystyle \tau$">|; 

$key = q/displaystyletau=frac{4pi}{3},frac{c^{,2},rho,a^{,2},b}{L}simeq7times10^8,a^{,2},b,{rmyears}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img2853.png"
 ALT="$\displaystyle \tau = \frac{4\pi}{3} \frac{c^{ 2} \rho a^{ 2} b}{L}\simeq 7\times 10^8 a^{ 2} b {\rm years}.$">|; 

$key = q/displaystyletau=frac{8pi,m,c^{,2},a^{,2}}{5,L,A},e^{-8slash5},(1-e^{,2})^{,2}int_0^efrac{y^{,3slash5}}{(1-y^{,2})^{3slash2}},dy.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img2922.png"
 ALT="$\displaystyle \tau = \frac{8\pi m c^{ 2} a^{ 2}}{5 L A} e^{-8/5} (1-e^{ 2})^{ 2}\int_0^e \frac{y^{ 3/5}}{(1-y^{ 2})^{3/2}} dy.
$">|; 

$key = q/displaystyletau=frac{pi,m,c^{,2},a^{,2}}{L,A}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2852.png"
 ALT="$\displaystyle \tau = \frac{\pi m c^{ 2} a^{ 2}}{L A}.$">|; 

$key = q/displaystyletau_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1829.png"
 ALT="$\displaystyle \tau_x$">|; 

$key = q/displaystyletau_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1831.png"
 ALT="$\displaystyle \tau_y$">|; 

$key = q/displaystyletau_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1833.png"
 ALT="$\displaystyle \tau_z$">|; 

$key = q/displaystyletau_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1563.png"
 ALT="$\displaystyle \tau_{x'}$">|; 

$key = q/displaystyletau_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1565.png"
 ALT="$\displaystyle \tau_{y'}$">|; 

$key = q/displaystyletau_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1567.png"
 ALT="$\displaystyle \tau_{z'}$">|; 

$key = q/displaystyletextbf{emI},skew{3}hat{mbox{boldmathomega}}_i=lambda_i,skew{3}hat{mbox{boldmathomega}}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1543.png"
 ALT="$\displaystyle \textbf{\em I}  \skew{3}\hat{\mbox{\boldmath$\omega$}}_i = \lambda_i \skew{3}\hat{\mbox{\boldmath$\omega$}}_i ,$">|; 

$key = q/displaystyletextbf{emI}=left({array}{ccc}{calI}_{xx},&0,&00,&{calI}_{yy},&00,&0,&{calI}_{zz}{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 7.58ex; vertical-align: -3.25ex; " SRC="|."$dir".q|img1549.png"
 ALT="$\displaystyle \textbf{\em I} =
\left(\begin{array}{ccc}
{\cal I}_{xx},&amp;0,&amp;0\\\\
0,&amp;{\cal I}_{yy},&amp;0\\\\
0,&amp;0,&amp;{\cal I}_{zz}
\end{array}\right).$">|; 

$key = q/displaystyletheta(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1779.png"
 ALT="$\displaystyle \theta(t)$">|; 

$key = q/displaystyletheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img787.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/displaystyletheta=(1-e^{,2})^{1slash2}int_0^{calM}left(frac{dE}{d{calM}}right)^2,d{calM}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4062.png"
 ALT="$\displaystyle \theta = (1-e^{ 2})^{1/2}\int_0^{\cal M} \left(\frac{dE}{d{\cal M}}\right)^2 d{\cal M}.$">|; 

$key = q/displaystyletheta_{dev}simeq-frac{{mitOmega}^{,2},R}{2,g},sin(2,lambda)simeq-0.1^circ,sin(2,lambda).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1115.png"
 ALT="$\displaystyle \theta_{dev} \simeq - \frac{{\mit\Omega}^{ 2} R}{2 g} \sin(2 \lambda)\simeq
-0.1^\circ \sin(2 \lambda).$">|; 

$key = q/displaystyletilde{alpha}=left(frac{1+zeta}{1+zeta'}right)alpha.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4961.png"
 ALT="$\displaystyle \tilde{\alpha} = \left(\frac{1+\zeta}{1+\zeta'}\right)\alpha.$">|; 

$key = q/displaystyletilde{mu}=frac{19}{2},frac{mu}{rho,g,a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4321.png"
 ALT="$\displaystyle \tilde{\mu} = \frac{19}{2} \frac{\mu}{\rho g a}$">|; 

$key = q/displaystyletilde{mu}=frac{57}{8pi},frac{mu}{G,gamma^{,2},R'^{,2}}simeq51.5,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1310.png"
 ALT="$\displaystyle \tilde{\mu} = \frac{57}{8\pi} \frac{\mu}{G \gamma^{ 2} R'^{ 2}}\simeq 51.5,$">|; 

$key = q/displaystyletilde{mu}=frac{57}{8pi},frac{mu}{G,gamma^{,2},R^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1183.png"
 ALT="$\displaystyle \tilde{\mu} = \frac{57}{8\pi} \frac{\mu}{G \gamma^{ 2} R^{ 2}}$">|; 

$key = q/displaystyletilde{mu}simeq3.35.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1251.png"
 ALT="$\displaystyle \tilde{\mu} \simeq 3.35.$">|; 

$key = q/displaystyletimes(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1079.png"
 ALT="$\displaystyle \times($">|; 

$key = q/displaystyletimesdot{bfr}=-mu_1,frac{({bfr}-{bfr}_1)}{rho_1^{,3}}-mu_2,frac{({bfr}-{bfr}_2)}{rho_2^{,3}}-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.46ex; " SRC="|."$dir".q|img2151.png"
 ALT="$\displaystyle \times \dot{\bf r}= - \mu_1 \frac{({\bf r}-{\bf r}_1)}{\rho_1^{ 3}} -
\mu_2 \frac{({\bf r}-{\bf r}_2)}{\rho_2^{ 3}} -$">|; 

$key = q/displaystyletimes{bfL}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1555.png"
 ALT="$\displaystyle \times{\bf L}.$">|; 

$key = q/displaystyletimes{bfR}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1094.png"
 ALT="$\displaystyle \times{\bf R}),$">|; 

$key = q/displaystyletimes{bfe},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4145.png"
 ALT="$\displaystyle \times {\bf e},$">|; 

$key = q/displaystyletimes{bfr})+2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1080.png"
 ALT="$\displaystyle \times{\bf r}) + 2 $">|; 

$key = q/displaystyletimes{bfr}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2152.png"
 ALT="$\displaystyle \times {\bf r}),$">|; 

$key = q/displaystyletimes{bfr})-2,m,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1086.png"
 ALT="$\displaystyle \times{\bf r}) -2 m $">|; 

$key = q/displaystyletimes{bfr}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1091.png"
 ALT="$\displaystyle \times{\bf r}).$">|; 

$key = q/displaystyletimes{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1072.png"
 ALT="$\displaystyle \times{\bf r},$">|; 

$key = q/displaystyletimes{bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1066.png"
 ALT="$\displaystyle \times{\bf r}.$">|; 

$key = q/displaystyletimes{bfr}_i).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1529.png"
 ALT="$\displaystyle \times {\bf r}_i).$">|; 

$key = q/displaystyletimes{bfr}_i)=frac{1}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1527.png"
 ALT="$\displaystyle \times
{\bf r}_i) = \frac{1}{2} $">|; 

$key = q/displaystyletimes{bfr}_i)=sum_{i=1,N}m_ileft[r_i^{,2},mbox{boldmathomega}-({bfr}_icdotmbox{boldmathomega}),{bfr}_iright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1497.png"
 ALT="$\displaystyle \times {\bf r}_i) = \sum_{i=1,N}m_i\left[r_i^{ 2} \mbox{\boldmath$\omega$}- ({\bf r}_i\cdot\mbox{\boldmath$\omega$}) {\bf r}_i\right],$">|; 

$key = q/displaystyletimes{bfr}_i)cdot(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1526.png"
 ALT="$\displaystyle \times
{\bf r}_i)\cdot($">|; 

$key = q/displaystyletimes{bfr}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1493.png"
 ALT="$\displaystyle \times {\bf r}_i.$">|; 

$key = q/displaystyletimes{bfr}|^{,2}simeq-frac{1}{2},{mitOmega}^{,2}left(x'^{,2}+y'^{,2}-2,l,x',y'-2,m,y',z'right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4456.png"
 ALT="$\displaystyle \times {\bf r}\vert^{ 2} \simeq - \frac{1}{2} {\mit\Omega}^{ 2}\left(x'^{ 2}+y'^{ 2} - 2 l x' y'-2 m y' z'\right).$">|; 

$key = q/displaystyletimes{bfv}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1081.png"
 ALT="$\displaystyle \times{\bf v}'.$">|; 

$key = q/displaystyleu(theta)=frac{G,M}{h^{,2}}left[1+e,cos(theta-theta_0)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img621.png"
 ALT="$\displaystyle u(\theta) = \frac{G M}{h^{ 2}}\left[1 + e \cos(\theta-\theta_0)\right],$">|; 

$key = q/displaystyleu(theta)=u_c,(1+e,costheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img655.png"
 ALT="$\displaystyle u(\theta) = u_c (1+e \cos\theta).$">|; 

$key = q/displaystylevarpi={mitOmega}+omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img752.png"
 ALT="$\displaystyle \varpi = {\mit\Omega} + \omega,$">|; 

$key = q/displaystylevarv=pmleft(frac{2,[E-U(x)]}{m}right)^{1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle \varv = \pm\left(\frac{2 [E-U(x)]}{m}\right)^{1/2},$">|; 

$key = q/displaystylevarv^{,2}=dot{r}^{,2}+(r,skew{5}dot{theta})^2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1417.png"
 ALT="$\displaystyle \varv^{ 2} = \dot{r}^{ 2} + (r \skew{5}\dot{\theta})^2.$">|; 

$key = q/displaystylevarv_x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle \varv_x'$">|; 

$key = q/displaystylevarv_y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle \varv_y'$">|; 

$key = q/displaystylevarv_z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \varv_z'$">|; 

$key = q/displaystylevarv_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1141.png"
 ALT="$\displaystyle \varv_{x'}$">|; 

$key = q/displaystylevarv_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1143.png"
 ALT="$\displaystyle \varv_{y'}$">|; 

$key = q/displaystylew_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1993.png"
 ALT="$\displaystyle w_x$">|; 

$key = q/displaystylew_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1995.png"
 ALT="$\displaystyle w_y$">|; 

$key = q/displaystylex',dot{y}'-y',dot{x}'=h,cos,I=[mu,a,(1-e^{,2})]^{1slash2},cos,Iequiv{calG},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4750.png"
 ALT="$\displaystyle x' \dot{y}'-y' \dot{x}' = h \cos I = [\mu a (1-e^{ 2})]^{1/2} \cos I \equiv {\cal G},$">|; 

$key = q/displaystylex',y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4472.png"
 ALT="$\displaystyle x' y'$">|; 

$key = q/displaystylex',z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img4474.png"
 ALT="$\displaystyle x' z'$">|; 

$key = q/displaystylex';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle x'$">|; 

$key = q/displaystylex'^{,2}+y'^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4466.png"
 ALT="$\displaystyle x'^{ 2}+y'^{ 2}$">|; 

$key = q/displaystylex'^{,2}+z'^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img4468.png"
 ALT="$\displaystyle x'^{ 2}+z'^{ 2}$">|; 

$key = q/displaystylex(t)=A,{rme}^{,k,t}+B,{rme}^{-k,t},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle x(t) = A {\rm e}^{ k t} + B {\rm e}^{-k t},$">|; 

$key = q/displaystylex(t)=a,cos(omega,t-phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img324.png"
 ALT="$\displaystyle x(t) = a \cos(\omega t-\phi).
$">|; 

$key = q/displaystylex(t)=a,sin(omega_0,t-phi_0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img238.png"
 ALT="$\displaystyle x(t) = a \sin(\omega_0 t -\phi_0).$">|; 

$key = q/displaystylex,dot{y}-y,dot{x}=h=[mu,a,(1-e^{,2})]^{1slash2}equivH,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4759.png"
 ALT="$\displaystyle x \dot{y}-y \dot{x} = h= [\mu a (1-e^{ 2})]^{1/2}\equiv H,$">|; 

$key = q/displaystylex;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img384.png"
 ALT="$\displaystyle x$">|; 

$key = q/displaystylex=a,sin(omega,t),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle x = a \sin (\omega t),$">|; 

$key = q/displaystylex=r-r_c.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img960.png"
 ALT="$\displaystyle x = r - r_c.$">|; 

$key = q/displaystylex_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3043.png"
 ALT="$\displaystyle x_1'$">|; 

$key = q/displaystylex_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3037.png"
 ALT="$\displaystyle x_1$">|; 

$key = q/displaystylex_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3577.png"
 ALT="$\displaystyle x_2$">|; 

$key = q/displaystylex_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3624.png"
 ALT="$\displaystyle x_3$">|; 

$key = q/displaystylex_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3447.png"
 ALT="$\displaystyle x_4$">|; 

$key = q/displaystylex_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3453.png"
 ALT="$\displaystyle x_5$">|; 

$key = q/displaystylex_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3531.png"
 ALT="$\displaystyle x_6$">|; 

$key = q/displaystylex_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3536.png"
 ALT="$\displaystyle x_7$">|; 

$key = q/displaystylex_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3477.png"
 ALT="$\displaystyle x_8$">|; 

$key = q/displaystylex_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3482.png"
 ALT="$\displaystyle x_9$">|; 

$key = q/displaystylex_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4009.png"
 ALT="$\displaystyle x_c$">|; 

$key = q/displaystylex_i,frac{partial{calR}_n}{partialx_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4219.png"
 ALT="$\displaystyle x_i \frac{\partial {\cal R}_n}{\partial x_i}$">|; 

$key = q/displaystylex_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3397.png"
 ALT="$\displaystyle x_j$">|; 

$key = q/displaystylex_j=x_j(q_1,q_2,cdots,q_{calF},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1377.png"
 ALT="$\displaystyle x_j = x_j(q_1,q_2,\cdots,q_{\cal F}, t)$">|; 

$key = q/displaystylex_{01}=frac{159}{256}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3458.png"
 ALT="$\displaystyle x_{01} = \frac{159}{256}.$">|; 

$key = q/displaystylex_{02}=-frac{1}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3574.png"
 ALT="$\displaystyle x_{02} = -\frac{1}{2}.$">|; 

$key = q/displaystylex_{03}=-frac{1}{4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3622.png"
 ALT="$\displaystyle x_{03} =-\frac{1}{4}.$">|; 

$key = q/displaystylex_{0i}=-frac{a_{0i}}{3,(1+m^{,2}slash2)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.41ex; vertical-align: -2.01ex; " SRC="|."$dir".q|img3392.png"
 ALT="$\displaystyle x_{0i} = -\frac{a_{0i}}{3 (1+m^{ 2}/2)},$">|; 

$key = q/displaystylex_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3487.png"
 ALT="$\displaystyle x_{10}$">|; 

$key = q/displaystylex_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3506.png"
 ALT="$\displaystyle x_{11}$">|; 

$key = q/displaystylex_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3514.png"
 ALT="$\displaystyle x_{12}$">|; 

$key = q/displaystylexi_i=A,r^{,2},frac{partialp_2}{partialx_i}+B,p_2,x_i+frac{partialphi_2}{partialx_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.96ex; " SRC="|."$dir".q|img4283.png"
 ALT="$\displaystyle \xi_i = A r^{ 2} \frac{\partial p_2}{\partial x_i} + B p_2 x_i + \frac{\partial\phi_2}{\partial x_i},$">|; 

$key = q/displaystylexi_r(a,theta,phi)=delta_2(theta,phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4276.png"
 ALT="$\displaystyle \xi_r(a,\theta,\phi)=\delta_2(\theta,\phi).$">|; 

$key = q/displaystylexi_r=frac{x_i,xi_i}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.46ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4274.png"
 ALT="$\displaystyle \xi_r = \frac{x_i \xi_i}{r},$">|; 

$key = q/displaystyley',z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4476.png"
 ALT="$\displaystyle y' z'$">|; 

$key = q/displaystyley';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle y'$">|; 

$key = q/displaystyley'^{,2}+z'^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4470.png"
 ALT="$\displaystyle y'^{ 2}+z'^{ 2}$">|; 

$key = q/displaystyley'simeq-g,{mitOmega},coslambda,frac{t^{,3}}{3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1132.png"
 ALT="$\displaystyle y' \simeq - g {\mit\Omega} \cos\lambda \frac{t^{ 3}}{3}.$">|; 

$key = q/displaystyley;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img386.png"
 ALT="$\displaystyle y$">|; 

$key = q/displaystyley^{,2}+2,r_c,(x-x_c)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4014.png"
 ALT="$\displaystyle y^{ 2} + 2 r_c (x-x_c) = 0,$">|; 

$key = q/displaystyley^{,2}+b,x=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3988.png"
 ALT="$\displaystyle y^{ 2} + b x = 0,$">|; 

$key = q/displaystyley_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3045.png"
 ALT="$\displaystyle y_1'$">|; 

$key = q/displaystyley_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3039.png"
 ALT="$\displaystyle y_1$">|; 

$key = q/displaystyley_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3579.png"
 ALT="$\displaystyle y_2$">|; 

$key = q/displaystyley_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3625.png"
 ALT="$\displaystyle y_3$">|; 

$key = q/displaystyley_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3449.png"
 ALT="$\displaystyle y_4$">|; 

$key = q/displaystyley_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3455.png"
 ALT="$\displaystyle y_5$">|; 

$key = q/displaystyley_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3533.png"
 ALT="$\displaystyle y_6$">|; 

$key = q/displaystyley_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3538.png"
 ALT="$\displaystyle y_7$">|; 

$key = q/displaystyley_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3479.png"
 ALT="$\displaystyle y_8$">|; 

$key = q/displaystyley_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3484.png"
 ALT="$\displaystyle y_9$">|; 

$key = q/displaystyley_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3399.png"
 ALT="$\displaystyle y_j$">|; 

$key = q/displaystyley_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3489.png"
 ALT="$\displaystyle y_{10}$">|; 

$key = q/displaystyley_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3508.png"
 ALT="$\displaystyle y_{11}$">|; 

$key = q/displaystyley_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3516.png"
 ALT="$\displaystyle y_{12}$">|; 

$key = q/displaystylez';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle z'$">|; 

$key = q/displaystylez'=h-frac{g,t^{,2}}{2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1129.png"
 ALT="$\displaystyle z' = h - \frac{g t^{ 2}}{2}.$">|; 

$key = q/displaystylez;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img388.png"
 ALT="$\displaystyle z$">|; 

$key = q/displaystylez_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img3047.png"
 ALT="$\displaystyle z_1'$">|; 

$key = q/displaystylez_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3041.png"
 ALT="$\displaystyle z_1$">|; 

$key = q/displaystylez_1=1-frac{1}{6},m^{,2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3607.png"
 ALT="$\displaystyle z_1 = 1-\frac{1}{6} m^{ 2}.$">|; 

$key = q/displaystylez_2=-frac{3}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3618.png"
 ALT="$\displaystyle z_2 = -\frac{3}{2}$">|; 

$key = q/displaystylez_3=frac{1}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img3620.png"
 ALT="$\displaystyle z_3 = \frac{1}{2}$">|; 

$key = q/displaystylez_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3608.png"
 ALT="$\displaystyle z_4$">|; 

$key = q/displaystylez_4=frac{3}{8},z_1+left(frac{91-12,g}{64}right),z_1,m.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3598.png"
 ALT="$\displaystyle z_4 = \frac{3}{8} z_1 + \left(\frac{91-12 g}{64}\right) z_1 m.$">|; 

$key = q/displaystylez_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3610.png"
 ALT="$\displaystyle z_5$">|; 

$key = q/displaystylez_5=frac{3}{16},z_1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3600.png"
 ALT="$\displaystyle z_5 =\frac{3}{16} z_1.$">|; 

$key = q/displaystylez_j=frac{m^{,alpha},c_j}{1+3,m^{,2}slash2-{mitOmega}_j^{,2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.72ex; " SRC="|."$dir".q|img3433.png"
 ALT="$\displaystyle z_j = \frac{m^{ \alpha} c_j}{1+3 m^{ 2}/2-{\mit\Omega}_j^{ 2}},$">|; 

$key = q/displaystylezeta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4953.png"
 ALT="$\displaystyle \zeta'$">|; 

$key = q/displaystylezeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4421.png"
 ALT="$\displaystyle \zeta$">|; 

$key = q/displaystylezeta=-5.62times10^{-8}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1249.png"
 ALT="$\displaystyle \zeta = -5.62\times 10^{-8}.$">|; 

$key = q/displaystylezeta=-frac{m'}{m}left(frac{R}{a}right)^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1241.png"
 ALT="$\displaystyle \zeta = - \frac{m'}{m}\left(\frac{R}{a}\right)^3$">|; 

$key = q/displaystylezeta=1.15times10^{-3}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1191.png"
 ALT="$\displaystyle \zeta = 1.15\times 10^{-3}.$">|; 

$key = q/displaystylezeta=2.70times10^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1203.png"
 ALT="$\displaystyle \zeta = 2.70\times 10^{-2}.$">|; 

$key = q/displaystylezeta=frac{{mitOmega}^{,2},R^{,3}}{3,G,M};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1159.png"
 ALT="$\displaystyle \zeta = \frac{{\mit\Omega}^{ 2} R^{ 3}}{3 G M}$">|; 

$key = q/displaystylezeta=frac{{mitOmega}^{,2},R^{,3}}{3,G,M}=frac{{mitOmega}^{,2}}{4pi,G,bar{rho}(R)}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.35ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4367.png"
 ALT="$\displaystyle \zeta =\frac{{\mit\Omega}^{ 2} R^{ 3}}{3 G M} = \frac{{\mit\Omega}^{ 2}}{4\pi G \bar{\rho}(R)}.$">|; 

$key = q/displaystylezeta=left(frac{m_1-m_2}{m_1+m_2}right)left(frac{a}{a'}right)=0.002507.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3114.png"
 ALT="$\displaystyle \zeta=\left(\frac{m_1-m_2}{m_1+m_2}\right)\left(\frac{a}{a'}\right)= 0.002507.$">|; 

$key = q/displaystylezeta_2(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4312.png"
 ALT="$\displaystyle \zeta_2(\theta,\phi)$">|; 

$key = q/displaystylezeta_2(theta,phi)=-g^{,-1}chi_2(a,theta,phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4281.png"
 ALT="$\displaystyle \zeta_2(\theta,\phi) = - g^{ -1}\chi_2(a,\theta,\phi).$">|; 

$key = q/displaystylezeta_c=frac{2}{19},frac{sigma_c}{mu},(1+tilde{mu}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img1185.png"
 ALT="$\displaystyle \zeta_c = \frac{2}{19} \frac{\sigma_c}{\mu} (1+\tilde{\mu}).$">|; 

$key = q/displaystylezeta_csimeq9times10^{-4}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1187.png"
 ALT="$\displaystyle \zeta_c\simeq 9\times 10^{-4}.$">|; 

$key = q/displaystyle{bf1}'=left({array}{ccc}1,&0,&0[0.5ex]0,&1,&0[0.5ex]0,&0,&0{array}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.20ex; vertical-align: -3.58ex; " SRC="|."$dir".q|img2329.png"
 ALT="$\displaystyle {\bf 1}' = \left(\begin{array}{ccc} 1, &amp; 0, &amp;0\ [0.5ex]
0,&amp;1,&amp;0\ [0.5ex]
0,&amp;0,&amp;0\end{array}\right),
$">|; 

$key = q/displaystyle{bf1}=left({array}{ccc}1,&0,&0[0.5ex]0,&1,&0[0.5ex]0,&0,&1{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.20ex; vertical-align: -3.58ex; " SRC="|."$dir".q|img2320.png"
 ALT="$\displaystyle {\bf 1} = \left(\begin{array}{ccc} 1, &amp; 0, &amp;0\ [0.5ex]
0,&amp;1,&amp;0\ [0.5ex]
0,&amp;0,&amp;1\end{array}\right).
$">|; 

$key = q/displaystyle{bfA},{bfx}=lambda,{bfx}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4074.png"
 ALT="$\displaystyle {\bf A}  {\bf x} = \lambda {\bf x}.$">|; 

$key = q/displaystyle{bfA},{bfx}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4089.png"
 ALT="$\displaystyle {\bf A} {\bf x}_i$">|; 

$key = q/displaystyle{bfA},{bfx}_i=lambda_i,{bfx}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4079.png"
 ALT="$\displaystyle {\bf A} {\bf x}_i = \lambda_i {\bf x}_i,$">|; 

$key = q/displaystyle{bfA},{bfx}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4091.png"
 ALT="$\displaystyle {\bf A} {\bf x}_j$">|; 

$key = q/displaystyle{bfA}=A_r,{bfe}_r+A_theta,{bfe}_theta+A_phi,{bfe}_phi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3978.png"
 ALT="$\displaystyle {\bf A} = A_r {\bf e}_r + A_\theta {\bf e}_\theta+ A_\phi {\bf e}_\phi,$">|; 

$key = q/displaystyle{bfA}=A_r,{bfe}_r+A_theta,{bfe}_theta+A_z,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3968.png"
 ALT="$\displaystyle {\bf A} = A_r {\bf e}_r+ A_\theta {\bf e}_\theta + A_z {\bf e}_z,$">|; 

$key = q/displaystyle{bfA}=left(frac{partialV}{partialx},,frac{partialV}{partialy},,frac{partialV}{partialz}right)equivnablaV.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3952.png"
 ALT="$\displaystyle {\bf A} = \left(\frac{\partial V}{\partial x}, \frac{\partial V}{\partial y}, \frac{\partial V}{\partial z}\right)\equiv \nabla V.$">|; 

$key = q/displaystyle{bfA}=left({array}{ccc}cosomegat,&sinomegat,&0[0.5ex]-sinomegat,&cosomegat,&0[0.5ex]0,&0,&1{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.25ex; vertical-align: -3.58ex; " SRC="|."$dir".q|img2318.png"
 ALT="$\displaystyle {\bf A} = \left(\begin{array}{ccc} \cos \omega t, &amp; \sin \omega t,&amp;0\ [0.5ex]
-\sin\omega t,&amp;\cos\omega t,&amp;0\ [0.5ex]
0,&amp;0,&amp;1\end{array}\right).
$">|; 

$key = q/displaystyle{bfB}=left({array}{ccc}sinomegat,&-cosomegat&0[0.5ex]cosomegat,&sinomegat&0[0.5ex]0,&0,&0{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.25ex; vertical-align: -3.58ex; " SRC="|."$dir".q|img2327.png"
 ALT="$\displaystyle {\bf B} = \left(\begin{array}{ccc} \sin \omega t, &amp; -\cos \omega t&amp;0\ [0.5ex]
\cos\omega t,&amp;\sin\omega t&amp;0\ [0.5ex]
0,&amp;0,&amp;0\end{array}\right).
$">|; 

$key = q/displaystyle{bfC}=left({array}{ccc}0,&1,&0[0.5ex]-1,&0,&0[0.5ex]0,&0,&0{array}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 8.20ex; vertical-align: -3.58ex; " SRC="|."$dir".q|img2330.png"
 ALT="$\displaystyle {\bf C} = \left(\begin{array}{ccc} 0,&amp; 1, &amp;0\ [0.5ex]
-1,&amp;0,&amp;0\ [0.5ex]
0,&amp;0,&amp;0\end{array}\right).
$">|; 

$key = q/displaystyle{bfF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img275.png"
 ALT="$\displaystyle {\bf F}$">|; 

$key = q/displaystyle{bfF}=-frac{1}{2},frac{rho,C_D,A}{m},|dot{bfr}|,dot{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2729.png"
 ALT="$\displaystyle {\bf F} = -\frac{1}{2} \frac{\rho C_D A}{m} \vert\dot{\bf r}\vert \dot{\bf r},$">|; 

$key = q/displaystyle{bfF}=F_r,{bfe}_r+F_theta,{bfe}_theta+F_z,{bfe}_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5093.png"
 ALT="$\displaystyle {\bf F} = F_r {\bf e}_r + F_\theta {\bf e}_\theta + F_z {\bf e}_z.$">|; 

$key = q/displaystyle{bfF}=frac{{mitDelta}{bfP}}{m},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2815.png"
 ALT="$\displaystyle {\bf F} = \frac{{\mit\Delta}{\bf P}}{m},$">|; 

$key = q/displaystyle{bfF}=sum_{i=1,N}{bfF}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle {\bf F} = \sum_{i=1,N} {\bf F}_i$">|; 

$key = q/displaystyle{bfF}={bfF}_{rmrad}+{bfF}_{rmPR},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2816.png"
 ALT="$\displaystyle {\bf F} = {\bf F}_{\rm rad} + {\bf F}_{\rm PR},$">|; 

$key = q/displaystyle{bfF}_{rmPR}=-frac{L,A}{4pi,r^{,2},m,c^{,2}},{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2818.png"
 ALT="$\displaystyle {\bf F}_{\rm PR} = - \frac{L A}{4\pi r^{ 2} m c^{ 2}} {\bf v}.$">|; 

$key = q/displaystyle{bfF}_{rmrad}=frac{L,A}{4pi,r^{,2},m,c}left(1-frac{v_r}{c}right){bfe}_r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2817.png"
 ALT="$\displaystyle {\bf F}_{\rm rad} = \frac{L A}{4\pi r^{ 2} m c}\left(1-\frac{v_r}{c}\right){\bf e}_r,$">|; 

$key = q/displaystyle{bfL};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img331.png"
 ALT="$\displaystyle {\bf L}$">|; 

$key = q/displaystyle{bfL}=({calI}_{x'x'},omega_{x'},,{calI}_{y'y'},omega_{y'},,{calI}_{z'z'},omega_{z'}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1559.png"
 ALT="$\displaystyle {\bf L} = ({\cal I}_{x'x'} \omega_{x'}, {\cal I}_{y'y'} \omega_{y'}, {\cal I}_{z'z'} \omega_{z'}),$">|; 

$key = q/displaystyle{bfL}=left({calI}_{xx},omega_x,,{calI}_{yy},omega_y,{calI}_{zz},omega_zright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1551.png"
 ALT="$\displaystyle {\bf L} = \left({\cal I}_{xx} \omega_x, {\cal I}_{yy} \omega_y,{\cal I}_{zz} \omega_z\right),$">|; 

$key = q/displaystyle{bfL}=sum_{i=1,N}m_i,{bfr}_itimesfrac{d{bfr}_i}{dt}=sum_{i=1,N}m_i,{bfr}_itimes(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1496.png"
 ALT="$\displaystyle {\bf L} = \sum_{i=1,N} m_i {\bf r}_i\times\frac{d{\bf r}_i}{dt} =
\sum_{i=1,N}m_i {\bf r}_i\times($">|; 

$key = q/displaystyle{bfL}=sum_{i=1,N}{bfl}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img172.png"
 ALT="$\displaystyle {\bf L} = \sum_{i=1,N} {\bf l}_i$">|; 

$key = q/displaystyle{bfL}=textbf{emI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1520.png"
 ALT="$\displaystyle {\bf L} = \textbf{\em I} $">|; 

$key = q/displaystyle{bfP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img329.png"
 ALT="$\displaystyle {\bf P}$">|; 

$key = q/displaystyle{bfP}=sum_{i=1,N}m_i,frac{d{bfr}_i}{dt}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.80ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img167.png"
 ALT="$\displaystyle {\bf P} = \sum_{i=1,N} m_i \frac{d {\bf r}_i}{dt}.$">|; 

$key = q/displaystyle{bfP}_{rmabs}'simeq{bfP}_{rmabs}-frac{{calE}_{rmabs}}{c^{,2}},{bfv}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2806.png"
 ALT="$\displaystyle {\bf P}_{\rm abs}' \simeq {\bf P}_{\rm abs} - \frac{{\cal E}_{\rm abs}}{c^{ 2}} {\bf v}.$">|; 

$key = q/displaystyle{bfP}_{rmabs};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2809.png"
 ALT="$\displaystyle {\bf P}_{\rm abs}$">|; 

$key = q/displaystyle{bfP}_{rmem}'={bf0}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2802.png"
 ALT="$\displaystyle {\bf P}_{\rm em}' = {\bf0}.$">|; 

$key = q/displaystyle{bfR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1108.png"
 ALT="$\displaystyle {\bf R}$">|; 

$key = q/displaystyle{bfa}'={bfa}-frac{d{bfu}}{dt},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle {\bf a}' = {\bf a} - \frac{d{\bf u}}{dt},$">|; 

$key = q/displaystyle{bfa}'={bfa}-{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1226.png"
 ALT="$\displaystyle {\bf a}' = {\bf a} - {\bf r},$">|; 

$key = q/displaystyle{bfa}'={bfa}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle {\bf a}' = {\bf a}.$">|; 

$key = q/displaystyle{bfa}=(skew{3}ddot{r}-r,skew{5}dot{theta}^{,2}),{bfe}_r+(r,skew{5}ddot{theta}+2,skew{3}dot{r},skew{5}dot{theta}),{bfe}_theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img601.png"
 ALT="$\displaystyle {\bf a} = (\skew{3}\ddot{r}-r \skew{5}\dot{\theta}^{ 2}) {\bf ...
...ew{5}\ddot{\theta} + 2 \skew{3}\dot{r} \skew{5}\dot{\theta}) {\bf e}_\theta.$">|; 

$key = q/displaystyle{bfa}=frac{mbox{boldmathnu}times{bfp}}{sinI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.24ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img2007.png"
 ALT="$\displaystyle {\bf a} = \frac{\mbox{\boldmath$\nu$}\times {\bf p}}{\sin I},$">|; 

$key = q/displaystyle{bfa}=left(frac{d}{dt'}+mbox{boldmathOmega},timesright)left({bfv}'+mbox{boldmathOmega}times{bfr}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1077.png"
 ALT="$\displaystyle {\bf a} = \left(\frac{d}{dt'}+ \mbox{\boldmath$\Omega$} \times\right)\left({\bf v}' + \mbox{\boldmath$\Omega$}\times{\bf r}\right),$">|; 

$key = q/displaystyle{bfa}={bfa}'+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1078.png"
 ALT="$\displaystyle {\bf a} = {\bf a}' +$">|; 

$key = q/displaystyle{bfa}cdot{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3925.png"
 ALT="$\displaystyle {\bf a}\cdot{\bf b}$">|; 

$key = q/displaystyle{bfa}cdot{bfe};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2009.png"
 ALT="$\displaystyle {\bf a}\cdot{\bf e}$">|; 

$key = q/displaystyle{bfa}simeqI^{,-1}left(nu_y-p_y,,,p_x-nu_x,,,nu_x,p_y-nu_y,p_xright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2008.png"
 ALT="$\displaystyle {\bf a} \simeq I^{ -1}\left(\nu_y-p_y,  p_x-\nu_x,  \nu_x p_y-\nu_y p_x\right).$">|; 

$key = q/displaystyle{bfa}simeqleft(cospsi,,,-sinpsi,,,nu_y,sinpsi-nu_x,cospsiright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2017.png"
 ALT="$\displaystyle {\bf a} \simeq \left(\cos\psi,  -\sin\psi,  \nu_y \sin\psi-\nu_x \cos\psi\right).$">|; 

$key = q/displaystyle{bfa}times({bfb}times{bfc});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3930.png"
 ALT="$\displaystyle {\bf a}\times ({\bf b}\times {\bf c})$">|; 

$key = q/displaystyle{bfa}times{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3927.png"
 ALT="$\displaystyle {\bf a}\times {\bf b}$">|; 

$key = q/displaystyle{bfa}times{bfe}cdot{bfp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2011.png"
 ALT="$\displaystyle {\bf a}\times {\bf e}\cdot{\bf p}$">|; 

$key = q/displaystyle{bfe}=e,costheta,,{bfe}_r-e,sintheta,,{bfe}_theta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img873.png"
 ALT="$\displaystyle {\bf e} = e \cos\theta  {\bf e}_r-e \sin\theta  {\bf e}_\theta,
$">|; 

$key = q/displaystyle{bfe}=frac{dot{bfr}times{bfh}}{G,M}-frac{bfr}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img872.png"
 ALT="$\displaystyle {\bf e} = \frac{\dot{\bf r}\times {\bf h}}{G M} - \frac{\bf r}{r},
$">|; 

$key = q/displaystyle{bfe}=frac{skew{2}dot{bfr}times{bfh}}{mu}-frac{{bfr}}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4139.png"
 ALT="$\displaystyle {\bf e} = \frac{\skew{2}\dot{\bf r}\times {\bf h}}{\mu} - \frac{{\bf r}}{r},$">|; 

$key = q/displaystyle{bfe}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img589.png"
 ALT="$\displaystyle {\bf e}_r$">|; 

$key = q/displaystyle{bfe}_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img591.png"
 ALT="$\displaystyle {\bf e}_\theta$">|; 

$key = q/displaystyle{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1627.png"
 ALT="$\displaystyle {\bf e}_z$">|; 

$key = q/displaystyle{bfe}_{x''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1629.png"
 ALT="$\displaystyle {\bf e}_{x''}$">|; 

$key = q/displaystyle{bfe}equivfrac{dot{bfr}times{bfh}}{mu}-frac{{bfr}}{r}=e,{bfe}_x.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img5089.png"
 ALT="$\displaystyle {\bf e} \equiv \frac{\dot{\bf r}\times {\bf h}}{\mu} - \frac{{\bf r}}{r} = e {\bf e}_x.$">|; 

$key = q/displaystyle{bfe}simeq(1,,e_y,,e_z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1968.png"
 ALT="$\displaystyle {\bf e} \simeq (1, e_y, e_z),$">|; 

$key = q/displaystyle{bff}({bfr})=-nablaU,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle {\bf f}({\bf r}) = - \nabla U,$">|; 

$key = q/displaystyle{bff}({bfr})=m,{bfg}({bfr}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img368.png"
 ALT="$\displaystyle {\bf f}({\bf r}) = m  {\bf g}({\bf r}).$">|; 

$key = q/displaystyle{bff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3021.png"
 ALT="$\displaystyle {\bf f}$">|; 

$key = q/displaystyle{bff}=-frac{G,M,m}{r^{,3}},{bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img572.png"
 ALT="$\displaystyle {\bf f} = - \frac{G M m}{r^{ 3}} {\bf r}.$">|; 

$key = q/displaystyle{bff}=-frac{G,m_1,m_2}{r^{,3}},{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img849.png"
 ALT="$\displaystyle {\bf f} = - \frac{G m_1 m_2}{r^{ 3}} {\bf r},$">|; 

$key = q/displaystyle{bff}=-nablaU,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img575.png"
 ALT="$\displaystyle {\bf f} = - \nabla U,$">|; 

$key = q/displaystyle{bff}_i=sum_{j=1,N}^{jneqi}{bff}_{ij}+{bfF}_i,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img181.png"
 ALT="$\displaystyle {\bf f}_i = \sum_{j=1,N}^{j\neq i} {\bf f}_{ij} + {\bf F}_i,$">|; 

$key = q/displaystyle{bff}_{ij}=-{bff}_{ji}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle {\bf f}_{ij} = - {\bf f}_{ji}.$">|; 

$key = q/displaystyle{bfg}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3024.png"
 ALT="$\displaystyle {\bf g}'$">|; 

$key = q/displaystyle{bfg}'=-nablachi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1319.png"
 ALT="$\displaystyle {\bf g}' = - \nabla\chi,$">|; 

$key = q/displaystyle{bfg}'=frac{2,G,m',R}{a^{,3}},{bfe}_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1323.png"
 ALT="$\displaystyle {\bf g}' = \frac{2 G m' R}{a^{ 3}} {\bf e}_z.$">|; 

$key = q/displaystyle{bfg}'=frac{2,G,m'}{a^{,3}}left(-frac{x}{2},{bfe}_x-frac{y}{2},{bfe}_y+z,{bfe}_zright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img1321.png"
 ALT="$\displaystyle {\bf g}' = \frac{2 G m'}{a^{ 3}}\left(-\frac{x}{2} {\bf e}_x- \frac{y}{2} {\bf e}_y+ z {\bf e}_z\right).$">|; 

$key = q/displaystyle{bfg}'=left(-{mitOmega}^{,2},R,coslambda,sinlambda,,0,,-g+{mitOmega}^{,2},R,cos^2lambdaright).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img1112.png"
 ALT="$\displaystyle {\bf g}' = \left(-{\mit\Omega}^{ 2} R \cos\lambda \sin\lambda, 0, 
-g + {\mit\Omega}^{ 2} R \cos^2\lambda\right).$">|; 

$key = q/displaystyle{bfg}'={bfg}-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1093.png"
 ALT="$\displaystyle {\bf g}' = {\bf g} -$">|; 

$key = q/displaystyle{bfg}({bfr})=-nabla{mitPhi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4231.png"
 ALT="$\displaystyle {\bf g}({\bf r}) = -\nabla {\mit\Phi},$">|; 

$key = q/displaystyle{bfg}({bfr})=-nabla{mitPhi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img367.png"
 ALT="$\displaystyle {\bf g}({\bf r}) = - \nabla{\mit\Phi}.$">|; 

$key = q/displaystyle{bfg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1110.png"
 ALT="$\displaystyle {\bf g}$">|; 

$key = q/displaystyle{bfg}=-frac{G,m}{R^{,2}},{bfe}_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1324.png"
 ALT="$\displaystyle {\bf g} = - \frac{G m}{R^{ 2}} {\bf e}_z.$">|; 

$key = q/displaystyle{bfg}=-nabla({mitPhi}+chi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1157.png"
 ALT="$\displaystyle {\bf g} = - \nabla({\mit\Phi}+\chi).$">|; 

$key = q/displaystyle{bfg}=-nabla{mitPhi},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img356.png"
 ALT="$\displaystyle {\bf g}= -\nabla{\mit\Phi},$">|; 

$key = q/displaystyle{bfg}=G,m',frac{{bfr}'-{bfr}}{|{bfr}'-{bfr}|^{,3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img348.png"
 ALT="$\displaystyle {\bf g} = G m' \frac{{\bf r}'-{\bf r}}{\vert{\bf r}'-{\bf r}\vert^{ 3}}.$">|; 

$key = q/displaystyle{bfg}_c=-nablachi',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1218.png"
 ALT="$\displaystyle {\bf g}_c = - \nabla\chi',$">|; 

$key = q/displaystyle{bfg}_c=-omega^{,2},rho,{bfe}_z.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1217.png"
 ALT="$\displaystyle {\bf g}_c = - \omega^{ 2} \rho {\bf e}_z.$">|; 

$key = q/displaystyle{bfg}_c=r,{mitOmega}^{,2},sin^2theta,,{bfe}_r+r,{mitOmega}^{,2},sintheta,costheta,,{bfe}_theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1154.png"
 ALT="$\displaystyle {\bf g}_c = r {\mit\Omega}^{ 2} \sin^2\theta  {\bf e}_r +r {\mit\Omega}^{ 2} \sin\theta \cos\theta  {\bf e}_\theta.$">|; 

$key = q/displaystyle{bfg}_g=-nabla{mitPhi}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1223.png"
 ALT="$\displaystyle {\bf g}_g = -\nabla{\mit\Phi}',$">|; 

$key = q/displaystyle{bfh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img938.png"
 ALT="$\displaystyle {\bf h}$">|; 

$key = q/displaystyle{bfh}={bfr}timesdot{bfr}=h,{bfe}_z,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5087.png"
 ALT="$\displaystyle {\bf h} = {\bf r}\times \dot{\bf r} = h {\bf e}_z,$">|; 

$key = q/displaystyle{bfh}cdot{bfr}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img580.png"
 ALT="$\displaystyle {\bf h}\cdot{\bf r} = 0.$">|; 

$key = q/displaystyle{bfl}_i=m_i,{bfr}_itimesfrac{d{bfr}_i}{dt};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle {\bf l}_i = m_i {\bf r}_i\times \frac{d{\bf r}_i}{dt}$">|; 

$key = q/displaystyle{bfp}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2788.png"
 ALT="$\displaystyle {\bf p}'$">|; 

$key = q/displaystyle{bfp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1962.png"
 ALT="$\displaystyle {\bf p}$">|; 

$key = q/displaystyle{bfp}cdot{bfe}simeqp_x+e_z=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2004.png"
 ALT="$\displaystyle {\bf p}\cdot{\bf e} \simeq p_x+ e_z= 0,$">|; 

$key = q/displaystyle{bfr}'={bfr}_3-left(frac{m_1,{bfr}_1+m_2,{bfr}_2}{m_1+m_2}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2960.png"
 ALT="$\displaystyle {\bf r}' = {\bf r}_3-\left(\frac{m_1 {\bf r}_1+m_2 {\bf r}_2}{m_1+m_2}\right)$">|; 

$key = q/displaystyle{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1844.png"
 ALT="$\displaystyle {\bf r}$">|; 

$key = q/displaystyle{bfr}=(r,costheta,,r,sintheta,,0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img854.png"
 ALT="$\displaystyle {\bf r} = (r \cos\theta, r \sin\theta,  0),$">|; 

$key = q/displaystyle{bfr}=a,{bfe}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1971.png"
 ALT="$\displaystyle {\bf r} = a {\bf e}.$">|; 

$key = q/displaystyle{bfr}=frac{{bfF}timesmbox{boldmathtau}}{F^{,2}}+lambda,frac{{bfF}}{F},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle {\bf r} = \frac{{\bf F}\times\mbox{\boldmath $\tau$}}{F^{ 2}} + \lambda \frac{{\bf F}}{F},
$">|; 

$key = q/displaystyle{bfr}=r,{bfe}_r.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img593.png"
 ALT="$\displaystyle {\bf r} = r {\bf e}_r.$">|; 

$key = q/displaystyle{bfr}={bfr}_2-{bfr}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2959.png"
 ALT="$\displaystyle {\bf r}= {\bf r}_2-{\bf r}_1$">|; 

$key = q/displaystyle{bfr}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img267.png"
 ALT="$\displaystyle {\bf r}_1$">|; 

$key = q/displaystyle{bfr}_2-{bfr}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2979.png"
 ALT="$\displaystyle {\bf r}_2-{\bf r}_1$">|; 

$key = q/displaystyle{bfr}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img269.png"
 ALT="$\displaystyle {\bf r}_2$">|; 

$key = q/displaystyle{bfr}_3-{bfr}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2981.png"
 ALT="$\displaystyle {\bf r}_3-{\bf r}_1$">|; 

$key = q/displaystyle{bfr}_3-{bfr}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2983.png"
 ALT="$\displaystyle {\bf r}_3-{\bf r}_2$">|; 

$key = q/displaystyle{bfr}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2977.png"
 ALT="$\displaystyle {\bf r}_3$">|; 

$key = q/displaystyle{bfr}_itimes{bff}_{ij}+{bfr}_jtimes{bff}_{ji}=({bfr}_i-{bfr}_j)times{bff}_{ij}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img177.png"
 ALT="$\displaystyle {\bf r}_i\times {\bf f}_{ij}+{\bf r}_j\times {\bf f}_{ji} =
({\bf r}_i-{\bf r}_j)\times {\bf f}_{ij}.$">|; 

$key = q/displaystyle{bfr}_itimes{bff}_{ij}+{bfr}_jtimes{bff}_{ji}={bf0},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle {\bf r}_i\times {\bf f}_{ij}+{\bf r}_j\times {\bf f}_{ji} = {\bf0},$">|; 

$key = q/displaystyle{bfr}_msimeqa_m,left(coslambda_m,,sinlambda_m,,I_m,sin(lambda_m-alpha_n)right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1748.png"
 ALT="$\displaystyle {\bf r}_m \simeq a_m \left(\cos\lambda_m, \sin\lambda_m, I_m \sin(\lambda_m-\alpha_n)\right),$">|; 

$key = q/displaystyle{bfr}_s=a_s,(coslambda_s,,sinlambda_s,,0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1710.png"
 ALT="$\displaystyle {\bf r}_s = a_s (\cos\lambda_s, \sin\lambda_s, 0).$">|; 

$key = q/displaystyle{bfr}_{cm}=frac{m_1,{bfr}_1+m_2,{bfr}_2}{m_1+m_2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.95ex; " SRC="|."$dir".q|img266.png"
 ALT="$\displaystyle {\bf r}_{cm} = \frac{m_1 {\bf r}_1+ m_2 {\bf r}_2}{m_1 + m_2}.$">|; 

$key = q/displaystyle{bfr}_{cm}=frac{sum_{i=1,N}m_i,{bfr}_i}{sum_{i=1,N}m_i}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.28ex; " SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle {\bf r}_{cm} = \frac{\sum_{i=1,N} m_i {\bf r}_i}{\sum_{i=1,N} m_i}.$">|; 

$key = q/displaystyle{bfr}cdot{bfr}'=r,r',F,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img398.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf r}' = r r' F,$">|; 

$key = q/displaystyle{bfr}cdot{bfr}'=r,r',costheta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2985.png"
 ALT="$\displaystyle {\bf r}\cdot{\bf r}' = r r' \cos\theta.$">|; 

$key = q/displaystyle{bfr}times{bfF}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img278.png"
 ALT="$\displaystyle {\bf r}\times{\bf F} =$">|; 

$key = q/displaystyle{bfv}'={bfv}-{bfu}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle {\bf v}' = {\bf v} - {\bf u}.$">|; 

$key = q/displaystyle{bfv}=frac{d{bfr}}{dt}=skew{3}dot{r},{bfe}_r+r,dot{bfe}_r,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img594.png"
 ALT="$\displaystyle {\bf v} = \frac{d{\bf r}}{dt} = \skew{3}\dot{r} {\bf e}_r + r \dot{\bf e}_r,$">|; 

$key = q/displaystyle{bfv}=skew{3}dot{r},,{bfe}_r+r,skew{5}dot{theta},,{bfe}_theta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img598.png"
 ALT="$\displaystyle {\bf v} = \skew{3}\dot{r}  {\bf e}_r + r \skew{5}\dot{\theta}  {\bf e}_\theta.$">|; 

$key = q/displaystyle{bfv}=varv_0,(costheta,-sintheta,,0).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1136.png"
 ALT="$\displaystyle {\bf v} = \varv_0 (\cos\theta,-\sin\theta, 0).$">|; 

$key = q/displaystyle{bfv}={bfv}'+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1075.png"
 ALT="$\displaystyle {\bf v} = {\bf v}' +$">|; 

$key = q/displaystyle{bfw}simeq(w_x,,w_y,,1),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1974.png"
 ALT="$\displaystyle {\bf w}\simeq (w_x, w_y, 1),$">|; 

$key = q/displaystyle{bfx}={bfA},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2316.png"
 ALT="$\displaystyle {\bf x} = {\bf A} $">|; 

$key = q/displaystyle{bfx}_i';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4103.png"
 ALT="$\displaystyle {\bf x}_i'$">|; 

$key = q/displaystyle{bfx}_i^T,{bfA},{bfx}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.62ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4096.png"
 ALT="$\displaystyle {\bf x}_i^T {\bf A} {\bf x}_j$">|; 

$key = q/displaystyle{bfx}_i^{ast,T},{bfA},{bfx}_i=lambda_i^{,ast},{bfx}_i^{ast,T}{bfx}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4084.png"
 ALT="$\displaystyle {\bf x}_i^{\ast T} {\bf A} {\bf x}_i = \lambda_i^{ \ast} {\bf x}_i^{\ast T}{\bf x}_i.$">|; 

$key = q/displaystyle{bfx}_i^{ast,T},{bfA}=lambda_i^{,ast},{bfx}_i^{ast,T},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4080.png"
 ALT="$\displaystyle {\bf x}_i^{\ast T} {\bf A} = \lambda_i^{ \ast} {\bf x}_i^{\ast T},$">|; 

$key = q/displaystyle{bfx}_i^{ast,T}{bfA},{bfx}_i=lambda_i,{bfx}_i^{ast,T}{bfx}_i.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4083.png"
 ALT="$\displaystyle {\bf x}_i^{\ast T} {\bf A} {\bf x}_i = \lambda_i {\bf x}_i^{\ast T}{\bf x}_i.$">|; 

$key = q/displaystyle{bfx}_j';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img4105.png"
 ALT="$\displaystyle {\bf x}_j'$">|; 

$key = q/displaystyle{calC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4409.png"
 ALT="$\displaystyle {\cal C}$">|; 

$key = q/displaystyle{calC}=frac{2}{3}left[1-frac{2}{5},(1+eta_0)^{1slash2}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4402.png"
 ALT="$\displaystyle {\cal C} =\frac{2}{3}\left[1-\frac{2}{5} (1+\eta_0)^{1/2}\right].$">|; 

$key = q/displaystyle{calC}=frac{2}{3}left[1-frac{2}{5}left(frac{15}{2},frac{zeta}{epsilon_0}-1right)^{1slash2}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img4405.png"
 ALT="$\displaystyle {\cal C} =\frac{2}{3}\left[1-\frac{2}{5}\left(\frac{15}{2} \frac{\zeta}{\epsilon_0}-1\right)^{1/2}\right].$">|; 

$key = q/displaystyle{calC}=frac{{calI}_parallel}{M,R^{,2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img4401.png"
 ALT="$\displaystyle {\cal C} = \frac{{\cal I}_\parallel}{M R^{ 2}}.$">|; 

$key = q/displaystyle{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img940.png"
 ALT="$\displaystyle {\cal E}$">|; 

$key = q/displaystyle{calE}=-frac{G,M}{2,a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img657.png"
 ALT="$\displaystyle {\cal E} = - \frac{G M}{2 a}.$">|; 

$key = q/displaystyle{calE}=-frac{mu}{2,a};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.07ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img5086.png"
 ALT="$\displaystyle {\cal E} = -\frac{\mu}{2 a};$">|; 

$key = q/displaystyle{calE}=frac{h^{,2}}{2}left[left(frac{du}{dtheta}right)^2+u^{,2}-2,u,u_cright],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.26ex; " SRC="|."$dir".q|img652.png"
 ALT="$\displaystyle {\cal E} = \frac{h^{ 2}}{2}\left[\left(\frac{du}{d\theta}\right)^2
+ u^{ 2} - 2 u u_c\right],$">|; 

$key = q/displaystyle{calE}=frac{skew{3}dot{r}^{,2}+r^{,2},skew{5}dot{theta}^{,2}}{2}-frac{G,M}{r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img651.png"
 ALT="$\displaystyle {\cal E} = \frac {\skew{3}\dot{r}^{ 2} + r^{ 2} \skew{5}\dot{\theta}^{ 2}}{2} - \frac{G M}{r}.$">|; 

$key = q/displaystyle{calE}=frac{skew{3}dot{r}^{,2}}{2}+frac{h^{,2}}{2,r^{,2}}-frac{G,M}{r},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img676.png"
 ALT="$\displaystyle {\cal E} = \frac{\skew{3}\dot{r}^{ 2}}{2} + \frac{h^{ 2}}{2 r^{ 2}} - \frac{G M}{r},$">|; 

$key = q/displaystyle{calE}=frac{varv^{,2}}{2}-frac{G,M}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img577.png"
 ALT="$\displaystyle {\cal E} = \frac{\varv^{ 2}}{2} - \frac{G M}{r}$">|; 

$key = q/displaystyle{calE}_{rmabs};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2807.png"
 ALT="$\displaystyle {\cal E}_{\rm abs}$">|; 

$key = q/displaystyle{calE}_{rmem}'={calE}_{rmabs}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img2801.png"
 ALT="$\displaystyle {\cal E}_{\rm em}' = {\cal E}_{\rm abs}'.$">|; 

$key = q/displaystyle{calE}equivfrac{1}{2}left(skew{3}dot{xi}^{,2}+skew{3}dot{eta}^{,2}+skew{3}dot{zeta}^{,2}right)-frac{1}{r}=-frac{1}{2,a}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2129.png"
 ALT="$\displaystyle {\cal E} \equiv \frac{1}{2}\left(\skew{3}\dot{\xi}^{ 2}+\skew{3}...
...eta}^{ 2} + \skew{3}\dot{\zeta}^{ 2}\right) - \frac{1}{r} = - \frac{1}{2 a}.$">|; 

$key = q/displaystyle{calE}simeqfrac{2}{alpha^{,2}}left(n^{-1},frac{dphi}{dt}-1right)^2-cos2phi.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1895.png"
 ALT="$\displaystyle {\cal E} \simeq \frac{2}{\alpha^{ 2}}\left(n^{-1} \frac{d\phi}{dt}-1\right)^2-\cos 2\phi.$">|; 

$key = q/displaystyle{calE}simeqfrac{4}{7,e,alpha^{,2}}left(n^{-1},frac{dphi}{dt}-frac{3}{2}right)^2-cos2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1897.png"
 ALT="$\displaystyle {\cal E} \simeq \frac{4}{7 e \alpha^{ 2}}\left(n^{-1} \frac{d\phi}{dt}-\frac{3}{2}\right)^2-\cos 2\phi$">|; 

$key = q/displaystyle{calE}simeqfrac{4}{e,alpha^{,2}}left(n^{-1},frac{dphi}{dt}-frac{1}{2}right)^2+cos2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.86ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1896.png"
 ALT="$\displaystyle {\cal E} \simeq \frac{4}{e \alpha^{ 2}}\left(n^{-1} \frac{d\phi}{dt}-\frac{1}{2}\right)^2+\cos 2\phi$">|; 

$key = q/displaystyle{calG};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4798.png"
 ALT="$\displaystyle {\cal G}$">|; 

$key = q/displaystyle{calI}_parallel,skew{5}dot{mitOmega}=-tau,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1287.png"
 ALT="$\displaystyle {\cal I}_\parallel \skew{5}\dot{\mit\Omega} = -\tau,$">|; 

$key = q/displaystyle{calI}_parallel=0.331,M,R^{,2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img4605.png"
 ALT="$\displaystyle {\cal I}_\parallel = 0.331 M R^{ 2},$">|; 

$key = q/displaystyle{calI}_parallel=frac{8pi}{3}int_0^Rrho(a),a^{,4},da.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img4396.png"
 ALT="$\displaystyle {\cal I}_\parallel =\frac{8\pi}{3}\int_0^R \rho(a) a^{ 4} da.$">|; 

$key = q/displaystyle{calI}_parallel=frac{8pi}{9},bar{rho}(R),R^{,5}left[1-frac{2}{5},(1+eta_0)^{1slash2}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4400.png"
 ALT="$\displaystyle {\cal I}_\parallel = \frac{8\pi}{9} \bar{\rho}(R) R^{ 5}\left[1-\frac{2}{5} (1+\eta_0)^{1/2}\right].$">|; 

$key = q/displaystyle{calI}_parallel=int(x^{,2}+y^{,2}),gamma,d^{,3}{bfr}=intr^{,2},gamma,(1-cos^2theta),d^{,3}{bfr}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.97ex; " SRC="|."$dir".q|img1662.png"
 ALT="$\displaystyle {\cal I}_\parallel = \int (x^{ 2}+y^{ 2}) \gamma d^{ 3}{\bf r} = \int r^{ 2} \gamma (1-\cos^2\theta) d^{ 3}{\bf r}.$">|; 

$key = q/displaystyle{calI}_perp,frac{domega_{x'}}{dt'}+({calI}_{parallel}-{calI}_{perp}),omega_{z'},omega_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1573.png"
 ALT="$\displaystyle {\cal I}_\perp \frac{d\omega_{x'}}{dt'} + ({\cal I}_{\parallel}-{\cal I}_{\perp}) \omega_{z'} \omega_{y'}$">|; 

$key = q/displaystyle{calI}_perp,frac{domega_{y'}}{dt'}-({calI}_{parallel}-{calI}_{perp}),omega_{z'},omega_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1574.png"
 ALT="$\displaystyle {\cal I}_\perp \frac{d\omega_{y'}}{dt'} - ({\cal I}_{\parallel}-{\cal I}_{\perp}) 
\omega_{z'} \omega_{x'}$">|; 

$key = q/displaystyle{calI}_perp,skew{5}ddot{theta}-frac{partial{calL}}{partialtheta}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.68ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1727.png"
 ALT="$\displaystyle {\cal I}_\perp \skew{5}\ddot{\theta} - \frac{\partial {\cal L}}{\partial \theta} = 0.$">|; 

$key = q/displaystyle{calI}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1663.png"
 ALT="$\displaystyle {\cal I}_\perp$">|; 

$key = q/displaystyle{calI}_{x'x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4483.png"
 ALT="$\displaystyle {\cal I}_{x'x'}$">|; 

$key = q/displaystyle{calI}_{x'y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4487.png"
 ALT="$\displaystyle {\cal I}_{x'y'}$">|; 

$key = q/displaystyle{calI}_{x'z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4489.png"
 ALT="$\displaystyle {\cal I}_{x'z'}$">|; 

$key = q/displaystyle{calI}_{xx},skew{5}dot{omega}_x-({calI}_{yy}-{calI}_{zz}),omega_z,omega_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1835.png"
 ALT="$\displaystyle {\cal I}_{xx} \skew{5}\dot{\omega}_x - ({\cal I}_{yy}-{\cal I}_{zz}) \omega_z \omega_y$">|; 

$key = q/displaystyle{calI}_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1499.png"
 ALT="$\displaystyle {\cal I}_{xx}$">|; 

$key = q/displaystyle{calI}_{xy}={calI}_{yx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1505.png"
 ALT="$\displaystyle {\cal I}_{xy}={\cal I}_{yx}$">|; 

$key = q/displaystyle{calI}_{xz}={calI}_{zx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1509.png"
 ALT="$\displaystyle {\cal I}_{xz}={\cal I}_{zx}$">|; 

$key = q/displaystyle{calI}_{y'y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4485.png"
 ALT="$\displaystyle {\cal I}_{y'y'}$">|; 

$key = q/displaystyle{calI}_{y'z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4491.png"
 ALT="$\displaystyle {\cal I}_{y'z'}$">|; 

$key = q/displaystyle{calI}_{yy},skew{5}dot{omega}_y-({calI}_{zz}-{calI}_{xx}),omega_x,omega_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1837.png"
 ALT="$\displaystyle {\cal I}_{yy} \skew{5}\dot{\omega}_y - ({\cal I}_{zz}-{\cal I}_{xx}) \omega_x \omega_z$">|; 

$key = q/displaystyle{calI}_{yy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1501.png"
 ALT="$\displaystyle {\cal I}_{yy}$">|; 

$key = q/displaystyle{calI}_{yz}={calI}_{zy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1507.png"
 ALT="$\displaystyle {\cal I}_{yz}={\cal I}_{zy}$">|; 

$key = q/displaystyle{calI}_{z'z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4478.png"
 ALT="$\displaystyle {\cal I}_{z'z'}$">|; 

$key = q/displaystyle{calI}_{zz},skew{5}dot{omega}_z-({calI}_{xx}-{calI}_{yy}),omega_y,omega_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1839.png"
 ALT="$\displaystyle {\cal I}_{zz}  \skew{5}\dot{\omega}_z - ({\cal I}_{xx}-{\cal I}_{yy}) \omega_y \omega_x$">|; 

$key = q/displaystyle{calI}_{zz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1503.png"
 ALT="$\displaystyle {\cal I}_{zz}$">|; 

$key = q/displaystyle{calL}=K-U.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.28ex; " SRC="|."$dir".q|img1414.png"
 ALT="$\displaystyle {\cal L} = K - U.$">|; 

$key = q/displaystyle{calL}=frac{1}{2},m,(dot{r}^{,2}+r^{,2},skew{5}dot{theta}^{,2})-U(r).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1418.png"
 ALT="$\displaystyle {\cal L} = \frac{1}{2} m (\dot{r}^{ 2} + r^{ 2} \skew{5}\dot{\theta}^{ 2}) - U(r).$">|; 

$key = q/displaystyle{calM}'=skew{5}bar{lambda}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3178.png"
 ALT="$\displaystyle {\cal M}' = \skew{5}\bar{\lambda}',$">|; 

$key = q/displaystyle{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img724.png"
 ALT="$\displaystyle {\cal M}$">|; 

$key = q/displaystyle{calM}=n,(t-tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img692.png"
 ALT="$\displaystyle {\cal M} = n (t-\tau)$">|; 

$key = q/displaystyle{calM}=n,t.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img1866.png"
 ALT="$\displaystyle {\cal M} = n t.$">|; 

$key = q/displaystyle{calM}=skew{5}bar{lambda}-alpha,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3175.png"
 ALT="$\displaystyle {\cal M} = \skew{5}\bar{\lambda} - \alpha,$">|; 

$key = q/displaystyle{calM}_0=-n,tau.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img757.png"
 ALT="$\displaystyle {\cal M}_0= -n \tau.$">|; 

$key = q/displaystyle{calR}'({bfr},{bfr}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2420.png"
 ALT="$\displaystyle {\cal R}' ({\bf r},{\bf r}')$">|; 

$key = q/displaystyle{calR}'=frac{tilde{mu}}{a},{calS}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4931.png"
 ALT="$\displaystyle {\cal R}' = \frac{\tilde{\mu}}{a} {\cal S}',$">|; 

$key = q/displaystyle{calR}(r,theta)=mu'left[frac{1}{(r^{,2}+r'^{,2}-2,r,r',beta)^{1slash2}}-frac{beta,r}{r'^{,2}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4188.png"
 ALT="$\displaystyle {\cal R}(r,\theta) = \mu'\left[\frac{1}{(r^{ 2} + r'^{ 2}-2 r r' \beta)^{1/2}}-\frac{\beta r}{r'^{ 2}}\right],$">|; 

$key = q/displaystyle{calR}(r,vartheta)=-J_2,frac{mu,R^{,2}}{r^{,3}},P_2(cosvartheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2689.png"
 ALT="$\displaystyle {\cal R}(r,\vartheta) = -J_2 \frac{\mu R^{ 2}}{r^{ 3}} P_2(\cos\vartheta).$">|; 

$key = q/displaystyle{calR}({bfr},{bfr}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2418.png"
 ALT="$\displaystyle {\cal R}({\bf r},{\bf r}')$">|; 

$key = q/displaystyle{calR}({bfr},{bfr}')=mu'left(frac{1}{|{bfr}-{bfr}'|}-frac{{bfr}cdot{bfr}'}{r'^{,3}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4137.png"
 ALT="$\displaystyle {\cal R}({\bf r},{\bf r}')= \mu'\left(\frac{1}{\vert{\bf r}-{\bf r}'\vert} - \frac{{\bf r}\cdot{\bf r}'}{r'^{ 3}}\right),$">|; 

$key = q/displaystyle{calR}=frac{1}{2}sum_ik_i,skew{3}dot{x}_i^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; vertical-align: -2.61ex; " SRC="|."$dir".q|img1483.png"
 ALT="$\displaystyle {\cal R} = \frac{1}{2} \sum_i k_i \skew{3}\dot{x}_i^{ 2}
$">|; 

$key = q/displaystyle{calR}=frac{J_2}{2},frac{mu,R^{,2}}{r^{,3}}left[1-frac{3}{2},sin^2I+frac{3}{2},sin^2I,cos(2,omega+2,theta)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img2706.png"
 ALT="$\displaystyle {\cal R} = \frac{J_2}{2} \frac{\mu R^{ 2}}{r^{ 3}}\left[1-\frac{3}{2} \sin^2 I + \frac{3}{2} \sin^2 I \cos(2 \omega+2 \theta)\right].$">|; 

$key = q/displaystyle{calR}=frac{mu,h^{,2}}{c^{,2},r^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2889.png"
 ALT="$\displaystyle {\cal R} = \frac{\mu h^{ 2}}{c^{ 2} r^{ 3}}
$">|; 

$key = q/displaystyle{calR}=frac{tilde{mu}'}{a'},{calS},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img4883.png"
 ALT="$\displaystyle {\cal R} = \frac{\tilde{\mu}'}{a'} {\cal S},$">|; 

$key = q/displaystyle{calR}_n(r,theta,phi)proptor^{,n},{calS}_n(theta,phi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4216.png"
 ALT="$\displaystyle {\cal R}_n(r,\theta,\phi) \propto r^{ n} {\cal S}_n(\theta,\phi).$">|; 

$key = q/displaystyle{calS}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img4944.png"
 ALT="$\displaystyle {\cal S}'$">|; 

$key = q/displaystyle{calS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img4942.png"
 ALT="$\displaystyle {\cal S}$">|; 

$key = q/displaystyle{calS}^{(j)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img5041.png"
 ALT="$\displaystyle {\cal S}^{(j)}$">|; 

$key = q/displaystyle{calS}_0';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img2486.png"
 ALT="$\displaystyle {\cal S}_0'$">|; 

$key = q/displaystyle{calS}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2453.png"
 ALT="$\displaystyle {\cal S}_0$">|; 

$key = q/displaystyle{calS}_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2488.png"
 ALT="$\displaystyle {\cal S}_1'$">|; 

$key = q/displaystyle{calS}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2455.png"
 ALT="$\displaystyle {\cal S}_1$">|; 

$key = q/displaystyle{calS}_2';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2495.png"
 ALT="$\displaystyle {\cal S}_2'$">|; 

$key = q/displaystyle{calS}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2462.png"
 ALT="$\displaystyle {\cal S}_2$">|; 

$key = q/displaystyle{calS}_D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4965.png"
 ALT="$\displaystyle {\cal S}_D$">|; 

$key = q/displaystyle{calS}_D=(1+zeta')^{-1},left[1-2,tilde{alpha},cos(vartheta-vartheta')+tilde{alpha}^2-2,tilde{alpha},deltaright]^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4960.png"
 ALT="$\displaystyle {\cal S}_D = (1+\zeta')^{-1} \left[1-2 \tilde{\alpha} \cos(\vartheta-\vartheta')+\tilde{\alpha}^2 -2 \tilde{\alpha} \delta\right]^{-1/2},$">|; 

$key = q/displaystyle{calS}_D=a'left(r'^{,2}-2,r',r,cospsi+r^{,2}right)^{-1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.68ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img4951.png"
 ALT="$\displaystyle {\cal S}_D = a' \left(r'^{ 2}-2 r' r \cos\psi + r^{ 2}\right)^{-1/2}.$">|; 

$key = q/displaystyle{calS}_D=frac{a'}{|{bfr}'-{bfr}|},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img4946.png"
 ALT="$\displaystyle {\cal S}_D = \frac{a'}{\vert{\bf r}'-{\bf r}\vert},$">|; 

$key = q/displaystyle{calS}_D=sum_{j=-infty,infty},{calS}^{(j)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.07ex; vertical-align: -2.90ex; " SRC="|."$dir".q|img5040.png"
 ALT="$\displaystyle {\cal S}_D=
\sum_{j=-\infty,\infty} {\cal S}^{(j)},$">|; 

$key = q/displaystyle{calS}_Dsimeq(1+zeta')^{-1}left[F+(tilde{alpha}-alpha),D,F+frac{1}{2},(tilde{alpha}-alpha)^2,D^{,2},Fright]+delta,alpha,F^{,3},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4962.png"
 ALT="$\displaystyle {\cal S}_D \simeq (1+\zeta')^{-1}\left[F + (\tilde{\alpha}-\alpha...
...c{1}{2} (\tilde{\alpha}-\alpha)^2 D^{ 2} F\right]+
\delta \alpha F^{ 3},$">|; 

$key = q/displaystyle{calS}_E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4947.png"
 ALT="$\displaystyle {\cal S}_E$">|; 

$key = q/displaystyle{calS}_I;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4949.png"
 ALT="$\displaystyle {\cal S}_I$">|; 

$key = q/displaystyle{calS}_n(theta,phi)=sum_{m=-n,+n},alpha_{n,m},Y_n^{,m}(theta,phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img4210.png"
 ALT="$\displaystyle {\cal S}_n(\theta,\phi) = \sum_{m=-n,+n} \alpha_{n,m} Y_n^{ m}(\theta,\phi),$">|; 

$key = q/displaystyle{calS}_s'={calS}_{0,s}'+{calS}_{2,s'}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img2528.png"
 ALT="$\displaystyle {\cal S}_s' = {\cal S}_{0 s}'+{\cal S}_{2 s'}',$">|; 

$key = q/displaystyle{calS}_s={calS}_{0,s}+{calS}_{2,s},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2501.png"
 ALT="$\displaystyle {\cal S}_s = {\cal S}_{0 s}+{\cal S}_{2 s},$">|; 

$key = q/displaystyle{calS}_{0,s}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img2529.png"
 ALT="$\displaystyle {\cal S}_{0 s}'$">|; 

$key = q/displaystyle{calS}_{0,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2502.png"
 ALT="$\displaystyle {\cal S}_{0 s}$">|; 

$key = q/displaystyle{calS}_{2,s}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.69ex; " SRC="|."$dir".q|img2531.png"
 ALT="$\displaystyle {\cal S}_{2 s}'$">|; 

$key = q/displaystyle{calS}_{2,s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2504.png"
 ALT="$\displaystyle {\cal S}_{2 s}$">|; 

$key = q/displaystyle{calT}_J=frac{1}{a}+2sqrt{a,(1-e^{,2})},cosI.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.57ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2137.png"
 ALT="$\displaystyle {\cal T}_J = \frac{1}{a} + 2\sqrt{a (1-e^{ 2})} \cos I.$">|; 

$key = q/displaystyle{mitDelta}=left(frac{-3+4,g}{2}right)m^{,2}+frac{9}{16},m^{,3}+{calO}(m^{,4}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3605.png"
 ALT="$\displaystyle {\mit\Delta} = \left(\frac{-3+4 g}{2}\right)m^{ 2} +\frac{9}{16} m^{ 3} + {\cal O}(m^{ 4}).$">|; 

$key = q/displaystyle{mitDelta}=left(frac{3-4,c}{2}right)m^{,2}+frac{255}{16},m^{,3}+{calO}(m^{,4}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img3560.png"
 ALT="$\displaystyle {\mit\Delta} = \left(\frac{3-4 c}{2}\right)m^{ 2} + \frac{255}{16} m^{ 3} +{\cal O}(m^{ 4}).$">|; 

$key = q/displaystyle{mitDelta}K=-{mitDelta}U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img146.png"
 ALT="$\displaystyle {\mit\Delta} K = - {\mit\Delta} U$">|; 

$key = q/displaystyle{mitDelta}K=int_{t_1}^{t_2}{bff}cdot{bfv},dt=int_P^Q{bff}cdotd{bfr},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.63ex; vertical-align: -2.27ex; " SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle {\mit\Delta}K = \int_{t_1}^{t_2} {\bf f}\cdot{\bf v} dt
=\int_P^Q {\bf f}\cdot d{\bf r},$">|; 

$key = q/displaystyle{mitDelta}R=-(epsilon'-epsilon),R=-frac{3}{2}left(frac{tilde{mu}}{1+tilde{mu}}right)zeta,R.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1270.png"
 ALT="$\displaystyle {\mit\Delta} R = -(\epsilon'-\epsilon) R = -\frac{3}{2}\left(\frac{\tilde{\mu}}{1+\tilde{\mu}}\right)\zeta R.$">|; 

$key = q/displaystyle{mitDelta}R=R_+-R_-=-epsilon,R=0.14,{rmm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1263.png"
 ALT="$\displaystyle {\mit\Delta} R = R_+-R_- = -\epsilon R = 0.14 {\rm m}.$">|; 

$key = q/displaystyle{mitDelta}R=R_+-R_-=-epsilon,R=0.31,{rmm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1255.png"
 ALT="$\displaystyle {\mit\Delta} R = R_+-R_- = -\epsilon R = 0.31 {\rm m}.$">|; 

$key = q/displaystyle{mitDelta}R=R_e-R_p=epsilon,R=27.5,{rmkm}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1193.png"
 ALT="$\displaystyle {\mit\Delta} R = R_e-R_p = \epsilon R = 27.5 {\rm km}.$">|; 

$key = q/displaystyle{mitDelta}beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3712.png"
 ALT="$\displaystyle {\mit\Delta}\beta$">|; 

$key = q/displaystyle{mitDelta}equivA_{xx},A_{yy}-A_{xy},A_{y,x}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3559.png"
 ALT="$\displaystyle {\mit\Delta} \equiv A_{xx} A_{yy}- A_{xy} A_{y x}= 0.$">|; 

$key = q/displaystyle{mitDelta}equiv{mitOmega}_1^{,2}-1-frac{3}{2},m^{,2}+frac{9}{16},m^{,3}=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img3604.png"
 ALT="$\displaystyle {\mit\Delta}\equiv {\mit\Omega}_1^{ 2} -1 -\frac{3}{2} m^{ 2} + \frac{9}{16} m^{ 3}=0.$">|; 

$key = q/displaystyle{mitDelta}lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3710.png"
 ALT="$\displaystyle {\mit\Delta}\lambda$">|; 

$key = q/displaystyle{mitDelta}skew{5}bar{lambda}_{rmautumn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img825.png"
 ALT="$\displaystyle {\mit\Delta}\skew{5}\bar{\lambda}_{\rm autumn}$">|; 

$key = q/displaystyle{mitDelta}skew{5}bar{lambda}_{rmspring};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img821.png"
 ALT="$\displaystyle {\mit\Delta}\skew{5}\bar{\lambda}_{\rm spring}$">|; 

$key = q/displaystyle{mitDelta}skew{5}bar{lambda}_{rmsummer};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img823.png"
 ALT="$\displaystyle {\mit\Delta}\skew{5}\bar{\lambda}_{\rm summer}$">|; 

$key = q/displaystyle{mitDelta}skew{5}bar{lambda}_{rmwinter};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img827.png"
 ALT="$\displaystyle {\mit\Delta}\skew{5}\bar{\lambda}_{\rm winter}$">|; 

$key = q/displaystyle{mitDelta}t=frac{T}{12pi}left[left(frac{r_1+r_2+s}{a}right)^{3slash2}-left(frac{r_1+r_2-s}{a}right)^{3slash2}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img920.png"
 ALT="$\displaystyle {\mit\Delta} t = \frac{T}{12\pi}\left[\left(\frac{r_1+r_2+s}{a}\right)^{3/2}-\left(\frac{r_1+r_2-s}{a}\right)^{3/2}\right],
$">|; 

$key = q/displaystyle{mitDelta}t=frac{T}{2pi}left[(eta-sineta)-(xi-sinxi)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img915.png"
 ALT="$\displaystyle {\mit\Delta} t =\frac{T}{2\pi}\left[ (\eta -\sin\eta) -(\xi - \sin\xi)\right],
$">|; 

$key = q/displaystyle{mitDelta}t=frac{T}{2pi}left[(sinheta-eta)-(sinhxi-xi)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img921.png"
 ALT="$\displaystyle {\mit\Delta} t =\frac{T}{2\pi}\left[ (\sinh\eta-\eta) -(\sinh\xi-\xi)\right],
$">|; 

$key = q/displaystyle{mitDelta}{bfP}'={bfP}_{rmabs}'-{bfP}_{rmem}'={bfP}_{rmabs}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img2804.png"
 ALT="$\displaystyle {\mit\Delta}{\bf P}' = {\bf P}_{\rm abs}'-{\bf P}_{\rm em}'= {\bf P}_{\rm abs}'.$">|; 

$key = q/displaystyle{mitDelta}{bfP}simeqE,N,Aleft(1-frac{v_r}{c}right){bfe}_r-E,N,A,frac{{bfv}}{c}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.29ex; vertical-align: -1.68ex; " SRC="|."$dir".q|img2812.png"
 ALT="$\displaystyle {\mit\Delta} {\bf P} \simeq E N A\left(1-\frac{v_r}{c}\right) {\bf e}_r - E N A \frac{{\bf v}}{c}.$">|; 

$key = q/displaystyle{mitDelta}{bfP}simeq{mitDelta}{bfP}'+frac{{mitDelta}{calE}'}{c^{,2}},{bfv}={mitDelta}{bfP}'={bfP}_{rmabs}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2805.png"
 ALT="$\displaystyle {\mit\Delta} {\bf P} \simeq {\mit\Delta} {\bf P}' + \frac{{\mit\Delta}{\cal E}'}{c^{ 2}} {\bf v} = {\mit\Delta} {\bf P}' = {\bf P}_{\rm abs}'.$">|; 

$key = q/displaystyle{mitDelta}{calE}'={calE}_{rmabs}'-{calE}_{rmem}'=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.70ex; " SRC="|."$dir".q|img2803.png"
 ALT="$\displaystyle {\mit\Delta}{\cal E}' = {\cal E}_{\rm abs}'-{\cal E}_{\rm em}'= 0,$">|; 

$key = q/displaystyle{mitGamma}=frac{A-2pmsqrt{A,(9,A-8)}}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.85ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2293.png"
 ALT="$\displaystyle {\mit\Gamma} = \frac{A-2\pm\sqrt{A (9 A-8)}}{2},$">|; 

$key = q/displaystyle{mitGamma}^{,2}+(2-A),{mitGamma}+(1-A),(1+2,A)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2291.png"
 ALT="$\displaystyle {\mit\Gamma}^{ 2} + (2-A) {\mit\Gamma} + (1-A) (1+2 A) = 0,$">|; 

$key = q/displaystyle{mitGamma}^{,2}+{mitGamma}+frac{27}{4},mu_2,(1-mu_2)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2305.png"
 ALT="$\displaystyle {\mit\Gamma}^{ 2} + {\mit\Gamma} + \frac{27}{4} \mu_2 (1-\mu_2) = 0$">|; 

$key = q/displaystyle{mitI}equivsum_{i=1,N}m_i,r_i^{,2},sin^2psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1689.png"
 ALT="$\displaystyle {\mit I} \equiv \sum_{i=1,N} m_i r_i^{ 2} \sin^2\psi$">|; 

$key = q/displaystyle{mitOmega}(t)={mitOmega}_0+skew{5}dot{mitOmega},,t,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4553.png"
 ALT="$\displaystyle {\mit\Omega}(t) = {\mit\Omega}_0+\skew{5}\dot{\mit\Omega}  t,$">|; 

$key = q/displaystyle{mitOmega}=0.003284,omega,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1653.png"
 ALT="$\displaystyle {\mit\Omega} = 0.003284 \omega,$">|; 

$key = q/displaystyle{mitOmega}=frac{2pi}{23^{rmh},56^{rmm},04^{rms}}=7.2921times10^{-5},{rmrad.,s}^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1087.png"
 ALT="$\displaystyle {\mit\Omega} = \frac{2\pi}{23^{\rm h} 56^{\rm m} 04^{\rm s}}=7.2921\times 10^{-5} {\rm rad. s}^{-1}.$">|; 

$key = q/displaystyle{mitOmega}=omega,cosalphaleft(frac{{calI}_parallel}{{calI}_perp}-1right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.41ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1592.png"
 ALT="$\displaystyle {\mit\Omega} =\omega \cos\alpha \left(\frac{{\cal I}_\parallel}{{\cal I}_\perp}-1\right).$">|; 

$key = q/displaystyle{mitOmega}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3436.png"
 ALT="$\displaystyle {\mit\Omega}_1$">|; 

$key = q/displaystyle{mitOmega}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3438.png"
 ALT="$\displaystyle {\mit\Omega}_2$">|; 

$key = q/displaystyle{mitOmega}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3440.png"
 ALT="$\displaystyle {\mit\Omega}_3$">|; 

$key = q/displaystyle{mitOmega}_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3442.png"
 ALT="$\displaystyle {\mit\Omega}_4$">|; 

$key = q/displaystyle{mitOmega}_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3444.png"
 ALT="$\displaystyle {\mit\Omega}_5$">|; 

$key = q/displaystyle{mitOmega}_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1794.png"
 ALT="$\displaystyle {\mit\Omega}_\phi$">|; 

$key = q/displaystyle{mitOmega}_phi=frac{3}{2},frac{skew{3}tilde{epsilon},n_s^{,2}}{omega},costheta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.64ex; " SRC="|."$dir".q|img1734.png"
 ALT="$\displaystyle {\mit\Omega}_\phi = \frac{3}{2} \frac{\skew{3}\tilde{\epsilon} n_s^{ 2}}{\omega} \cos\theta,$">|; 

$key = q/displaystyle{mitPhi}'=-frac{G,m'}{a'}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img1224.png"
 ALT="$\displaystyle {\mit\Phi}' = -\frac{G m'}{a'}.$">|; 

$key = q/displaystyle{mitPhi}'simeq-frac{G,m'}{a}left[1+frac{r}{a},P_1(costheta)+frac{r^{,2}}{a^{,2}},P_2(costheta)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img1233.png"
 ALT="$\displaystyle {\mit\Phi}' \simeq - \frac{G m'}{a}\left[1+ \frac{r}{a} P_1(\cos\theta) + \frac{r^{ 2}}{a^{ 2}} P_2(\cos\theta)\right],$">|; 

$key = q/displaystyle{mitPhi}(R'_theta,theta)+chi(R'_theta,theta)=c.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img1267.png"
 ALT="$\displaystyle {\mit\Phi}(R'_\theta,\theta) + \chi(R'_\theta,\theta) = c.$">|; 

$key = q/displaystyle{mitPhi}(R_theta,theta)+chi(R_theta,theta)=c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1163.png"
 ALT="$\displaystyle {\mit\Phi}(R_\theta,\theta)+\chi(R_\theta,\theta) = c,$">|; 

$key = q/displaystyle{mitPhi}(R_theta,theta)=-frac{G,M}{R_theta}+J_2,frac{G,M,R^{,2}}{R_theta^{,3}},P_2(costheta)+{calO}(epsilon^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.69ex; vertical-align: -2.45ex; " SRC="|."$dir".q|img487.png"
 ALT="$\displaystyle {\mit\Phi}(R_\theta, \theta) = - \frac{G M}{R_\theta} +J_2 \frac{G M R^{ 2}}{R_\theta^{ 3}} P_2(\cos\theta) + {\cal O}(\epsilon^2),$">|; 

$key = q/displaystyle{mitPhi}(R_theta,theta)simeq-frac{G,M}{R}left[1+frac{4}{15},epsilon,P_2(costheta)+{calO}(epsilon^2)right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img490.png"
 ALT="$\displaystyle {\mit\Phi}(R_\theta,\theta) \simeq - \frac{G M}{R} \left[1+\frac{4}{15} \epsilon P_2(\cos\theta) + {\cal O}(\epsilon^2)\right].$">|; 

$key = q/displaystyle{mitPhi}(R_theta,theta)simeq-frac{G,M}{R}left[1+left(frac{2}{3},epsilon-J_2right)P_2(costheta)+{calO}(epsilon^2)right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img488.png"
 ALT="$\displaystyle {\mit\Phi}(R_\theta,\theta) \simeq - \frac{G M}{R} \left[1+\left(\frac{2}{3} \epsilon-J_2\right)P_2(\cos\theta) + {\cal O}(\epsilon^2)\right],$">|; 

$key = q/displaystyle{mitPhi}(a,theta)={mitPhi}_0'(a)+{mitPhi}_2'(a),P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img4347.png"
 ALT="$\displaystyle {\mit\Phi}(a,\theta)= {\mit\Phi}_0'(a)+{\mit\Phi}_2'(a) P_2(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r)=-frac{2pi,G,gamma}{3},(3,R^{,2}-r^{,2})=-G,M,frac{(3,R^{,2}-r^{,2})}{2,R^{,3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img455.png"
 ALT="$\displaystyle {\mit\Phi}(r) = - \frac{2\pi G \gamma}{3} (3 R^{ 2}-r^{ 2}) = - G M \frac{(3 R^{ 2}-r^{ 2})}{2 R^{ 3}}$">|; 

$key = q/displaystyle{mitPhi}(r)=-frac{4pi,G,gamma}{3},frac{R^{,3}}{r}=-frac{G,M}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img456.png"
 ALT="$\displaystyle {\mit\Phi}(r) = -\frac{4\pi G \gamma}{3} \frac{R^{ 3}}{r} = - \frac{G M}{r}$">|; 

$key = q/displaystyle{mitPhi}(r)=-frac{G,M}{a}sum_{n=0,infty}[P_n(0)]^2left(frac{a}{r}right)^{n+1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.91ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img514.png"
 ALT="$\displaystyle {\mit\Phi}(r) = - \frac{G M}{a}\sum_{n=0,\infty} [P_n(0)]^2\left(\frac{a}{r}\right)^{n+1}.$">|; 

$key = q/displaystyle{mitPhi}(r)=-frac{G,M}{a}sum_{n=0,infty}[P_n(0)]^2left(frac{r}{a}right)^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img526.png"
 ALT="$\displaystyle {\mit\Phi}(r) = - \frac{G M}{a}\sum_{n=0,\infty} [P_n(0)]^2\left(\frac{r}{a}\right)^{n},$">|; 

$key = q/displaystyle{mitPhi}(r)=-frac{G,M}{r}-frac{G,M,h^{,2}}{c^{,2},r^{,3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.63ex; " SRC="|."$dir".q|img2887.png"
 ALT="$\displaystyle {\mit\Phi}(r) = -\frac{G M}{r}-\frac{G M h^{ 2}}{c^{ 2} r^{ 3}},
$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-2pi,Gint_0^inftyint_0^pir'^{,2},rho(r',theta'),sintheta',langle|{bfr}-{bfr}'|^{-1}rangle,dtheta',dr',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.13ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img395.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = - 2\pi G\int_0^\infty\int_0^\pi
r'^{ 2}\...
...a') \sin\theta' \langle\vert{\bf r}-{\bf r}'\vert^{-1}\rangle d\theta' dr',$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-Gint_0^inftyint_0^piint_0^{2pi}frac{r'^{,2},rho(r',theta'),sintheta'}{|{bfr}-{bfr}'|},dphi',dtheta',dr',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img392.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = - G\int_0^\infty\int_0^\pi\int_0^{2\pi}
\f...
...o(r',\theta') \sin\theta'}{\vert{\bf r}-{\bf r}'\vert} d\phi' d\theta' dr',$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-frac{G,M}{r}+J_2,frac{G,M,R^{,2}}{r^{,3}},P_2(costheta)+{calO}(epsilon^2),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img485.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = - \frac{G M}{r} +J_2 \frac{G M R^{ 2}}{r^{ 3}} P_2(\cos\theta) + {\cal O}(\epsilon^2),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-frac{G,M}{r}+frac{2}{5},epsilon,frac{G,M,R^{,2}}{r^{,3}},P_2(costheta)+{calO}(epsilon^2).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img484.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = - \frac{G M}{r} +\frac{2}{5} \epsilon \frac{G M R^{ 2}}{r^{ 3}} P_2(\cos\theta) + {\cal O}(\epsilon^2).$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-frac{G,M}{r}left(1-sum_{n=1,infty}J_n,frac{R^{,n}}{r^{,n}},P_n(costheta)right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img505.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta)= -\frac{G M}{r} \left(1-\sum_{n=1,\infty}J_n \frac{R^{ n}}{r^{ n}} P_n(\cos\theta)\right),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-frac{G,m}{r}+frac{2}{5},epsilon,frac{G,m,R^{,2}}{r^{,3}},P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1265.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = -\frac{G m}{r} + \frac{2}{5} \epsilon \frac{G m R^{ 2}}{r^{ 3}} P_2(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=-frac{G,m}{r}+frac{epsilon}{5},frac{G,m,R^{,2}}{r^{,3}}left[3,cos^2(theta-delta)-1right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.91ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img1280.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = -\frac{G m}{r} +\frac{\epsilon}{5} \frac{G m R^{ 2}}{r^{ 3}}
\left[3 \cos^2(\theta-\delta)-1\right],$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=frac{G,M}{R}sum_{n=0,infty}J_nleft(frac{R}{r}right)^{n+1}P_n(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.13ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img473.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = \frac{G M}{R}\sum_{n=0,\infty} J_n\left(\frac{R}{r}\right)^{n+1}P_n(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)=sum_{n=0,infty}{mitPhi}_n(r),P_n(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.02ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img438.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) = \sum_{n=0,\infty} {\mit\Phi}_n(r) P_n(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)={mitPhi}_0(r)+{mitPhi}_2(r),P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4342.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta)={\mit\Phi}_0(r)+ {\mit\Phi}_2(r) P_2(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)simeq-frac{G,M}{r}+J_2,frac{G,M,R^{,2}}{r^{,3}},P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1162.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) \simeq - \frac{G M}{r} +J_2 \frac{G M R^{ 2}}{r^{ 3}} P_2(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)simeq-frac{G,M}{r}+frac{G,({calI}_parallel-{calI}_perp)}{r^{,3}},P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1669.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta) \simeq - \frac{G M}{r} + \frac{G ({\cal I}_\parallel - {\cal I}_\perp)}{r^{ 3}} P_2(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}(r,theta)simeq-frac{G,M}{r}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.52ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img508.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta)\simeq -\frac{G M}{r}.$">|; 

$key = q/displaystyle{mitPhi}(r,theta,phi)={mitPhi}_0(r)+{mitPhi}_2(r,theta,phi),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4233.png"
 ALT="$\displaystyle {\mit\Phi}(r,\theta,\phi) = {\mit\Phi}_0(r) + {\mit\Phi}_2(r,\theta,\phi),$">|; 

$key = q/displaystyle{mitPhi}(r,vartheta)simeq-frac{G,M}{r}+J_2,frac{G,M,R^{,2}}{r^{,3}},P_2(cosvartheta).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.80ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2685.png"
 ALT="$\displaystyle {\mit\Phi}(r,\vartheta) \simeq - \frac{G M}{r} +J_2  \frac{G M R^{ 2}}{r^{ 3}} P_2(\cos\vartheta).$">|; 

$key = q/displaystyle{mitPhi}(r,vartheta)simeq-frac{G,M}{r}+frac{G,({calI}_parallel-{calI}_perp)}{r^{,3}},P_2(cosvartheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img2681.png"
 ALT="$\displaystyle {\mit\Phi}(r,\vartheta) \simeq - \frac{G M}{r} + \frac{G ({\cal I}_\parallel-{\cal I}_\perp)}{r^{ 3}} P_2(\cos\vartheta),$">|; 

$key = q/displaystyle{mitPhi}({bfr})=-Gintfrac{rho({bfr}')}{|{bfr}'-{bfr}|},d^{,3}{bfr}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img364.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r}) = - G\int\frac{\rho({\bf r}')}{\vert{\bf r}'-{\bf r}\vert} d^{ 3}{\bf r}',$">|; 

$key = q/displaystyle{mitPhi}({bfr})=-Gintfrac{rho({bfr}')}{|{bfr}'-{bfr}|},d^{,3}{bfr}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img382.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r}) = -G\int \frac{\rho({\bf r}')}
{\vert{\bf r}' - {\bf r}\vert} d^{ 3}{\bf r}'$">|; 

$key = q/displaystyle{mitPhi}({bfr})=-Gsum_{i=1,N}frac{m_i}{|{bfr}_i-{bfr}|},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.24ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1678.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r}) = -G\sum_{i=1,N}\frac{m_i}{\vert{\bf r}_i-{\bf r}\vert},$">|; 

$key = q/displaystyle{mitPhi}({bfr})=-frac{G,m'}{|{bfr}'-{bfr}|}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img371.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r})= - \frac{G m'}{\vert{\bf r}' - {\bf r}\vert}.$">|; 

$key = q/displaystyle{mitPhi}({bfr})=-frac{G,m'}{|{bfr}'-{bfr}|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -1.98ex; " SRC="|."$dir".q|img357.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r})= - \frac{G m'}{\vert{\bf r}'-{\bf r}\vert}$">|; 

$key = q/displaystyle{mitPhi}({bfr})=-frac{G}{r}sum_{i=1,N}m_ileft(1-2,frac{r_i}{r},cospsi+frac{r_i^{,2}}{r^{,2}}right)^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.64ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1679.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r})=-\frac{G}{r}\sum_{i=1,N}m_i\left(1-2 \frac{r_i}{r} \cos\psi + \frac{r_i^{ 2}}{r^{ 2}}\right)^{-1/2},$">|; 

$key = q/displaystyle{mitPhi}({bfr})simeq-frac{G,M}{r}+frac{G,({calI}_parallel-{calI}_perp)}{r^{,3}},P_2(costheta),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.63ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1697.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r}) \simeq - \frac{G M}{r} + \frac{G ({\cal I}_\parallel - {\cal I}_\perp)}{r^{ 3}} P_2(\cos\theta),$">|; 

$key = q/displaystyle{mitPhi}({bfr})simeq-frac{G,M}{r}-frac{G,({calI}_{xx}+{calI}_{yy}+{calI}_{zz}-3,{calI})}{2,r^{,3}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.74ex; vertical-align: -1.62ex; " SRC="|."$dir".q|img1690.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r}) \simeq -\frac{G M}{r} - \frac{G ({\cal I}_{xx}+{\cal I}_{yy}+{\cal I}_{zz}-3 {\cal I})}{2 r^{ 3}}.$">|; 

$key = q/displaystyle{mitPhi}({bfr})simeq-frac{G,M}{r}-frac{G}{2,r^{,3}}sum_{i=1,N}m_i,r_i^{,2},(2-3,sin^2psi).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.74ex; vertical-align: -2.83ex; " SRC="|."$dir".q|img1685.png"
 ALT="$\displaystyle {\mit\Phi}({\bf r}) \simeq - \frac{G M}{r} - \frac{G}{2 r^{ 3}}\sum_{i=1,N} m_i r_i^{ 2} (2-3 \sin^2\psi).$">|; 

$key = q/displaystyle{mitPhi}_0'(a)=-4pi,Gleft[frac{1}{a}int_0^arho(a'),a'^{,2},da'+int_a^inftyrho(a'),a',da'right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4348.png"
 ALT="$\displaystyle {\mit\Phi}_0'(a)= -4\pi G\left[\frac{1}{a}\int_0^a\rho(a') a'^{ 2} da'+\int_a^\infty \rho(a') a' da'\right],$">|; 

$key = q/displaystyle{mitPhi}_0(r)=-4pi,Gleft[frac{1}{r}int_0^rrho(r'),r'^{,2},dr'+int_r^inftyrho(r'),r',dr'right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img4343.png"
 ALT="$\displaystyle {\mit\Phi}_0(r)=-4\pi G\left[\frac{1}{r}\int_0^r\rho(r') r'^{ 2} dr'+\int_r^\infty \rho(r') r' dr'\right],$">|; 

$key = q/displaystyle{mitPhi}_0(r)=-frac{4pi,G,gamma}{r}int_0^Rr'^{,2},dr';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img452.png"
 ALT="$\displaystyle {\mit\Phi}_0(r) = - \frac{4\pi G \gamma}{r}\int_0^R r'^{ 2} dr'$">|; 

$key = q/displaystyle{mitPhi}_0(r)=-frac{4pi,G,gamma}{r}int_0^rr'^{,2},dr'-4pi,G,gammaint_r^Rr',dr';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img450.png"
 ALT="$\displaystyle {\mit\Phi}_0(r) = -\frac{4\pi G \gamma}{r}\int_0^r r'^{ 2} dr' - 4\pi G \gamma
\int_r^R r' dr'$">|; 

$key = q/displaystyle{mitPhi}_0(r)=-frac{G}{r}int_0^R4pi,r'^{,2},rho_0(r'),dr'=-frac{G,M}{r};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; vertical-align: -2.07ex; " SRC="|."$dir".q|img461.png"
 ALT="$\displaystyle {\mit\Phi}_0(r) = - \frac{G}{r}\int_0^R 4\pi r'^{ 2} \rho_0(r') dr' = -\frac{G M}{r}$">|; 

$key = q/displaystyle{mitPhi}_0(r>a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4249.png"
 ALT="$\displaystyle {\mit\Phi}_0(r&gt;a)$">|; 

$key = q/displaystyle{mitPhi}_0(rleqa);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4247.png"
 ALT="$\displaystyle {\mit\Phi}_0(r\leq a)$">|; 

$key = q/displaystyle{mitPhi}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4237.png"
 ALT="$\displaystyle {\mit\Phi}_0$">|; 

$key = q/displaystyle{mitPhi}_2'(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img4349.png"
 ALT="$\displaystyle {\mit\Phi}_2'(a)$">|; 

$key = q/displaystyle{mitPhi}_2(r>a,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4253.png"
 ALT="$\displaystyle {\mit\Phi}_2(r&gt;a,\theta,\phi)$">|; 

$key = q/displaystyle{mitPhi}_2(rleqa,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4251.png"
 ALT="$\displaystyle {\mit\Phi}_2(r\leq a,\theta,\phi)$">|; 

$key = q/displaystyle{mitPhi}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4239.png"
 ALT="$\displaystyle {\mit\Phi}_2$">|; 

$key = q/displaystyle{mitPhi}_i=-Gsum_{j=1,N}^{jneqi}frac{m_j}{|{bfr}_j-{bfr}_i|};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.69ex; vertical-align: -2.93ex; " SRC="|."$dir".q|img380.png"
 ALT="$\displaystyle {\mit\Phi}_i =- G\sum_{j=1,N}^{j\neq i}
\frac{m_j}{\vert{\bf r}_j - {\bf r}_i\vert}$">|; 

$key = q/displaystyle{mitPhi}_n(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img439.png"
 ALT="$\displaystyle {\mit\Phi}_n(r)$">|; 

$key = q/displaystyle{rme}^x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3808.png"
 ALT="$\displaystyle {\rm e}^x$">|; 

$key = q/displaystyle{rme}^{,{rmi},E}=sum_{n=-infty,infty}A_n,{rme}^{,{rmi},n,{calM}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img4040.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} E} = \sum_{n=-\infty,\infty} A_n {\rm e}^{ {\rm i} n {\cal M}},$">|; 

$key = q/displaystyle{rme}^{,{rmi},x,sinphi}equivsum_{n=-infty,infty}J_n(x),{rme}^{,{rmi},n,phi}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 4.96ex; vertical-align: -2.80ex; " SRC="|."$dir".q|img4024.png"
 ALT="$\displaystyle {\rm e}^{ {\rm i} x \sin\phi}\equiv \sum_{n=-\infty,\infty}J_n(x) {\rm e}^{ {\rm i} n \phi}.$">|; 

$key = q/displaystyle|I_{ik}|>sum_{l=1,8}^{lneqk,lneq5}|I_{il}|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.52ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2613.png"
 ALT="$\displaystyle \vert I_{ik}\vert&gt;\sum_{l=1,8}^{l\neq k, l\neq 5} \vert I_{il}\vert.$">|; 

$key = q/displaystyle|e_{ik}|>sum_{l=1,8}^{lneqk}|e_{il}|.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 6.47ex; vertical-align: -2.84ex; " SRC="|."$dir".q|img2608.png"
 ALT="$\displaystyle \vert e_{ik}\vert&gt;\sum_{l=1,8}^{l\neq k} \vert e_{il}\vert.$">|; 

$key = q/displaystyle|{bfA}-lambda,{bf1}|=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4077.png"
 ALT="$\displaystyle \vert{\bf A} - \lambda {\bf 1}\vert = 0,$">|; 

$key = q/displaystyle|{bfa}|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3923.png"
 ALT="$\displaystyle \vert{\bf a}\vert$">|; 

$key = q/displaystyle|{bfr}'-{bfr}|^{-1}=(r^{,2}-2,r,r',F+r'^{,2})^{-1slash2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img400.png"
 ALT="$\displaystyle \vert{\bf r}'-{\bf r}\vert^{-1} = (r^{ 2}-2 r r' F + r'^{ 2})^{-1/2}.$">|; 

$key = q/displaystyle|{bfr}'-{bfr}|^{-1}=(r^{,2}-2,{bfr}cdot{bfr}'+r'^{,2})^{-1slash2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img397.png"
 ALT="$\displaystyle \vert{\bf r}'-{\bf r}\vert^{-1} = (r^{ 2}-2 {\bf r}\cdot{\bf r}' + r'^{ 2})^{-1/2},$">|; 

$key = q/dm=rho,d^{,3}{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1518.png"
 ALT="$dm = \rho d^{ 3}{\bf r}$">|; 

$key = q/dot{E}<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1307.png"
 ALT="$\dot{E}&lt;0$">|; 

$key = q/dot{X};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4670.png"
 ALT="$\dot{X}$">|; 

$key = q/dot{X}_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4698.png"
 ALT="$\dot{X}_l$">|; 

$key = q/dot{Z}=dot{z}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img4745.png"
 ALT="$\dot{Z} = \dot{z}'$">|; 

$key = q/dot{bfh}={bfr}timesskew{2}ddot{bfr}={bfr}timesnabla{calR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img4142.png"
 ALT="$\dot{\bf h} = {\bf r}\times \skew{2}\ddot{\bf r}= {\bf r}\times \nabla{\cal R}$">|; 

$key = q/dot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2731.png"
 ALT="$\dot{\bf r}$">|; 

$key = q/dot{bfr}=ddot{bfr}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2176.png"
 ALT="$\dot{\bf r} =\ddot{\bf r} = {\bf0}$">|; 

$key = q/dot{bfx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2325.png"
 ALT="$\dot{\bf x}$">|; 

$key = q/dot{phantomomega}=dslashdt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1569.png"
 ALT="$\dot{\phantom\omega}=d/dt'$">|; 

$key = q/dot{phantomr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.28ex; vertical-align: 1.04ex; " SRC="|."$dir".q|img595.png"
 ALT="$\dot{\phantom r}$">|; 

$key = q/dot{phantom{X}}equivdslashdT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3118.png"
 ALT="$\dot{\phantom{X}}\equiv d/dT$">|; 

$key = q/dot{phantom{r}}equivdslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img334.png"
 ALT="$\dot{\phantom{r}}\equiv d/dt$">|; 

$key = q/dot{phantom{x}}equivdslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img328.png"
 ALT="$\dot{\phantom{x}}\equiv d/dt$">|; 

$key = q/dot{varpi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1028.png"
 ALT="$\dot{\varpi}$">|; 

$key = q/dot{varpi}_{obs}('',{rmyr}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img999.png"
 ALT="$\dot{\varpi}_{obs}('' {\rm yr}^{-1})$">|; 

$key = q/dot{varpi}_{th}('',{rmyr}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1000.png"
 ALT="$\dot{\varpi}_{th}('' {\rm yr}^{-1})$">|; 

$key = q/dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img326.png"
 ALT="$\dot{x}$">|; 

$key = q/dot{x}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img327.png"
 ALT="$\dot{x}^{ 2}$">|; 

$key = q/dot{z}'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img4754.png"
 ALT="$\dot{z}''$">|; 

$key = q/dslashdalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4977.png"
 ALT="$d/d\alpha$">|; 

$key = q/dslashdt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1068.png"
 ALT="$d/dt'$">|; 

$key = q/dslashdt({bfr}slashr)={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img869.png"
 ALT="$d/dt({\bf r}/r)={\bf0}$">|; 

$key = q/dslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img596.png"
 ALT="$d/dt$">|; 

$key = q/dslashdtllomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1787.png"
 ALT="$d/dt\ll \omega$">|; 

$key = q/dslashdtneqdslashdt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1069.png"
 ALT="$d/dt\neq d/dt'$">|; 

$key = q/dx;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3949.png"
 ALT="$dx$">|; 

$key = q/d{Omega}=sintheta,dtheta,dphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4482.png"
 ALT="$d{\Omega}=\sin\theta d\theta d\phi$">|; 

$key = q/d{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img139.png"
 ALT="$d{\bf r}$">|; 

$key = q/d{bfr}slashdt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1070.png"
 ALT="$d{\bf r}/dt'$">|; 

$key = q/d{calM}'=(1-e'^{,2})^{-1slash2},(r'slasha')^2,dtheta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4198.png"
 ALT="$d{\cal M}'= (1-e'^{ 2})^{-1/2} (r'/a')^2 d\theta'$">|; 

$key = q/d{calM}'=n',dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4196.png"
 ALT="$d{\cal M}'=n' dt$">|; 

$key = q/d{calM}=n,dt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4195.png"
 ALT="$d{\cal M} = n dt$">|; 

$key = q/d{calM}slashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2724.png"
 ALT="$d{\cal M}/dt$">|; 

$key = q/d{calM}slashdt=n+langleskew{5}dot{calM}_0rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2834.png"
 ALT="$d{\cal M}/dt = n+ \langle\skew{5}\dot{\cal M}_0\rangle$">|; 

$key = q/d{calM}slashdt=n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1861.png"
 ALT="$d{\cal M}/dt = n$">|; 

$key = q/e';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2133.png"
 ALT="$e'$">|; 

$key = q/e'=0.016711;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3035.png"
 ALT="$e'=0.016711$">|; 

$key = q/e'^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3668.png"
 ALT="$e'^{ 2}$">|; 

$key = q/e,Irightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4876.png"
 ALT="$e, I\rightarrow 0$">|; 

$key = q/e,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img642.png"
 ALT="$e a$">|; 

$key = q/e,coshphi=1-n,(1-e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img929.png"
 ALT="$e \cosh\phi = 1-n (1-e)$">|; 

$key = q/e,gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1918.png"
 ALT="$e \gamma$">|; 

$key = q/e,hslash[r_p,(1+e)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img885.png"
 ALT="$e h/[r_p (1+e)]$">|; 

$key = q/e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img10.png"
 ALT="$e$">|; 

$key = q/e<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img627.png"
 ALT="$e&lt;1$">|; 

$key = q/e=(h^{,2}+k^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2677.png"
 ALT="$e=(h^{ 2}+k^{ 2})^{1/2}$">|; 

$key = q/e=0.0068;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1018.png"
 ALT="$e=0.0068$">|; 

$key = q/e=0.0151;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img43.png"
 ALT="$e=0.0151$">|; 

$key = q/e=0.01673;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img819.png"
 ALT="$e=0.01673$">|; 

$key = q/e=0.05488;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3055.png"
 ALT="$e=0.05488$">|; 

$key = q/e=0.05;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img34.png"
 ALT="$e=0.05$">|; 

$key = q/e=0.123;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img45.png"
 ALT="$e=0.123$">|; 

$key = q/e=0.781;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2141.png"
 ALT="$e=0.781$">|; 

$key = q/e=0.800;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2144.png"
 ALT="$e=0.800$">|; 

$key = q/e=0.8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img863.png"
 ALT="$e=0.8$">|; 

$key = q/e=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img640.png"
 ALT="$e=0$">|; 

$key = q/e=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img628.png"
 ALT="$e=1$">|; 

$key = q/e=sec(phislash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2313.png"
 ALT="$e=\sec(\phi/2)$">|; 

$key = q/e>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img629.png"
 ALT="$e&gt;1$">|; 

$key = q/e^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3667.png"
 ALT="$e^{ 2}$">|; 

$key = q/e_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2907.png"
 ALT="$e_0$">|; 

$key = q/e_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2548.png"
 ALT="$e_i$">|; 

$key = q/e_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4585.png"
 ALT="$e_m$">|; 

$key = q/e_m=0.05488;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4599.png"
 ALT="$e_m=0.05488$">|; 

$key = q/e_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4580.png"
 ALT="$e_s$">|; 

$key = q/e_s=0.016711;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4598.png"
 ALT="$e_s=0.016711$">|; 

$key = q/e_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2001.png"
 ALT="$e_z$">|; 

$key = q/e_{ik};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2607.png"
 ALT="$e_{ik}$">|; 

$key = q/e_{il};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img72.png"
 ALT="$e_{il}$">|; 

$key = q/e_{rmfree};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2675.png"
 ALT="$e_{\rm free}$">|; 

$key = q/e_{rmmax};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2618.png"
 ALT="$e_{\rm max}$">|; 

$key = q/e_{rmmin};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2617.png"
 ALT="$e_{\rm min}$">|; 

$key = q/egeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img624.png"
 ALT="$e\geq 0$">|; 

$key = q/epsilon';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1268.png"
 ALT="$\epsilon'$">|; 

$key = q/epsilon'=m'slashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2885.png"
 ALT="$\epsilon'=m'/M$">|; 

$key = q/epsilon'=tilde{mu}'slashmu=m'slash(M+m)ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2434.png"
 ALT="$\epsilon'=\tilde{\mu}'/\mu=m'/(M+m)\ll 1$">|; 

$key = q/epsilon'lle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2512.png"
 ALT="$\epsilon'\ll e$">|; 

$key = q/epsilon(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4329.png"
 ALT="$\epsilon(a)$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img464.png"
 ALT="$\epsilon$">|; 

$key = q/epsilon<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img470.png"
 ALT="$\epsilon&lt;0$">|; 

$key = q/epsilon=-2.2times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1262.png"
 ALT="$\epsilon=-2.2\times 10^{-8}$">|; 

$key = q/epsilon=0.0649;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1205.png"
 ALT="$\epsilon=0.0649$">|; 

$key = q/epsilon=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img471.png"
 ALT="$\epsilon=0$">|; 

$key = q/epsilon=3.35times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1194.png"
 ALT="$\epsilon=3.35\times 10^{-3}$">|; 

$key = q/epsilon=mslashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2868.png"
 ALT="$\epsilon=m/M$">|; 

$key = q/epsilon=tilde{mu}slashmu'=mslash(M+m')ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2499.png"
 ALT="$\epsilon=\tilde{\mu}/\mu' = m/(M+m')\ll 1$">|; 

$key = q/epsilon>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img469.png"
 ALT="$\epsilon&gt;0$">|; 

$key = q/epsilon_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4439.png"
 ALT="$\epsilon_0$">|; 

$key = q/epsilon_0=epsilon(R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4404.png"
 ALT="$\epsilon_0=\epsilon(R)$">|; 

$key = q/equiv(omega_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1841.png"
 ALT="$\equiv (\omega_x$">|; 

$key = q/erightarrow1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img641.png"
 ALT="$e\rightarrow 1$">|; 

$key = q/erightarrowe,[1-(15slash8),m,cos(2,D)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3688.png"
 ALT="$e\rightarrow
e [1-(15/8) m \cos (2  D)]$">|; 

$key = q/eta(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4390.png"
 ALT="$\eta(a)$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1846.png"
 ALT="$\eta$">|; 

$key = q/eta=0.57;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4391.png"
 ALT="$\eta=0.57$">|; 

$key = q/eta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1926.png"
 ALT="$\eta=0$">|; 

$key = q/eta_0=0.58;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4425.png"
 ALT="$\eta_0=0.58$">|; 

$key = q/eta_0=1.12;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4434.png"
 ALT="$\eta_0=1.12$">|; 

$key = q/eta_0=eta(R);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4399.png"
 ALT="$\eta_0=\eta(R)$">|; 

$key = q/eta_o=deltalambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3738.png"
 ALT="$\eta_o=\delta\lambda$">|; 

$key = q/eta_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3739.png"
 ALT="$\eta_p$">|; 

$key = q/exp(,{rmi},x,sinphi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4023.png"
 ALT="$\exp( {\rm i} x \sin\phi)$">|; 

$key = q/f(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img967.png"
 ALT="$f(r)$">|; 

$key = q/f(r)=-a,r^{,-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1050.png"
 ALT="$f(r) = -a r^{ -3}$">|; 

$key = q/f(r)=-c,exp(-rslasha)slashr^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1048.png"
 ALT="$f(r) = -c \exp(-r/a)/r^{ 2}$">|; 

$key = q/f(r)=-c,r^{,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img982.png"
 ALT="$f(r) = -c r^{ n}$">|; 

$key = q/f(r)=-dVslashdr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img956.png"
 ALT="$f(r)=-dV/dr$">|; 

$key = q/f(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img192.png"
 ALT="$f(x)$">|; 

$key = q/f(x)=-c,x^{,-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img292.png"
 ALT="$f(x) = - c x^{ -2}$">|; 

$key = q/f(x)=-m,mu,(a^{,5}slashx^{,2})^{1slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img295.png"
 ALT="$f(x)=-m \mu (a^{ 5}/x^{ 2})^{1/3}$">|; 

$key = q/f(x_1,x_2,cdots,x_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img537.png"
 ALT="$f(x_1,x_2,\cdots,x_n)$">|; 

$key = q/f({bfr})=+nablaU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img144.png"
 ALT="$f({\bf r})=+\nabla U$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1020.png"
 ALT="$f$">|; 

$key = q/f<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img210.png"
 ALT="$f &lt;0$">|; 

$key = q/f^{(n)}(x)=d^{,n}f(x)slashdx^{,n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3803.png"
 ALT="$f^{(n)}(x)=d^{ n}f(x)/dx^{ n}$">|; 

$key = q/f_1,f_2,f_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1382.png"
 ALT="$f_1, f_2, f_3$">|; 

$key = q/f_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2624.png"
 ALT="$f_1$">|; 

$key = q/f_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4668.png"
 ALT="$f_2$">|; 

$key = q/f_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4669.png"
 ALT="$f_3$">|; 

$key = q/f_4,f_5,f_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1383.png"
 ALT="$f_4, f_5, f_6$">|; 

$key = q/f_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2600.png"
 ALT="$f_5$">|; 

$key = q/f_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2627.png"
 ALT="$f_6$">|; 

$key = q/f_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2629.png"
 ALT="$f_7$">|; 

$key = q/f_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2631.png"
 ALT="$f_8$">|; 

$key = q/f_i=-k_i,skew{3}dot{x}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1481.png"
 ALT="$f_i = -k_i \skew{3}\dot{x}_i$">|; 

$key = q/f_i=-left.d{mitPhi}_islashdrright|_{r=a_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img993.png"
 ALT="$f_i= - \left.d{\mit\Phi}_i/dr\right\vert _{r=a_i}$">|; 

$key = q/f_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1381.png"
 ALT="$f_j$">|; 

$key = q/f_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2616.png"
 ALT="$f_k$">|; 

$key = q/f_l('',{rmyr}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2594.png"
 ALT="$f_l('' {\rm yr}^{-1})$">|; 

$key = q/f_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2590.png"
 ALT="$f_l$">|; 

$key = q/f_{x_1}=cos(n,t),f_x+sin(n,t),f_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3074.png"
 ALT="$f_{x_1}=\cos(n t) f_x+\sin(n t) f_y$">|; 

$key = q/f_{y_1}=-sin(n,t),f_x+cos(n,t),f_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3075.png"
 ALT="$f_{y_1}=-\sin(n t) f_x+\cos(n t) f_y$">|; 

$key = q/f_{z_1}=f_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img3076.png"
 ALT="$f_{z_1}=f_z$">|; 

$key = q/g(r)=(4pislash3),G,gamma,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img494.png"
 ALT="$g(r)= (4\pi/3) G \gamma r$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img530.png"
 ALT="$g$">|; 

$key = q/g=G,MslashR^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4462.png"
 ALT="$g=G M/R^{ 2}$">|; 

$key = q/g_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2623.png"
 ALT="$g_1$">|; 

$key = q/g_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2625.png"
 ALT="$g_4$">|; 

$key = q/g_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2626.png"
 ALT="$g_5$">|; 

$key = q/g_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2628.png"
 ALT="$g_6$">|; 

$key = q/g_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2630.png"
 ALT="$g_8$">|; 

$key = q/g_9=2,g_5-g_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2634.png"
 ALT="$g_9=2 g_5-g_6$">|; 

$key = q/g_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2611.png"
 ALT="$g_k$">|; 

$key = q/g_l('',{rmyr}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2593.png"
 ALT="$g_l('' {\rm yr}^{-1})$">|; 

$key = q/g_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2589.png"
 ALT="$g_l$">|; 

$key = q/g_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img354.png"
 ALT="$g_y$">|; 

$key = q/g_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img355.png"
 ALT="$g_z$">|; 

$key = q/g_{10}=2,g_6-g_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2635.png"
 ALT="$g_{10}=2 g_6-g_5$">|; 

$key = q/gamma';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3659.png"
 ALT="$\gamma'$">|; 

$key = q/gamma'=0.053463;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3671.png"
 ALT="$\gamma' = 0.053463$">|; 

$key = q/gamma(theta,theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4203.png"
 ALT="$\gamma(\theta,\theta')$">|; 

$key = q/gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img446.png"
 ALT="$\gamma$">|; 

$key = q/gamma=(1-v^{,2}slashc^{,2})^{-1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2790.png"
 ALT="$\gamma=(1-v^{ 2}/c^{ 2})^{-1/2}$">|; 

$key = q/gamma=3.3times10^3,{rmm,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1313.png"
 ALT="$\gamma=3.3\times 10^3 {\rm m s}^{-1}$">|; 

$key = q/gamma=cslash(k,a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1047.png"
 ALT="$\gamma = c/(k a)$">|; 

$key = q/gamma=phi-n,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1948.png"
 ALT="$\gamma=\phi-n t$">|; 

$key = q/gamma=phi-ntmspace+thinmuskip{.1667em}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img48.png"
 ALT="$\gamma =\phi -n\tmspace +\thinmuskip {.1667em}t$">|; 

$key = q/gamma=phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1878.png"
 ALT="$\gamma=\phi$">|; 

$key = q/gamma_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1920.png"
 ALT="$\gamma_0$">|; 

$key = q/gamma_l(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2596.png"
 ALT="$\gamma_l(^\circ)$">|; 

$key = q/gamma_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2592.png"
 ALT="$\gamma_l$">|; 

$key = q/gamma_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1744.png"
 ALT="$\gamma_m$">|; 

$key = q/gamma_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1707.png"
 ALT="$\gamma_s$">|; 

$key = q/gammarightarrowgamma-(3slash8),m,sin(2,D);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3692.png"
 ALT="$\gamma\rightarrow \gamma - (3/8) m \sin (2  D)$">|; 

$key = q/gammasim3.5times10^3,{rmkg},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img491.png"
 ALT="$\gamma\sim
3.5\times 10^3 {\rm kg} {\rm m}^{-3}$">|; 

$key = q/gammasimeq5times10^3,{rmkg,m^{-3}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1176.png"
 ALT="$\gamma\simeq 5\times 10^3 {\rm kg m^{-3}}$">|; 

$key = q/gammasimeqleft[sqrt{(21slash8),mu_2}+{calO}(mu_2)right]omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2354.png"
 ALT="$\gamma\simeq \left[\sqrt{(21/8) \mu_2} + {\cal O}(\mu_2)\right]\omega $">|; 

$key = q/gsimeq(3slash4),epsilon',n,alpha^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2880.png"
 ALT="$g\simeq (3/4) \epsilon' n \alpha^{ 3}$">|; 

$key = q/gsimeq(3slash4),epsilon,n',alpha^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2883.png"
 ALT="$g\simeq (3/4) \epsilon n' \alpha^{ 2}$">|; 

$key = q/gsimeq9.82,{rmm,s}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1097.png"
 ALT="$g\simeq 9.82 {\rm m s}^{-2}$">|; 

$key = q/gslashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2061.png"
 ALT="$g/n$">|; 

$key = q/gslashn=4.0185times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2070.png"
 ALT="$g/n=4.0185\times 10^{-3}$">|; 

$key = q/h'(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2874.png"
 ALT="$h'(t)$">|; 

$key = q/h'(t)=skew{3}hat{e},',sin(g,t+beta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2862.png"
 ALT="$h'(t)=\skew{3}\hat{e} ' \sin(g t+\beta)$">|; 

$key = q/h';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2469.png"
 ALT="$h'$">|; 

$key = q/h'=e',sinvarpi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2858.png"
 ALT="$h'=e' \sin\varpi'$">|; 

$key = q/h'equivr'^{,2},skew{5}dot{theta}'=(1-e'^{,2})^{1slash2},n',a'^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4197.png"
 ALT="$h'\equiv r'^{ 2} \skew{5}\dot{\theta}'=(1-e'^{ 2})^{1/2} n' a'^{ 2}$">|; 

$key = q/h(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2872.png"
 ALT="$h(t)$">|; 

$key = q/h(t)=skew{3}hat{e},sin(g,t+beta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2860.png"
 ALT="$h(t)=\skew{3}\hat{e} \sin(g t+\beta)$">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img496.png"
 ALT="$h$">|; 

$key = q/h=!sqrt{G,M,r_p,(1+e)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.84ex; " SRC="|."$dir".q|img677.png"
 ALT="$h =\! \sqrt{G M r_p (1+e)}$">|; 

$key = q/h=381;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1333.png"
 ALT="$h=381$">|; 

$key = q/h=a-R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2918.png"
 ALT="$h=a-R$">|; 

$key = q/h=e,sinvarpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2430.png"
 ALT="$h=e \sin\varpi$">|; 

$key = q/h=r^{,2},skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img870.png"
 ALT="$h=r^{ 2} \skew{5}\dot{\theta}$">|; 

$key = q/h^{,2}=G,M,r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1026.png"
 ALT="$h^{ 2}=G M r$">|; 

$key = q/h^{,2}slash(R-h);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img528.png"
 ALT="$h^{ 2}/(R-h)$">|; 

$key = q/h^{,2}slash(c^{,2},r^{,2})ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1023.png"
 ALT="$h^{ 2}/(c^{ 2} r^{ 2})\ll 1$">|; 

$key = q/h_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4309.png"
 ALT="$h_2$">|; 

$key = q/h_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img4464.png"
 ALT="$h_2=0$">|; 

$key = q/h_2=5slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4463.png"
 ALT="$h_2=5/2$">|; 

$key = q/h_2simeq0.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1258.png"
 ALT="$h_2\simeq 0.6$">|; 

$key = q/h_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2562.png"
 ALT="$h_i$">|; 

$key = q/h_i=e_i,sinvarpi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2552.png"
 ALT="$h_i=e_i \sin\varpi_i$">|; 

$key = q/hequivr^{,2},skew{5}dot{theta}=(1-e^{,2})^{1slash2},n,a^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2710.png"
 ALT="$h\equiv r^{ 2} \skew{5}\dot{\theta}=(1-e^{ 2})^{1/2} n a^{ 2}$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img150.png"
 ALT="$i$">|; 

$key = q/i=1,3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1544.png"
 ALT="$i=1, 3$">|; 

$key = q/i=1,5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2226.png"
 ALT="$i=1,5$">|; 

$key = q/i=1,8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img990.png"
 ALT="$i=1,8$">|; 

$key = q/i=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img3744.png"
 ALT="$i=1,$">|; 

$key = q/i=1,N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img358.png"
 ALT="$i=1, N$">|; 

$key = q/i=1,{calF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img1370.png"
 ALT="$i=1,{\cal F}$">|; 

$key = q/i=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2605.png"
 ALT="$i=1$">|; 

$key = q/includegraphics[height=1.25in]{Chapter05slashfig5_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="129" STYLE=""
 SRC="|."$dir".q|img1216.png"
 ALT="\includegraphics[height=1.25in]{Chapter05/fig5_07.eps}">;WIDTH="457" HEIGHT="129"|; 

$key = q/includegraphics[height=1.2in]{Chapter05slashfig5_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="136" STYLE=""
 SRC="|."$dir".q|img1245.png"
 ALT="\includegraphics[height=1.2in]{Chapter05/fig5_09.eps}">;WIDTH="527" HEIGHT="136"|; 

$key = q/includegraphics[height=1.5in]{Chapter03slashfig3_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="169" STYLE=""
 SRC="|."$dir".q|img608.png"
 ALT="\includegraphics[height=1.5in]{Chapter03/fig3_02.eps}">;WIDTH="411" HEIGHT="169"|; 

$key = q/includegraphics[height=1.75in]{AppendixAslashfigA_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="192" STYLE=""
 SRC="|."$dir".q|img3959.png"
 ALT="\includegraphics[height=1.75in]{AppendixA/figA_01.eps}">;WIDTH="231" HEIGHT="192"|; 

$key = q/includegraphics[height=1.75in]{Chapter03slashfig3_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="200" STYLE=""
 SRC="|."$dir".q|img643.png"
 ALT="\includegraphics[height=1.75in]{Chapter03/fig3_03.eps}">;WIDTH="476" HEIGHT="200"|; 

$key = q/includegraphics[height=1.75in]{Chapter05slashfig5_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="198" STYLE=""
 SRC="|."$dir".q|img1279.png"
 ALT="\includegraphics[height=1.75in]{Chapter05/fig5_10.eps}">;WIDTH="528" HEIGHT="198"|; 

$key = q/includegraphics[height=1.75in]{Chapter06slashfig6_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="196" STYLE=""
 SRC="|."$dir".q|img1484.png"
 ALT="\includegraphics[height=1.75in]{Chapter06/fig6_01.eps}">;WIDTH="243" HEIGHT="196"|; 

$key = q/includegraphics[height=1in]{Chapter05slashfig5_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="107" STYLE=""
 SRC="|."$dir".q|img1211.png"
 ALT="\includegraphics[height=1in]{Chapter05/fig5_06.eps}">;WIDTH="449" HEIGHT="107"|; 

$key = q/includegraphics[height=2.25in]{AppendixAslashfigA_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="365" HEIGHT="252" STYLE=""
 SRC="|."$dir".q|img3984.png"
 ALT="\includegraphics[height=2.25in]{AppendixA/figA_04.eps}">;WIDTH="365" HEIGHT="252"|; 

$key = q/includegraphics[height=2.25in]{AppendixAslashfigA_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="257" STYLE=""
 SRC="|."$dir".q|img3990.png"
 ALT="\includegraphics[height=2.25in]{AppendixA/figA_05.eps}">;WIDTH="322" HEIGHT="257"|; 

$key = q/includegraphics[height=2.25in]{AppendixAslashfigA_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="255" STYLE=""
 SRC="|."$dir".q|img4003.png"
 ALT="\includegraphics[height=2.25in]{AppendixA/figA_06.eps}">;WIDTH="230" HEIGHT="255"|; 

$key = q/includegraphics[height=2.25in]{Chapter02slashfig2_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="255" STYLE=""
 SRC="|."$dir".q|img472.png"
 ALT="\includegraphics[height=2.25in]{Chapter02/fig2_01.eps}">;WIDTH="287" HEIGHT="255"|; 

$key = q/includegraphics[height=2.25in]{Chapter02slashfig2_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="259" STYLE=""
 SRC="|."$dir".q|img504.png"
 ALT="\includegraphics[height=2.25in]{Chapter02/fig2_02.eps}">;WIDTH="356" HEIGHT="259"|; 

$key = q/includegraphics[height=2.25in]{Chapter02slashfig2_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="259" STYLE=""
 SRC="|."$dir".q|img510.png"
 ALT="\includegraphics[height=2.25in]{Chapter02/fig2_03.eps}">;WIDTH="345" HEIGHT="259"|; 

$key = q/includegraphics[height=2.25in]{Chapter03slashfig3_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="252" STYLE=""
 SRC="|."$dir".q|img582.png"
 ALT="\includegraphics[height=2.25in]{Chapter03/fig3_01.eps}">;WIDTH="264" HEIGHT="252"|; 

$key = q/includegraphics[height=2.25in]{Chapter05slashfig5_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="257" STYLE=""
 SRC="|."$dir".q|img1169.png"
 ALT="\includegraphics[height=2.25in]{Chapter05/fig5_04.eps}">;WIDTH="258" HEIGHT="257"|; 

$key = q/includegraphics[height=2.25in]{Chapter07slashfig7_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="256" STYLE=""
 SRC="|."$dir".q|img1675.png"
 ALT="\includegraphics[height=2.25in]{Chapter07/fig7_03.eps}">;WIDTH="475" HEIGHT="256"|; 

$key = q/includegraphics[height=2.25in]{Chapter07slashfig7_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="256" STYLE=""
 SRC="|."$dir".q|img1702.png"
 ALT="\includegraphics[height=2.25in]{Chapter07/fig7_04.eps}">;WIDTH="342" HEIGHT="256"|; 

$key = q/includegraphics[height=2.25in]{Chapter08slashfig8_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="246" STYLE=""
 SRC="|."$dir".q|img2089.png"
 ALT="\includegraphics[height=2.25in]{Chapter08/fig8_01.eps}">;WIDTH="379" HEIGHT="246"|; 

$key = q/includegraphics[height=2.25in]{Chapter08slashfig8_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="250" STYLE=""
 SRC="|."$dir".q|img2149.png"
 ALT="\includegraphics[height=2.25in]{Chapter08/fig8_05.eps}">;WIDTH="360" HEIGHT="250"|; 

$key = q/includegraphics[height=2.5in]{AppendixAslashfigA_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="281" STYLE=""
 SRC="|."$dir".q|img4016.png"
 ALT="\includegraphics[height=2.5in]{AppendixA/figA_07.eps}">;WIDTH="253" HEIGHT="281"|; 

$key = q/includegraphics[height=2.5in]{Chapter01slashfig1_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="438" HEIGHT="284" STYLE=""
 SRC="|."$dir".q|img203.png"
 ALT="\includegraphics[height=2.5in]{Chapter01/fig1_04.eps}">;WIDTH="438" HEIGHT="284"|; 

$key = q/includegraphics[height=2.5in]{Chapter05slashfig5_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="286" STYLE=""
 SRC="|."$dir".q|img1090.png"
 ALT="\includegraphics[height=2.5in]{Chapter05/fig5_01.eps}">;WIDTH="439" HEIGHT="286"|; 

$key = q/includegraphics[height=2.5in]{Chapter05slashfig5_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="287" STYLE=""
 SRC="|."$dir".q|img1103.png"
 ALT="\includegraphics[height=2.5in]{Chapter05/fig5_02.eps}">;WIDTH="420" HEIGHT="287"|; 

$key = q/includegraphics[height=2.5in]{Chapter07slashfig7_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="280" STYLE=""
 SRC="|."$dir".q|img1495.png"
 ALT="\includegraphics[height=2.5in]{Chapter07/fig7_01.eps}">;WIDTH="318" HEIGHT="280"|; 

$key = q/includegraphics[height=2.5in]{Chapter07slashfig7_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="280" STYLE=""
 SRC="|."$dir".q|img1852.png"
 ALT="\includegraphics[height=2.5in]{Chapter07/fig7_07.eps}">;WIDTH="420" HEIGHT="280"|; 

$key = q/includegraphics[height=2.5in]{Chapter10slashfig10_1.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="280" STYLE=""
 SRC="|."$dir".q|img2958.png"
 ALT="\includegraphics[height=2.5in]{Chapter10/fig10_1.eps}">;WIDTH="528" HEIGHT="280"|; 

$key = q/includegraphics[height=2.75in]{AppendixAslashfigA_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="306" STYLE=""
 SRC="|."$dir".q|img3974.png"
 ALT="\includegraphics[height=2.75in]{AppendixA/figA_02.eps}">;WIDTH="316" HEIGHT="306"|; 

$key = q/includegraphics[height=2.75in]{AppendixAslashfigA_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="309" STYLE=""
 SRC="|."$dir".q|img3983.png"
 ALT="\includegraphics[height=2.75in]{AppendixA/figA_03.eps}">;WIDTH="312" HEIGHT="309"|; 

$key = q/includegraphics[height=2.75in]{Chapter01slashfig1_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="444" HEIGHT="313" STYLE=""
 SRC="|."$dir".q|img94.png"
 ALT="\includegraphics[height=2.75in]{Chapter01/fig1_01.eps}">;WIDTH="444" HEIGHT="313"|; 

$key = q/includegraphics[height=2.75in]{Chapter01slashfig1_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="307" STYLE=""
 SRC="|."$dir".q|img157.png"
 ALT="\includegraphics[height=2.75in]{Chapter01/fig1_02.eps}">;WIDTH="417" HEIGHT="307"|; 

$key = q/includegraphics[height=2.75in]{Chapter01slashfig1_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="312" STYLE=""
 SRC="|."$dir".q|img174.png"
 ALT="\includegraphics[height=2.75in]{Chapter01/fig1_03.eps}">;WIDTH="374" HEIGHT="312"|; 

$key = q/includegraphics[height=2.75in]{Chapter01slashfig1_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="300" STYLE=""
 SRC="|."$dir".q|img246.png"
 ALT="\includegraphics[height=2.75in]{Chapter01/fig1_06.eps}">;WIDTH="338" HEIGHT="300"|; 

$key = q/includegraphics[height=2.75in]{Chapter01slashfig1_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="307" STYLE=""
 SRC="|."$dir".q|img265.png"
 ALT="\includegraphics[height=2.75in]{Chapter01/fig1_07.eps}">;WIDTH="411" HEIGHT="307"|; 

$key = q/includegraphics[height=2.75in]{Chapter05slashfig5_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="314" STYLE=""
 SRC="|."$dir".q|img1222.png"
 ALT="\includegraphics[height=2.75in]{Chapter05/fig5_08.eps}">;WIDTH="319" HEIGHT="314"|; 

$key = q/includegraphics[height=2.75in]{Chapter07slashfig7_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="308" STYLE=""
 SRC="|."$dir".q|img1649.png"
 ALT="\includegraphics[height=2.75in]{Chapter07/fig7_02.eps}">;WIDTH="423" HEIGHT="308"|; 

$key = q/includegraphics[height=2.75in]{Chapter09slashfig9_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="315" STYLE=""
 SRC="|."$dir".q|img2599.png"
 ALT="\includegraphics[height=2.75in]{Chapter09/fig9_02.eps}">;WIDTH="528" HEIGHT="315"|; 

$key = q/includegraphics[height=2.in]{Chapter09slashfig9_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="229" STYLE=""
 SRC="|."$dir".q|img2403.png"
 ALT="\includegraphics[height=2.in]{Chapter09/fig9_01.eps}">;WIDTH="312" HEIGHT="229"|; 

$key = q/includegraphics[height=2in]{Chapter01slashfig1_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="225" STYLE=""
 SRC="|."$dir".q|img214.png"
 ALT="\includegraphics[height=2in]{Chapter01/fig1_05.eps}">;WIDTH="502" HEIGHT="225"|; 

$key = q/includegraphics[height=3.25in]{Chapter03slashfig3_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="455" HEIGHT="372" STYLE=""
 SRC="|."$dir".q|img671.png"
 ALT="\includegraphics[height=3.25in]{Chapter03/fig3_04.eps}">;WIDTH="455" HEIGHT="372"|; 

$key = q/includegraphics[height=3.25in]{Chapter03slashfig3_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="372" STYLE=""
 SRC="|."$dir".q|img700.png"
 ALT="\includegraphics[height=3.25in]{Chapter03/fig3_05.eps}">;WIDTH="407" HEIGHT="372"|; 

$key = q/includegraphics[height=3.25in]{Chapter03slashfig3_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="368" STYLE=""
 SRC="|."$dir".q|img834.png"
 ALT="\includegraphics[height=3.25in]{Chapter03/fig3_07.eps}">;WIDTH="436" HEIGHT="368"|; 

$key = q/includegraphics[height=3.25in]{Chapter08slashfig8_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="389" HEIGHT="344" STYLE=""
 SRC="|."$dir".q|img2219.png"
 ALT="\includegraphics[height=3.25in]{Chapter08/fig8_06.eps}">;WIDTH="389" HEIGHT="344"|; 

$key = q/includegraphics[height=3.25in]{Chapter08slashfig8_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="370" STYLE=""
 SRC="|."$dir".q|img2239.png"
 ALT="\includegraphics[height=3.25in]{Chapter08/fig8_07.eps}">;WIDTH="404" HEIGHT="370"|; 

$key = q/includegraphics[height=3.25in]{Chapter08slashfig8_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="372" STYLE=""
 SRC="|."$dir".q|img2240.png"
 ALT="\includegraphics[height=3.25in]{Chapter08/fig8_08.eps}">;WIDTH="403" HEIGHT="372"|; 

$key = q/includegraphics[height=3.25in]{Chapter08slashfig8_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="372" STYLE=""
 SRC="|."$dir".q|img2241.png"
 ALT="\includegraphics[height=3.25in]{Chapter08/fig8_09.eps}">;WIDTH="404" HEIGHT="372"|; 

$key = q/includegraphics[height=3.25in]{Chapter08slashfig8_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="370" STYLE=""
 SRC="|."$dir".q|img2242.png"
 ALT="\includegraphics[height=3.25in]{Chapter08/fig8_10.eps}">;WIDTH="417" HEIGHT="370"|; 

$key = q/includegraphics[height=3.25in]{Chapter08slashfig8_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="371" STYLE=""
 SRC="|."$dir".q|img2243.png"
 ALT="\includegraphics[height=3.25in]{Chapter08/fig8_11.eps}">;WIDTH="364" HEIGHT="371"|; 

$key = q/includegraphics[height=3.25in]{Chapter09slashfig9_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="372" STYLE=""
 SRC="|."$dir".q|img2633.png"
 ALT="\includegraphics[height=3.25in]{Chapter09/fig9_04.eps}">;WIDTH="371" HEIGHT="372"|; 

$key = q/includegraphics[height=3.25in]{Chapter09slashfig9_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="373" STYLE=""
 SRC="|."$dir".q|img2636.png"
 ALT="\includegraphics[height=3.25in]{Chapter09/fig9_05.eps}">;WIDTH="372" HEIGHT="373"|; 

$key = q/includegraphics[height=3.5in]{AppendixDDslashfigDD_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="396" STYLE=""
 SRC="|."$dir".q|img4389.png"
 ALT="\includegraphics[height=3.5in]{AppendixDD/figDD_01.eps}">;WIDTH="397" HEIGHT="396"|; 

$key = q/includegraphics[height=3.5in]{Chapter03slashfig3_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="396" STYLE=""
 SRC="|."$dir".q|img738.png"
 ALT="\includegraphics[height=3.5in]{Chapter03/fig3_06.eps}">;WIDTH="527" HEIGHT="396"|; 

$key = q/includegraphics[height=3.5in]{Chapter03slashfig3_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="400" STYLE=""
 SRC="|."$dir".q|img864.png"
 ALT="\includegraphics[height=3.5in]{Chapter03/fig3_08.eps}">;WIDTH="399" HEIGHT="400"|; 

$key = q/includegraphics[height=3.5in]{Chapter04slashfig4_01.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="400" STYLE=""
 SRC="|."$dir".q|img1017.png"
 ALT="\includegraphics[height=3.5in]{Chapter04/fig4_01.eps}">;WIDTH="399" HEIGHT="400"|; 

$key = q/includegraphics[height=3.5in]{Chapter08slashfig8_02.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="400" STYLE=""
 SRC="|."$dir".q|img2132.png"
 ALT="\includegraphics[height=3.5in]{Chapter08/fig8_02.eps}">;WIDTH="397" HEIGHT="400"|; 

$key = q/includegraphics[height=3.5in]{Chapter08slashfig8_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="400" STYLE=""
 SRC="|."$dir".q|img2136.png"
 ALT="\includegraphics[height=3.5in]{Chapter08/fig8_03.eps}">;WIDTH="399" HEIGHT="400"|; 

$key = q/includegraphics[height=3.5in]{Chapter08slashfig8_13.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="400" STYLE=""
 SRC="|."$dir".q|img2283.png"
 ALT="\includegraphics[height=3.5in]{Chapter08/fig8_13.eps}">;WIDTH="400" HEIGHT="400"|; 

$key = q/includegraphics[height=3.75in]{Chapter08slashfig8_04.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="425" HEIGHT="428" STYLE=""
 SRC="|."$dir".q|img2139.png"
 ALT="\includegraphics[height=3.75in]{Chapter08/fig8_04.eps}">;WIDTH="425" HEIGHT="428"|; 

$key = q/includegraphics[height=3in]{Chapter05slashfig5_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="344" STYLE=""
 SRC="|."$dir".q|img1148.png"
 ALT="\includegraphics[height=3in]{Chapter05/fig5_03.eps}">;WIDTH="350" HEIGHT="344"|; 

$key = q/includegraphics[height=3in]{Chapter05slashfig5_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="344" STYLE=""
 SRC="|."$dir".q|img1199.png"
 ALT="\includegraphics[height=3in]{Chapter05/fig5_05.eps}">;WIDTH="357" HEIGHT="344"|; 

$key = q/includegraphics[height=3in]{Chapter07slashfig7_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="344" STYLE=""
 SRC="|."$dir".q|img1810.png"
 ALT="\includegraphics[height=3in]{Chapter07/fig7_06.eps}">;WIDTH="528" HEIGHT="344"|; 

$key = q/includegraphics[height=3in]{Chapter07slashfig7_13.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="339" STYLE=""
 SRC="|."$dir".q|img1958.png"
 ALT="\includegraphics[height=3in]{Chapter07/fig7_13.eps}">;WIDTH="270" HEIGHT="339"|; 

$key = q/includegraphics[height=4.25in]{Chapter07slashfig7_05.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="486" HEIGHT="489" STYLE=""
 SRC="|."$dir".q|img1808.png"
 ALT="\includegraphics[height=4.25in]{Chapter07/fig7_05.eps}">;WIDTH="486" HEIGHT="489"|; 

$key = q/includegraphics[height=4in]{Chapter07slashfig7_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="459" STYLE=""
 SRC="|."$dir".q|img1870.png"
 ALT="\includegraphics[height=4in]{Chapter07/fig7_08.eps}">;WIDTH="527" HEIGHT="459"|; 

$key = q/includegraphics[height=4in]{Chapter07slashfig7_09.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="459" STYLE=""
 SRC="|."$dir".q|img1890.png"
 ALT="\includegraphics[height=4in]{Chapter07/fig7_09.eps}">;WIDTH="527" HEIGHT="459"|; 

$key = q/includegraphics[height=4in]{Chapter07slashfig7_10.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img1939.png"
 ALT="\includegraphics[height=4in]{Chapter07/fig7_10.eps}">;WIDTH="456" HEIGHT="457"|; 

$key = q/includegraphics[height=4in]{Chapter07slashfig7_11.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img1944.png"
 ALT="\includegraphics[height=4in]{Chapter07/fig7_11.eps}">;WIDTH="456" HEIGHT="457"|; 

$key = q/includegraphics[height=4in]{Chapter07slashfig7_12.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img1949.png"
 ALT="\includegraphics[height=4in]{Chapter07/fig7_12.eps}">;WIDTH="460" HEIGHT="457"|; 

$key = q/includegraphics[height=4in]{Chapter08slashfig8_12.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="430" STYLE=""
 SRC="|."$dir".q|img2245.png"
 ALT="\includegraphics[height=4in]{Chapter08/fig8_12.eps}">;WIDTH="467" HEIGHT="430"|; 

$key = q/includegraphics[height=4in]{Chapter08slashfig8_14.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img2296.png"
 ALT="\includegraphics[height=4in]{Chapter08/fig8_14.eps}">;WIDTH="456" HEIGHT="457"|; 

$key = q/includegraphics[height=4in]{Chapter08slashfig8_15.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img2309.png"
 ALT="\includegraphics[height=4in]{Chapter08/fig8_15.eps}">;WIDTH="458" HEIGHT="457"|; 

$key = q/includegraphics[height=4in]{Chapter09slashfig9_06.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="456" HEIGHT="456" STYLE=""
 SRC="|."$dir".q|img2644.png"
 ALT="\includegraphics[height=4in]{Chapter09/fig9_06.eps}">;WIDTH="456" HEIGHT="456"|; 

$key = q/includegraphics[height=4in]{Chapter09slashfig9_07.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="510" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img2679.png"
 ALT="\includegraphics[height=4in]{Chapter09/fig9_07.eps}">;WIDTH="510" HEIGHT="457"|; 

$key = q/includegraphics[height=4in]{Chapter09slashfig9_08.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="510" HEIGHT="457" STYLE=""
 SRC="|."$dir".q|img2680.png"
 ALT="\includegraphics[height=4in]{Chapter09/fig9_08.eps}">;WIDTH="510" HEIGHT="457"|; 

$key = q/includegraphics[height=5.5in]{Chapter09slashfig9_03.eps};LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="632" STYLE=""
 SRC="|."$dir".q|img2632.png"
 ALT="\includegraphics[height=5.5in]{Chapter09/fig9_03.eps}">;WIDTH="528" HEIGHT="632"|; 

$key = q/int_P^Q{bfA}cdotd{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img3943.png"
 ALT="$\int_P^Q {\bf A}\cdot d{\bf r}$">|; 

$key = q/int_P^Q{bff}cdotd{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.29ex; vertical-align: -1.00ex; " SRC="|."$dir".q|img141.png"
 ALT="$\int_P^Q {\bf f}\cdot d{\bf r}$">|; 

$key = q/iota;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1957.png"
 ALT="$\iota$">|; 

$key = q/iota=1.59^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1956.png"
 ALT="$\iota=1.59^\circ$">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img154.png"
 ALT="$j$">|; 

$key = q/j=1,6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4690.png"
 ALT="$j=1,6$">|; 

$key = q/j=1,{calF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1374.png"
 ALT="$j=1,{\cal F}$">|; 

$key = q/j=2,11;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3401.png"
 ALT="$j=2,11$">|; 

$key = q/j=2,5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3434.png"
 ALT="$j=2,5$">|; 

$key = q/j=4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3435.png"
 ALT="$j=4$">|; 

$key = q/j=6,8,11;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3402.png"
 ALT="$j = 6,8,11$">|; 

$key = q/j=i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img159.png"
 ALT="$j=i$">|; 

$key = q/j_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3725.png"
 ALT="$j_1$">|; 

$key = q/j_1=223;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3730.png"
 ALT="$j_1=223$">|; 

$key = q/j_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3726.png"
 ALT="$j_2$">|; 

$key = q/j_2=239;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3731.png"
 ALT="$j_2=239$">|; 

$key = q/j_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3727.png"
 ALT="$j_3$">|; 

$key = q/j_3=242;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3732.png"
 ALT="$j_3=242$">|; 

$key = q/j_o;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1874.png"
 ALT="$j_o$">|; 

$key = q/j_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1875.png"
 ALT="$j_s$">|; 

$key = q/jneqi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img377.png"
 ALT="$j\neq i$">|; 

$key = q/k!=k,(k-1),(k-2)..2.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3802.png"
 ALT="$k!= k (k-1) (k-2)..2.1$">|; 

$key = q/k'(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2875.png"
 ALT="$k'(t)$">|; 

$key = q/k'(t)=skew{3}hat{e}',cos(g,t+beta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2863.png"
 ALT="$k'(t)=\skew{3}\hat{e}' \cos(g t+\beta)$">|; 

$key = q/k';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2470.png"
 ALT="$k'$">|; 

$key = q/k'=e',cosvarpi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2859.png"
 ALT="$k'=e' \cos\varpi'$">|; 

$key = q/k(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2873.png"
 ALT="$k(t)$">|; 

$key = q/k(t)=skew{3}hat{e},cos(g,t+beta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2861.png"
 ALT="$k(t)=\skew{3}\hat{e} \cos(g t+\beta)$">|; 

$key = q/k,a>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img310.png"
 ALT="$k, a&gt;0$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1042.png"
 ALT="$k$">|; 

$key = q/k=1,2,3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4645.png"
 ALT="$k=1,2,3$">|; 

$key = q/k=e,cosvarpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2431.png"
 ALT="$k=e \cos\varpi$">|; 

$key = q/k>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1038.png"
 ALT="$k&gt;0$">|; 

$key = q/k_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img316.png"
 ALT="$k_1$">|; 

$key = q/k_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img317.png"
 ALT="$k_2$">|; 

$key = q/k_i,k_j,|{bfr}_i-{bfr}_j|^{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img542.png"
 ALT="$k_i k_j \vert{\bf r}_i-{\bf r}_j\vert^{-n}$">|; 

$key = q/k_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img543.png"
 ALT="$k_i$">|; 

$key = q/k_i=e_i,cosvarpi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2553.png"
 ALT="$k_i=e_i \cos\varpi_i$">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1366.png"
 ALT="$l$">|; 

$key = q/l<R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1462.png"
 ALT="$l&lt; R$">|; 

$key = q/l=1,2,3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img4651.png"
 ALT="$l=1,2,3$">|; 

$key = q/l=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2606.png"
 ALT="$l=1$">|; 

$key = q/l=OP;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1455.png"
 ALT="$l=OP$">|; 

$key = q/l_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3368.png"
 ALT="$l_1$">|; 

$key = q/l_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3374.png"
 ALT="$l_4$">|; 

$key = q/l_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3381.png"
 ALT="$l_6$">|; 

$key = q/l_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3389.png"
 ALT="$l_{11}$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img24.png"
 ALT="$\lambda $">|; 

$key = q/lambda<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1117.png"
 ALT="$\lambda &lt; 0$">|; 

$key = q/lambda>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1116.png"
 ALT="$\lambda&gt;0$">|; 

$key = q/lambda^{(1)}sim{calO}(epsilon');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4907.png"
 ALT="$\lambda^{(1)}\sim {\cal O}(\epsilon')$">|; 

$key = q/lambda_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1542.png"
 ALT="$\lambda_i$">|; 

$key = q/lambda_i=lambda_i^{,ast};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img4086.png"
 ALT="$\lambda_i=\lambda_i^{ \ast}$">|; 

$key = q/lambda_i=lambda_j=lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4102.png"
 ALT="$\lambda_i=\lambda_j=\lambda$">|; 

$key = q/lambda_ineqlambda_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4093.png"
 ALT="$\lambda_i\neq \lambda_j$">|; 

$key = q/lambda_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1750.png"
 ALT="$\lambda_m$">|; 

$key = q/lambda_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1701.png"
 ALT="$\lambda_s$">|; 

$key = q/langle1rangle=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img405.png"
 ALT="$\langle 1\rangle =1$">|; 

$key = q/langlecdotsrangleequivoint(cdots),dphi'slash2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.84ex; vertical-align: -0.92ex; " SRC="|."$dir".q|img396.png"
 ALT="$\langle\cdots\rangle\equiv \oint (\cdots) d\phi'/2\pi$">|; 

$key = q/langlecos[(2,p-1),n,t]rangle=langlecos(n,t)rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1885.png"
 ALT="$\langle\cos[(2 p-1) n t]\rangle=\langle\cos( n t)\rangle =0$">|; 

$key = q/langlecos[2,(p-1),n,t]rangle=langle1rangle=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1884.png"
 ALT="$\langle \cos[2 (p-1) n t]\rangle=\langle 1\rangle =1$">|; 

$key = q/langlecos^2phi'rangle=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img407.png"
 ALT="$\langle \cos^2\phi'\rangle = 1/2$">|; 

$key = q/langlecosphi'rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img406.png"
 ALT="$\langle\cos\phi'\rangle = 0$">|; 

$key = q/langledot{I}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2832.png"
 ALT="$\langle\dot{I}\rangle$">|; 

$key = q/langledot{varpi}rangle('',{rmyr}^{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4207.png"
 ALT="$\langle\dot{\varpi}\rangle('' {\rm yr}^{-1})$">|; 

$key = q/langledot{varpi}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2619.png"
 ALT="$\langle\dot{\varpi}\rangle$">|; 

$key = q/langledot{{mitOmega}}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2622.png"
 ALT="$\langle\dot{{\mit\Omega}}\rangle$">|; 

$key = q/langleskew{3}dot{a}slasharangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2835.png"
 ALT="$\langle\skew{3}\dot{a}/a\rangle$">|; 

$key = q/langleskew{3}dot{e}slasherangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2836.png"
 ALT="$\langle\skew{3}\dot{e}/e\rangle$">|; 

$key = q/langleskew{3}dot{omega}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2831.png"
 ALT="$\langle\skew{3}\dot{\omega}\rangle$">|; 

$key = q/langleskew{3}dot{omega}rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2780.png"
 ALT="$\langle \skew{3}\dot{\omega} \rangle =0$">|; 

$key = q/langleskew{5}dot{calM}_0rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2837.png"
 ALT="$\langle\skew{5}\dot{\cal M}_0\rangle$">|; 

$key = q/langleskew{5}dot{calM}_0rangle=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2781.png"
 ALT="$\langle\skew{5}\dot{\cal M}_0 \rangle=0$">|; 

$key = q/langleskew{5}dot{calM}_0ranglegglangleskew{3}dot{a}slasharangle,langleskew{3}dot{e}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2838.png"
 ALT="$\langle\skew{5}\dot{\cal M}_0\rangle\gg \langle\skew{3}\dot{a}/a\rangle,
\langle\skew{3}\dot{e}\rangle$">|; 

$key = q/langleskew{5}dot{calM}_0rangleslashnll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2840.png"
 ALT="$\langle\skew{5}\dot{\cal M}_0\rangle/n\ll 1$">|; 

$key = q/langleskew{5}dot{mitOmega}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2833.png"
 ALT="$\langle\skew{5}\dot{\mit\Omega}\rangle$">|; 

$key = q/langle|{bfr}'-{bfr}|^{-1}rangle;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img433.png"
 ALT="$\langle\vert{\bf r}'-{\bf r}\vert^{-1}\rangle$">|; 

$key = q/m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img345.png"
 ALT="$m'$">|; 

$key = q/m'=1.99times10^{30},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1260.png"
 ALT="$m'=1.99\times 10^{30} {\rm kg}$">|; 

$key = q/m'=7.35times10^{22},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1248.png"
 ALT="$m'=7.35\times 10^{22} {\rm kg}$">|; 

$key = q/m'slashm=(rho'slashrho),(R'slashR)^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1329.png"
 ALT="$m'/m = (\rho'/\rho) (R'/R)^3$">|; 

$key = q/m,,m'llM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img2399.png"
 ALT="$m, m'\ll M$">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img26.png"
 ALT="$m$">|; 

$key = q/m=(4pislash3),rho,b^{,3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2843.png"
 ALT="$m= (4\pi/3) \rho b^{ 3}$">|; 

$key = q/m=0.07480;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3471.png"
 ALT="$m=0.07480$">|; 

$key = q/m=5.97times10^{24},{rmkg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1247.png"
 ALT="$m=5.97\times 10^{24} {\rm kg}$">|; 

$key = q/m=n'slashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3430.png"
 ALT="$m=n'/n$">|; 

$key = q/m^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3133.png"
 ALT="$m^{ 2}$">|; 

$key = q/m_1+m_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3015.png"
 ALT="$m_1+m_2$">|; 

$key = q/m_1,m_2,m_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1393.png"
 ALT="$m_1, m_2, m_3$">|; 

$key = q/m_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img53.png"
 ALT="$m_1$">|; 

$key = q/m_1geqm_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2175.png"
 ALT="$m_1\geq m_2$">|; 

$key = q/m_1ggm_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2126.png"
 ALT="$m_1\gg m_2$">|; 

$key = q/m_1slashm_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img865.png"
 ALT="$m_1/m_2$">|; 

$key = q/m_1slashm_2=0.4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img862.png"
 ALT="$m_1/m_2=0.4$">|; 

$key = q/m_1slashm_2=81.3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3029.png"
 ALT="$m_1/m_2=81.3$">|; 

$key = q/m_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img54.png"
 ALT="$m_2$">|; 

$key = q/m_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img60.png"
 ALT="$m_3$">|; 

$key = q/m_3slash(m_1+m_2)=3.29times10^{,5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3016.png"
 ALT="$m_3/(m_1+m_2)=3.29\times 10^{ 5}$">|; 

$key = q/m_4,m_5,m_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1394.png"
 ALT="$m_4, m_5, m_6$">|; 

$key = q/m_i,ddot{x}_i=-partialUslashpartialx_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img546.png"
 ALT="$m_i \ddot{x}_i=-\partial U/\partial x_i$">|; 

$key = q/m_i,ddot{y}_i=-partialUslashpartialy_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img547.png"
 ALT="$m_i \ddot{y}_i=-\partial U/\partial y_i$">|; 

$key = q/m_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img151.png"
 ALT="$m_i$">|; 

$key = q/m_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1409.png"
 ALT="$m_j$">|; 

$key = q/m_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1820.png"
 ALT="$m_p$">|; 

$key = q/m_pggm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1351.png"
 ALT="$m_p\gg m$">|; 

$key = q/mggm';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1291.png"
 ALT="$m\gg m'$">|; 

$key = q/mrightarrowzeta^{,3slash2},m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3696.png"
 ALT="$m\rightarrow \zeta^{ 3/2} m$">|; 

$key = q/mslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1365.png"
 ALT="$m/2$">|; 

$key = q/mslashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img18.png"
 ALT="$m/M$">|; 

$key = q/mu'=G,(M+m');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2415.png"
 ALT="$\mu'=G (M+m')$">|; 

$key = q/mu'=G,m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4138.png"
 ALT="$\mu'=G m'$">|; 

$key = q/mu,ddot{bfr}=-nablaU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img337.png"
 ALT="$\mu \ddot{\bf r} = -\nabla U$">|; 

$key = q/mu,ddot{bfr}={bff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img339.png"
 ALT="$\mu \ddot{\bf r} = {\bf f}$">|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img274.png"
 ALT="$\mu$">|; 

$key = q/mu=1times10^{11},{rmN,m}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4515.png"
 ALT="$\mu=1\times 10^{11} {\rm N m}^{-2}$">|; 

$key = q/mu=G,(M+m);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2414.png"
 ALT="$\mu= G (M+m)$">|; 

$key = q/mu=G,M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2688.png"
 ALT="$\mu=G M$">|; 

$key = q/mu=m_1,m_2slash(m_1+m_2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img850.png"
 ALT="$\mu= m_1 m_2/(m_1+m_2)$">|; 

$key = q/mu=m_1,m_2slashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img946.png"
 ALT="$\mu=m_1 m_2/M$">|; 

$key = q/mu=n^2,a^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4885.png"
 ALT="$\mu=n^2 a^3$">|; 

$key = q/mu>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1052.png"
 ALT="$\mu&gt;0$">|; 

$key = q/mu_1+mu_2=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2180.png"
 ALT="$\mu_1+\mu_2=1$">|; 

$key = q/mu_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2344.png"
 ALT="$\mu_1$">|; 

$key = q/mu_1=1-mu_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2215.png"
 ALT="$\mu_1=1-\mu_2$">|; 

$key = q/mu_1=G,m_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2099.png"
 ALT="$\mu_1=G m_1$">|; 

$key = q/mu_1=G,m_1simeqG,(m_1+m_2)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2127.png"
 ALT="$\mu_1=G m_1\simeq G (m_1+m_2)=1$">|; 

$key = q/mu_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img66.png"
 ALT="$\mu _2$">|; 

$key = q/mu_2=0.01;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img65.png"
 ALT="$\mu _2=0.01$">|; 

$key = q/mu_2=0.1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img57.png"
 ALT="$\mu _2=0.1$">|; 

$key = q/mu_2=1-zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2366.png"
 ALT="$\mu_2=1-\zeta$">|; 

$key = q/mu_2=9.533times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img51.png"
 ALT="$\mu _2=9.533\times 10^{-4}$">|; 

$key = q/mu_2=G,m_2=1-mu_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2100.png"
 ALT="$\mu_2=G m_2=1-\mu_1$">|; 

$key = q/mu_2=zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2363.png"
 ALT="$\mu_2=\zeta$">|; 

$key = q/mu_2ll0.0385;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2367.png"
 ALT="$\mu_2\ll 0.0385$">|; 

$key = q/mu_2ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2227.png"
 ALT="$\mu_2\ll 1$">|; 

$key = q/mu_2rightarrow0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2347.png"
 ALT="$\mu_2\rightarrow 0$">|; 

$key = q/mu_2slashmu_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2211.png"
 ALT="$\mu_2/\mu_1$">|; 

$key = q/mu_m=0.01215;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4600.png"
 ALT="$\mu_m=0.01215$">|; 

$key = q/mu_m=0.0123;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1805.png"
 ALT="$\mu_m=0.0123$">|; 

$key = q/musimeq1times10^{11},{rmN,m^{-2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1181.png"
 ALT="$\mu\simeq 1\times 10^{11} {\rm N m^{-2}}$">|; 

$key = q/musimeq5times10^{10},{rmN,m^{-2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1314.png"
 ALT="$\mu\simeq 5\times 10^{10} {\rm N m^{-2}}$">|; 

$key = q/n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img78.png"
 ALT="$n'$">|; 

$key = q/n'=(G,Mslasha'^{,3})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2886.png"
 ALT="$n'=(G M/a'^{ 3})^{1/2}$">|; 

$key = q/n'=(mu'slasha'^{,3})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2500.png"
 ALT="$n'=(\mu'/a'^{ 3})^{1/2}$">|; 

$key = q/n'=0.98560912^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3014.png"
 ALT="$n'=0.98560912^\circ$">|; 

$key = q/n'=0.9856^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3759.png"
 ALT="$n'=0.9856^\circ$">|; 

$key = q/n'slashn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2927.png"
 ALT="$n'/n$">|; 

$key = q/n(t)=n^{(0)}[1-(3slash2),epsilon',a^{(1)}(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2435.png"
 ALT="$n(t)=n^{(0)}[1-(3/2) \epsilon' a^{(1)}(t)]$">|; 

$key = q/n,a,eslashsqrt{1-e^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img884.png"
 ALT="$n a e/\sqrt{1-e^{ 2}}$">|; 

$key = q/n,a=(muslasha)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4800.png"
 ALT="$n a=(\mu/a)^{1/2}$">|; 

$key = q/n,aslashsqrt{1-e^{,2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img883.png"
 ALT="$n a/\sqrt{1-e^{ 2}}$">|; 

$key = q/n,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1872.png"
 ALT="$n t$">|; 

$key = q/n,t=i,2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1873.png"
 ALT="$n t=i 2\pi$">|; 

$key = q/n-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4218.png"
 ALT="$n-1$">|; 

$key = q/n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img77.png"
 ALT="$n$">|; 

$key = q/n=(G,Mslasha^{,3})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2639.png"
 ALT="$n=(G M/a^{ 3})^{1/2}$">|; 

$key = q/n=(muslasha^3)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4707.png"
 ALT="$n=(\mu/a^3)^{1/2}$">|; 

$key = q/n=(muslasha^{,3});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2825.png"
 ALT="$n=(\mu/a^{ 3})$">|; 

$key = q/n=(muslasha^{,3})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2692.png"
 ALT="$n=(\mu/a^{ 3})^{1/2}$">|; 

$key = q/n=-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img984.png"
 ALT="$n=-2$">|; 

$key = q/n=-3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img973.png"
 ALT="$n =-3$">|; 

$key = q/n=0,infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.41ex; " SRC="|."$dir".q|img418.png"
 ALT="$n=0,\infty$">|; 

$key = q/n=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4046.png"
 ALT="$n=0$">|; 

$key = q/n=1296000slasha^{,3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4205.png"
 ALT="$n=1296000/a^{ 3/2}$">|; 

$key = q/n=13.176359^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img3013.png"
 ALT="$n=13.176359^\circ$">|; 

$key = q/n=13.1764^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3742.png"
 ALT="$n= 13.1764^\circ$">|; 

$key = q/n=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img985.png"
 ALT="$n=1$">|; 

$key = q/n=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img987.png"
 ALT="$n=2$">|; 

$key = q/n=2pislashT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img650.png"
 ALT="$n=2\pi/T$">|; 

$key = q/n=2pislasha^{,3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img750.png"
 ALT="$n=2\pi/a^{ 3/2}$">|; 

$key = q/n=3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img988.png"
 ALT="$n=3$">|; 

$key = q/n=m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img429.png"
 ALT="$n=m$">|; 

$key = q/n>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img449.png"
 ALT="$n&gt;0$">|; 

$key = q/n^{(0)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2438.png"
 ALT="$n^{(0)}$">|; 

$key = q/n^{(0)}=(muslash[a^{(0)}]^3)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2436.png"
 ALT="$n^{(0)}=(\mu/[a^{(0)}]^3)^{1/2}$">|; 

$key = q/n^{-1},dgammaslashdt=n^{-1},dphislashdt-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1893.png"
 ALT="$n^{-1} d\gamma/dt= n^{-1} d\phi/dt-1$">|; 

$key = q/n^{-1},dphislashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1871.png"
 ALT="$n^{-1} d\phi/dt$">|; 

$key = q/n^{-1},dphislashdt=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1903.png"
 ALT="$n^{-1} d\phi/dt=1$">|; 

$key = q/n^{-1},dphislashdt=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1906.png"
 ALT="$n^{-1} d\phi/dt=1/2$">|; 

$key = q/n^{-1}tmspace+thinmuskip{.1667em}dphislashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img38.png"
 ALT="$n^{-1}\tmspace +\thinmuskip {.1667em}d\phi /dt$">|; 

$key = q/n^{-1}tmspace+thinmuskip{.1667em}dphislashdt=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img47.png"
 ALT="$n^{-1}\tmspace +\thinmuskip {.1667em}d\phi /dt = 1$">|; 

$key = q/n_0=[3,({calI}_{yy}-{calI}_{xx})slash{calI}_{zz}]^{1slash2},n=0.3446^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3741.png"
 ALT="$n_0= [3 ({\cal I}_{yy}-{\cal I}_{xx})/{\cal I}_{zz}]^{1/2} n = 0.3446^\circ$">|; 

$key = q/n_1=n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3751.png"
 ALT="$n_1=n$">|; 

$key = q/n_2=2,n_{rmdr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3752.png"
 ALT="$n_2=2 n_{\rm dr}$">|; 

$key = q/n_3=2,n_{rmsy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img3753.png"
 ALT="$n_3=2 n_{\rm sy}$">|; 

$key = q/n_4=2,n_{rmsy}-n_{rman};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img3754.png"
 ALT="$n_4=2 n_{\rm sy}-n_{\rm an}$">|; 

$key = q/n_5=n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3755.png"
 ALT="$n_5=n'$">|; 

$key = q/n_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1752.png"
 ALT="$n_m$">|; 

$key = q/n_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3716.png"
 ALT="$n_n$">|; 

$key = q/n_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3715.png"
 ALT="$n_p$">|; 

$key = q/n_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4579.png"
 ALT="$n_s$">|; 

$key = q/n_sslashn_m=T_m({rmyr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4591.png"
 ALT="$n_s/n_m = T_m({\rm yr})$">|; 

$key = q/n_sslash{mitOmega}_phi=T_phi({rmyr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4592.png"
 ALT="$n_s/{\mit\Omega}_\phi = T_\phi({\rm yr})$">|; 

$key = q/n_sslash|skew{5}dot{mitOmega}_m|=T_n({rmyr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4609.png"
 ALT="$n_s/\vert\skew{5}\dot{\mit\Omega}_m\vert=T_n({\rm yr})$">|; 

$key = q/n_{rman}=13.0650^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3758.png"
 ALT="$n_{\rm an}=13.0650^\circ$">|; 

$key = q/n_{rmdr}=13.2293^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3756.png"
 ALT="$n_{\rm dr}=13.2293^\circ$">|; 

$key = q/n_{rmsy}=12.1908^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.75ex; " SRC="|."$dir".q|img3757.png"
 ALT="$n_{\rm sy}=12.1908^\circ$">|; 

$key = q/nabla';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2427.png"
 ALT="$\nabla'$">|; 

$key = q/nabla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2426.png"
 ALT="$\nabla$">|; 

$key = q/nabla^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4111.png"
 ALT="$\nabla^{ 2}$">|; 

$key = q/nabla^{,2}p_2=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4271.png"
 ALT="$\nabla^{ 2} p_2=0$">|; 

$key = q/nabla^{,2}{mitPhi}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4242.png"
 ALT="$\nabla^{ 2}{\mit\Phi}=0$">|; 

$key = q/nabla^{,2}{mitPhi}=c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4245.png"
 ALT="$\nabla^{ 2}{\mit\Phi}=c$">|; 

$key = q/nablarhotimesnablaU={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4325.png"
 ALT="$\nabla \rho\times \nabla U = {\bf0}$">|; 

$key = q/ngeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img4027.png"
 ALT="$n\geq 0$">|; 

$key = q/ngeq3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img552.png"
 ALT="$n\geq 3$">|; 

$key = q/nproptoa^{-3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4781.png"
 ALT="$n\propto a^{-3/2}$">|; 

$key = q/nu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1952.png"
 ALT="$\nu$">|; 

$key = q/nu_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2002.png"
 ALT="$\nu_x$">|; 

$key = q/nu_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2003.png"
 ALT="$\nu_y$">|; 

$key = q/omega';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4173.png"
 ALT="$\omega'$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img737.png"
 ALT="$\omega$">|; 

$key = q/omega=!sqrt{kslashm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img225.png"
 ALT="$\omega =\! \sqrt{k/m}$">|; 

$key = q/omega=(omega_{x'}^2+omega_{y'}^2+omega_{z'}^2)^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.79ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img1585.png"
 ALT="$\omega=(\omega_{x'}^2+\omega_{y'}^2+\omega_{z'}^2)^{1/2}$">|; 

$key = q/omega=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2098.png"
 ALT="$\omega =1$">|; 

$key = q/omega=2.67times10^{-6},{rmrad.,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1294.png"
 ALT="$\omega=2.67\times 10^{-6} {\rm rad. s}^{-1}$">|; 

$key = q/omega=varpi-{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4878.png"
 ALT="$\omega=\varpi-{\mit\Omega}$">|; 

$key = q/omega>{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1285.png"
 ALT="$\omega &gt;{\mit\Omega}$">|; 

$key = q/omega_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img244.png"
 ALT="$\omega_0$">|; 

$key = q/omega_1=13.1889^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2048.png"
 ALT="$\omega_1=13.1889^\circ$">|; 

$key = q/omega_1simeqn,(1+3,tauslash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2036.png"
 ALT="$\omega_1 \simeq n (1+3 \tau/2)$">|; 

$key = q/omega_2=1.3304times10^{-2,circ};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2049.png"
 ALT="$\omega_2
= 1.3304\times 10^{-2 \circ}$">|; 

$key = q/omega_2simeq2,nsqrt{sigma,tau};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img2037.png"
 ALT="$\omega_2\simeq 2 n\sqrt{\sigma \tau}$">|; 

$key = q/omega_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1584.png"
 ALT="$\omega_\perp$">|; 

$key = q/omega_perp=omega,sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1587.png"
 ALT="$\omega_\perp = \omega \sin\alpha$">|; 

$key = q/omega_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1535.png"
 ALT="$\omega_x$">|; 

$key = q/omega_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1536.png"
 ALT="$\omega_y$">|; 

$key = q/omega_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1842.png"
 ALT="$\omega_z)$">|; 

$key = q/omega_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1537.png"
 ALT="$\omega_z$">|; 

$key = q/omega_z=skew{5}dot{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1847.png"
 ALT="$\omega_z=\skew{5}\dot{\phi}$">|; 

$key = q/omega_{x'}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1639.png"
 ALT="$\omega_{x'}=0$">|; 

$key = q/omega_{y'}=omega,sinalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1640.png"
 ALT="$\omega_{y'}=\omega \sin\alpha$">|; 

$key = q/omega_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1576.png"
 ALT="$\omega_{z'}$">|; 

$key = q/omega_{z'}=omega,cosalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1586.png"
 ALT="$\omega_{z'} = \omega \cos\alpha$">|; 

$key = q/omegasimeq(G,m_pslasha^{,3})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1352.png"
 ALT="$\omega \simeq (G m_p/a^{ 3})^{1/2}$">|; 

$key = q/omegaslashn_s=T_s({rmday});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img4590.png"
 ALT="$\omega/n_s = T_s({\rm day})$">|; 

$key = q/overline{calR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img2715.png"
 ALT="$\overline{\cal R}$">|; 

$key = q/p';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2471.png"
 ALT="$p'$">|; 

$key = q/p({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4264.png"
 ALT="$p({\bf r})$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2513.png"
 ALT="$p$">|; 

$key = q/p=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1882.png"
 ALT="$p=1$">|; 

$key = q/p=1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1886.png"
 ALT="$p=1/2$">|; 

$key = q/p=3slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1888.png"
 ALT="$p=3/2$">|; 

$key = q/p=j_oslashj_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1877.png"
 ALT="$p=j_o/j_s$">|; 

$key = q/p=m,skew{3}dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1438.png"
 ALT="$p=m \skew{3}\dot{x}$">|; 

$key = q/p=sinI,sin{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2432.png"
 ALT="$p=\sin I \sin {\mit\Omega}$">|; 

$key = q/p_0ggp_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img499.png"
 ALT="$p_0\gg p_c$">|; 

$key = q/p_0llp_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img498.png"
 ALT="$p_0\ll p_c$">|; 

$key = q/p_0slashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img307.png"
 ALT="$p_0/m$">|; 

$key = q/p_2({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4272.png"
 ALT="$p_2({\bf r})$">|; 

$key = q/p_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4273.png"
 ALT="$p_2$">|; 

$key = q/p_csim2times10^8,{rmN},{rmm}^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img492.png"
 ALT="$p_c\sim 2\times 10^8 {\rm N} {\rm m}^{-2}$">|; 

$key = q/p_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1443.png"
 ALT="$p_i$">|; 

$key = q/p_i=sinI_i,sin{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2554.png"
 ALT="$p_i=\sin I_i \sin{\mit\Omega}_i$">|; 

$key = q/p_k=[P_{2k}(0)]^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img992.png"
 ALT="$p_k=[P_{2k}(0)]^{ 2}$">|; 

$key = q/p_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1449.png"
 ALT="$p_\theta$">|; 

$key = q/partialX_lslashpartialtequivdot{X}_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4699.png"
 ALT="$\partial X_l/\partial t\equiv \dot{X}_l$">|; 

$key = q/partialXslashpartialc_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4681.png"
 ALT="$\partial X/\partial c_j$">|; 

$key = q/partialYslashpartialc_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4682.png"
 ALT="$\partial Y/\partial c_j$">|; 

$key = q/partialZslashpartialc_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4683.png"
 ALT="$\partial Z/\partial c_j$">|; 

$key = q/partialdot{X}_lslashpartialtequivddot{X}_l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4700.png"
 ALT="$\partial\dot{X}_l/\partial t\equiv \ddot{X}_l$">|; 

$key = q/partialsigmaslashpartialtheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1173.png"
 ALT="$\partial\sigma/\partial\theta$">|; 

$key = q/partialslashpartiala;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4857.png"
 ALT="$\partial/\partial a$">|; 

$key = q/partialslashpartialskew{5}bar{lambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4856.png"
 ALT="$\partial/\partial \skew{5}\bar{\lambda}$">|; 

$key = q/partialslashpartialtllomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4547.png"
 ALT="$\partial/\partial t\ll \omega$">|; 

$key = q/partial{calR}_nslashpartialx_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4217.png"
 ALT="$\partial {\cal R}_n/\partial x_i$">|; 

$key = q/partial{calS}_{0,s}slashpartialskew{5}bar{lambda}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2521.png"
 ALT="$\partial {\cal S}_{0 s}/\partial\skew{5}\bar{\lambda} = 0$">|; 

$key = q/phi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img394.png"
 ALT="$\phi'$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img37.png"
 ALT="$\phi $">|; 

$key = q/phi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img46.png"
 ALT="$\phi =0$">|; 

$key = q/phi=gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1894.png"
 ALT="$\phi = \gamma$">|; 

$key = q/phi=pmpislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1905.png"
 ALT="$\phi=\pm\pi/2$">|; 

$key = q/phi=tan^{-1}(bslasha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3993.png"
 ALT="$\phi=\tan^{-1}(b/a)$">|; 

$key = q/phi=tan^{-1}(yslashx);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3977.png"
 ALT="$\phi=\tan^{-1}(y/x)$">|; 

$key = q/phi_+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2387.png"
 ALT="$\phi_+$">|; 

$key = q/phi_-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2393.png"
 ALT="$\phi_-$">|; 

$key = q/phi_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img240.png"
 ALT="$\phi_0$">|; 

$key = q/phi_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img241.png"
 ALT="$\phi_0 = 0$">|; 

$key = q/phi_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2042.png"
 ALT="$\phi_1$">|; 

$key = q/phi_2({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4284.png"
 ALT="$\phi_2({\bf r})$">|; 

$key = q/phi_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2043.png"
 ALT="$\phi_2$">|; 

$key = q/pi,k,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1054.png"
 ALT="$\pi k a$">|; 

$key = q/pi,k^{,2},a^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1056.png"
 ALT="$\pi k^{ 2} a^{ 2}$">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img974.png"
 ALT="$\pi$">|; 

$key = q/pislash(4sqrt{mu});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.80ex; " SRC="|."$dir".q|img302.png"
 ALT="$\pi/(4\sqrt{\mu})$">|; 

$key = q/pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img986.png"
 ALT="$\pi/2$">|; 

$key = q/pm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img216.png"
 ALT="$\pm$">|; 

$key = q/pmpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1902.png"
 ALT="$\pm\pi$">|; 

$key = q/psi(eta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img81.png"
 ALT="$\psi (\eta )$">|; 

$key = q/psi(eta)simeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4393.png"
 ALT="$\psi(\eta)\simeq 1$">|; 

$key = q/psi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img980.png"
 ALT="$\psi$">|; 

$key = q/psi=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1641.png"
 ALT="$\psi=0$">|; 

$key = q/psimeqI,sin{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img5066.png"
 ALT="$p\simeq I \sin {\mit\Omega}$">|; 

$key = q/q';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2472.png"
 ALT="$q'$">|; 

$key = q/q'll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2515.png"
 ALT="$q'\ll 1$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2514.png"
 ALT="$q$">|; 

$key = q/q=m'slashm;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2869.png"
 ALT="$q=m'/m$">|; 

$key = q/q=sinI,cos{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2433.png"
 ALT="$q=\sin I \cos{\mit\Omega}$">|; 

$key = q/q_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1369.png"
 ALT="$q_i$">|; 

$key = q/q_i=sinI_i,cos{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2555.png"
 ALT="$q_i=\sin I_i \cos{\mit\Omega}_i$">|; 

$key = q/q_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1445.png"
 ALT="$q_k$">|; 

$key = q/qggalpha^{,1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2882.png"
 ALT="$q\gg \alpha^{ 1/2}$">|; 

$key = q/qsimeqI,cosomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img5067.png"
 ALT="$q\simeq I \cos\omega$">|; 

$key = q/r'(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4201.png"
 ALT="$r'(\theta)$">|; 

$key = q/r'>r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2402.png"
 ALT="$r'&gt;r$">|; 

$key = q/r'slashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img403.png"
 ALT="$r'/r$">|; 

$key = q/r(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4200.png"
 ALT="$r(\theta)$">|; 

$key = q/r,,theta,,phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img383.png"
 ALT="$r,  \theta,  \phi$">|; 

$key = q/r,costheta=a,(cosE-e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img717.png"
 ALT="$r \cos\theta = a (\cos E-e)$">|; 

$key = q/r,deltatheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img612.png"
 ALT="$r \delta\theta$">|; 

$key = q/r,sintheta,,{mitOmega}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1153.png"
 ALT="$r \sin\theta  {\mit\Omega}^{ 2}$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img11.png"
 ALT="$r$">|; 

$key = q/r<;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4215.png"
 ALT="$r&lt;$">|; 

$key = q/r<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img525.png"
 ALT="$r&lt;a$">|; 

$key = q/r<r';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img435.png"
 ALT="$r &lt; r'$">|; 

$key = q/r=(X^{,2}+Y^{,2}+Z^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2682.png"
 ALT="$r=(X^{ 2}+Y^{ 2}+Z^{ 2})^{1/2}$">|; 

$key = q/r=(f_1^{,2}+f_2^{,2}+f_3^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img4667.png"
 ALT="$r=(f_1^{ 2}+f_2^{ 2}+f_3^{ 2})^{1/2}$">|; 

$key = q/r=(x^{,2}+y^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img583.png"
 ALT="$r=(x^{ 2}+y^{ 2})^{1/2}$">|; 

$key = q/r=(x^{,2}+y^{,2}+z^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3975.png"
 ALT="$r=(x^{ 2}+y^{ 2}+z^{ 2})^{1/2}$">|; 

$key = q/r=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2338.png"
 ALT="$r=1$">|; 

$key = q/r=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4110.png"
 ALT="$r=$">|; 

$key = q/r=R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img460.png"
 ALT="$r=R$">|; 

$key = q/r=a,(1+costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1035.png"
 ALT="$r=a (1+\cos\theta)$">|; 

$key = q/r=a,[1-(2slash3),epsilon(a),P_2(costheta)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4360.png"
 ALT="$r=a [1-(2/3) \epsilon(a) P_2(\cos\theta)]$">|; 

$key = q/r=a,theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1039.png"
 ALT="$r=a \theta$">|; 

$key = q/r=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1981.png"
 ALT="$r=a$">|; 

$key = q/r=r_0,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1033.png"
 ALT="$r=r_0 \cos\theta$">|; 

$key = q/r=r_0,exp(k,theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img1036.png"
 ALT="$r=r_0 \exp(k \theta)$">|; 

$key = q/r=r_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img672.png"
 ALT="$r=r_p$">|; 

$key = q/r=u^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img615.png"
 ALT="$r = u^{-1}$">|; 

$key = q/r>R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img453.png"
 ALT="$r&gt;R$">|; 

$key = q/r>a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img513.png"
 ALT="$r&gt;a$">|; 

$key = q/r>r';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img401.png"
 ALT="$r &gt; r'$">|; 

$key = q/r^{,-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img972.png"
 ALT="$r^{ -3}$">|; 

$key = q/r^{,n},{calS}_n(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4243.png"
 ALT="$r^{ n} {\cal S}_n(\theta,\phi)$">|; 

$key = q/r^{-(n+1)},{calS}_n(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4244.png"
 ALT="$r^{-(n+1)} {\cal S}_n(\theta,\phi)$">|; 

$key = q/r^{-alpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img570.png"
 ALT="$r^{-\alpha}$">|; 

$key = q/r_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1037.png"
 ALT="$r_0$">|; 

$key = q/r_0<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1049.png"
 ALT="$r_0&lt;a$">|; 

$key = q/r_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1034.png"
 ALT="$r_0&gt;0$">|; 

$key = q/r_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img664.png"
 ALT="$r_1$">|; 

$key = q/r_1=(x^{,2}+y^{,2})^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3996.png"
 ALT="$r_1=(x^{ 2}+y^{ 2})^{1/2}$">|; 

$key = q/r_1=mu_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2101.png"
 ALT="$r_1 = \mu_2$">|; 

$key = q/r_1=r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3998.png"
 ALT="$r_1=r$">|; 

$key = q/r_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img665.png"
 ALT="$r_2$">|; 

$key = q/r_2=1-r_1=mu_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2102.png"
 ALT="$r_2=1-r_1=\mu_1$">|; 

$key = q/r_2=d-r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3999.png"
 ALT="$r_2 = d - r \cos\theta$">|; 

$key = q/r_2=d-x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3997.png"
 ALT="$r_2 = d-x$">|; 

$key = q/r_2>r_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img666.png"
 ALT="$r_2&gt; r_1$">|; 

$key = q/r_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3373.png"
 ALT="$r_4$">|; 

$key = q/r_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3380.png"
 ALT="$r_6$">|; 

$key = q/r_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3383.png"
 ALT="$r_8$">|; 

$key = q/r_c+x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img962.png"
 ALT="$r_c+x$">|; 

$key = q/r_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img959.png"
 ALT="$r_c$">|; 

$key = q/r_c=e,d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4002.png"
 ALT="$r_c=e d$">|; 

$key = q/r_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img566.png"
 ALT="$r_i$">|; 

$key = q/r_islashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1682.png"
 ALT="$r_i/r$">|; 

$key = q/r_islashrll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1681.png"
 ALT="$r_i/r\ll 1$">|; 

$key = q/r_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img886.png"
 ALT="$r_p$">|; 

$key = q/r_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3388.png"
 ALT="$r_{11}$">|; 

$key = q/rgeqR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img2737.png"
 ALT="$r\geq R$">|; 

$key = q/rggR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img507.png"
 ALT="$r\gg R$">|; 

$key = q/rho';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1330.png"
 ALT="$\rho'$">|; 

$key = q/rho(a)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4364.png"
 ALT="$\rho(a)=0$">|; 

$key = q/rho(r',theta');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img393.png"
 ALT="$\rho(r',\theta')$">|; 

$key = q/rho(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img554.png"
 ALT="$\rho(r)$">|; 

$key = q/rho(r,theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img445.png"
 ALT="$\rho(r,\theta)$">|; 

$key = q/rho(r,theta)=rho(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4330.png"
 ALT="$\rho(r,\theta)=\rho(a)$">|; 

$key = q/rho(r,theta)=rho_0(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img458.png"
 ALT="$\rho(r,\theta)=\rho_0(r)$">|; 

$key = q/rho({bfr}'),d^{,3}{bfr}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img360.png"
 ALT="$\rho({\bf r}') d^{ 3}{\bf r}'$">|; 

$key = q/rho({bfr}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img361.png"
 ALT="$\rho({\bf r}')$">|; 

$key = q/rho({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img366.png"
 ALT="$\rho({\bf r})$">|; 

$key = q/rho,g,h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img495.png"
 ALT="$\rho g h$">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img28.png"
 ALT="$\rho $">|; 

$key = q/rho<rho_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img321.png"
 ALT="$\rho&lt;\rho_0$">|; 

$key = q/rho_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img320.png"
 ALT="$\rho_0$">|; 

$key = q/rho_0simeq1.3,{rmkg},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2735.png"
 ALT="$\rho_0\simeq 1.3 {\rm kg} {\rm m}^{-3}$">|; 

$key = q/rho_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2343.png"
 ALT="$\rho_1$">|; 

$key = q/rho_1=1+rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2198.png"
 ALT="$\rho_1=1+\rho_2$">|; 

$key = q/rho_1=1-beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2207.png"
 ALT="$\rho_1=1-\beta$">|; 

$key = q/rho_1=1-rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2190.png"
 ALT="$\rho_1=1-\rho_2$">|; 

$key = q/rho_1=[(x+mu_2)^2+y^{,2}]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2335.png"
 ALT="$\rho_1=[(x+\mu_2)^2+y^{ 2}]^{1/2}$">|; 

$key = q/rho_1=rho_2=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2297.png"
 ALT="$\rho_1=\rho_2=1$">|; 

$key = q/rho_1^{,2}=(x+mu_2)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img2284.png"
 ALT="$\rho_1^{ 2} = (x+\mu_2)^2$">|; 

$key = q/rho_1simeq1-beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2352.png"
 ALT="$\rho_1\simeq1-\beta$">|; 

$key = q/rho_1simeqr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2128.png"
 ALT="$\rho_1\simeq r$">|; 

$key = q/rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2193.png"
 ALT="$\rho_2$">|; 

$key = q/rho_2=1+rho_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2205.png"
 ALT="$\rho_2=1+\rho_1$">|; 

$key = q/rho_2=[(x-mu_1)^2+y^{,2}]^{1slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2336.png"
 ALT="$\rho_2=[(x-\mu_1)^2+y^{ 2}]^{1/2}$">|; 

$key = q/rho_2^{,2}=(x-mu_1)^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img2285.png"
 ALT="$\rho_2^{ 2} = (x-\mu_1)^2$">|; 

$key = q/rho_2ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2192.png"
 ALT="$\rho_2\ll 1$">|; 

$key = q/rho_2simeqalpha+alpha^{,2}slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2350.png"
 ALT="$\rho_2\simeq \alpha+\alpha^{ 2}/3$">|; 

$key = q/rho_2simeqalpha-alpha^{,2}slash3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2348.png"
 ALT="$\rho_2\simeq \alpha-\alpha^{ 2}/3$">|; 

$key = q/rho_n(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4341.png"
 ALT="$\rho_n(r)$">|; 

$key = q/rho_n(r)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img448.png"
 ALT="$\rho_n(r)=0$">|; 

$key = q/rhosimeq1times10^3,{rmkg},{rmm}^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.58ex; " SRC="|."$dir".q|img2849.png"
 ALT="$\rho\simeq 1\times 10^3 {\rm kg} {\rm m}^{-3}$">|; 

$key = q/rhoslashbar{rho}<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4372.png"
 ALT="$\rho/\bar{\rho}&lt;1$">|; 

$key = q/rhoslashbar{rho}rightarrowbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4375.png"
 ALT="$\rho/\bar{\rho}\rightarrow \beta$">|; 

$key = q/rleqR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img451.png"
 ALT="$r\leq R$">|; 

$key = q/rleqa;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.22ex; " SRC="|."$dir".q|img4257.png"
 ALT="$r\leq a$">|; 

$key = q/rrightarrowinfty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4241.png"
 ALT="$r\rightarrow \infty$">|; 

$key = q/rsimeqR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1160.png"
 ALT="$r\simeq R$">|; 

$key = q/rslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1231.png"
 ALT="$r/a$">|; 

$key = q/rslasha=(1-e^{,2}),(1+e,costheta)^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2711.png"
 ALT="$r/a= (1-e^{ 2}) (1+e \cos\theta)^{-1}$">|; 

$key = q/rslashr';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img436.png"
 ALT="$r/r'$">|; 

$key = q/rslashr'simaslasha'=1slash389.2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2992.png"
 ALT="$r/r'\sim a/a'=1/389.2$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img914.png"
 ALT="$s$">|; 

$key = q/s=s'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img5013.png"
 ALT="$s=s'=0$">|; 

$key = q/sequivsin(Islash2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5000.png"
 ALT="$s\equiv\sin (I/2)$">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2044.png"
 ALT="$\sigma$">|; 

$key = q/sigma=X,P_2(costheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1170.png"
 ALT="$\sigma=X P_2(\cos\theta)$">|; 

$key = q/sigma_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1172.png"
 ALT="$\sigma_c$">|; 

$key = q/sigma_csimeq2times10^8,{rmN,m^{-2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1175.png"
 ALT="$\sigma_c\simeq 2\times 10^8 {\rm N m^{-2}}$">|; 

$key = q/sigma_{ij}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4261.png"
 ALT="$\sigma_{ij}({\bf r})$">|; 

$key = q/sin(lambda_m-phi),sin(lambda_m-alpha_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1763.png"
 ALT="$\sin(\lambda_m-\phi) \sin(\lambda_m-\alpha_n)$">|; 

$key = q/sinIsimeqI;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img778.png"
 ALT="$\sin I\simeq I$">|; 

$key = q/sin^2(lambda_m-phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1762.png"
 ALT="$\sin^2(\lambda_m-\phi)$">|; 

$key = q/sin^2lambda_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1714.png"
 ALT="$\sin^2\lambda_s$">|; 

$key = q/sin^2phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.45ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1666.png"
 ALT="$\sin^2\phi$">|; 

$key = q/singamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1947.png"
 ALT="$\sin\gamma$">|; 

$key = q/skew{3}bar{varv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img561.png"
 ALT="$\skew{3}\bar{\varv}$">|; 

$key = q/skew{3}ddot{r}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img957.png"
 ALT="$\skew{3}\ddot{r}=0$">|; 

$key = q/skew{3}ddot{x}=mu,(x+a^{,4}slashx^{,3});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img299.png"
 ALT="$\skew{3}\ddot{x}=\mu (x + a^{ 4}/x^{ 3})$">|; 

$key = q/skew{3}dot{mbox{boldmathxi}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2326.png"
 ALT="$\skew{3}\dot{\mbox{\boldmath $\xi$}}$">|; 

$key = q/skew{3}dot{q}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img1400.png"
 ALT="$\skew{3}\dot{q}_i$">|; 

$key = q/skew{3}dot{r}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img658.png"
 ALT="$\skew{3}\dot{r}=0$">|; 

$key = q/skew{3}dot{x};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1441.png"
 ALT="$\skew{3}\dot{x}$">|; 

$key = q/skew{3}dot{x}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1401.png"
 ALT="$\skew{3}\dot{x}_j$">|; 

$key = q/skew{3}dot{x}_j=skew{3}dot{x}_j(skew{3}dot{q}_1,skew{3}dot{q}_2,cdots,skew{3}dot{q}_{calF},q_1,q_2,cdots,q_{calF},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1398.png"
 ALT="$\skew{3}\dot{x}_j = \skew{3}\dot{x}_j(\skew{3}\dot{q}_1,\skew{3}\dot{q}_2,\cdots,
\skew{3}\dot{q}_{\cal F},q_1,q_2,\cdots,q_{\cal F},t)$">|; 

$key = q/skew{3}hat{e},';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2865.png"
 ALT="$\skew{3}\hat{e} '$">|; 

$key = q/skew{3}hat{e},'slashskew{3}hat{e}simeq(4slash5),alpha^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2884.png"
 ALT="$\skew{3}\hat{e} '/\skew{3}\hat{e}\simeq (4/5) \alpha^{-1}$">|; 

$key = q/skew{3}hat{e},'slashskew{3}hat{e}simeq-(5slash4),alpha^{,3slash2}slashq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.56ex; " SRC="|."$dir".q|img2881.png"
 ALT="$\skew{3}\hat{e} '/\skew{3}\hat{e}\simeq -(5/4) \alpha^{ 3/2}/q$">|; 

$key = q/skew{3}hat{e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2864.png"
 ALT="$\skew{3}\hat{e}$">|; 

$key = q/skew{3}hat{g}=gslash[(1slash4),epsilon,n,alpha,b^{(1)}_{3slash2}(alpha)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.07ex; vertical-align: -1.04ex; " SRC="|."$dir".q|img2867.png"
 ALT="$\skew{3}\hat{g}= g/[(1/4) \epsilon n \alpha b^{(1)}_{3/2}(\alpha)]$">|; 

$key = q/skew{3}hat{mbox{boldmathomega}}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1541.png"
 ALT="$\skew{3}\hat{\mbox{\boldmath $\omega$}}_i$">|; 

$key = q/skew{3}hat{nu}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2025.png"
 ALT="$\skew{3}\hat{\nu}_x$">|; 

$key = q/skew{3}hat{nu}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2026.png"
 ALT="$\skew{3}\hat{\nu}_y$">|; 

$key = q/skew{3}hat{nu}_yslashskew{3}hat{nu}_xsimeq-2sqrt{tauslashsigma};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2032.png"
 ALT="$\skew{3}\hat{\nu}_y/\skew{3}\hat{\nu}_x \simeq -2\sqrt{\tau/\sigma}$">|; 

$key = q/skew{3}hat{nu}_yslashskew{3}hat{nu}_xsimeq1-3,tauslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img2030.png"
 ALT="$\skew{3}\hat{\nu}_y/\skew{3}\hat{\nu}_x\simeq 1-3 \tau/2$">|; 

$key = q/skew{3}tilde{epsilon};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1784.png"
 ALT="$\skew{3}\tilde{\epsilon}$">|; 

$key = q/skew{3}tilde{epsilon}=0.00335;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1738.png"
 ALT="$\skew{3}\tilde{\epsilon}=0.00335$">|; 

$key = q/skew{3}tilde{epsilon}=epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4512.png"
 ALT="$\skew{3}\tilde{\epsilon}=\epsilon$">|; 

$key = q/skew{5}barlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2439.png"
 ALT="$\skew{5}\bar\lambda$">|; 

$key = q/skew{5}bar{lambda}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2468.png"
 ALT="$\skew{5}\bar{\lambda}'$">|; 

$key = q/skew{5}bar{lambda}(t)=skew{5}bar{lambda}_0+n^{(0)},t+skew{5}bar{lambda}^{(1)}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2429.png"
 ALT="$\skew{5}\bar{\lambda}(t) = \skew{5}\bar{\lambda}_0+n^{(0)} t + \skew{5}\bar{\lambda}^{(1)}(t)$">|; 

$key = q/skew{5}bar{lambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img798.png"
 ALT="$\skew{5}\bar{\lambda}$">|; 

$key = q/skew{5}bar{lambda}=skew{5}bar{lambda}_0+int_0^tn(t'),dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.18ex; vertical-align: -1.02ex; " SRC="|."$dir".q|img4882.png"
 ALT="$\skew{5}\bar{\lambda}= \skew{5}\bar{\lambda}_0+\int_0^t n(t') dt'$">|; 

$key = q/skew{5}bar{lambda}=varpi+pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img799.png"
 ALT="$\skew{5}\bar{\lambda}= \varpi+\pi$">|; 

$key = q/skew{5}bar{lambda}={mitOmega}+pislash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img802.png"
 ALT="$\skew{5}\bar{\lambda}={\mit\Omega}+\pi/2$">|; 

$key = q/skew{5}bar{lambda}={mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img800.png"
 ALT="$\skew{5}\bar{\lambda}={\mit\Omega}$">|; 

$key = q/skew{5}bar{lambda}^{(0)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4922.png"
 ALT="$\skew{5}\bar{\lambda}^{(0)}$">|; 

$key = q/skew{5}bar{lambda}^{(0)}=skew{5}bar{lambda}_0+n^{(0)},t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4920.png"
 ALT="$\skew{5}\bar{\lambda}^{(0)} = \skew{5}\bar{\lambda}_0+n^{(0)} t$">|; 

$key = q/skew{5}bar{lambda}_0(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img759.png"
 ALT="$\skew{5}\bar{\lambda}_0(^\circ)$">|; 

$key = q/skew{5}bar{lambda}_0+int_0^tn(t'),dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.18ex; vertical-align: -1.02ex; " SRC="|."$dir".q|img4844.png"
 ALT="$\skew{5}\bar{\lambda}_0+\int_0^t n(t') dt'$">|; 

$key = q/skew{5}bar{lambda}_0+n^{(0)},t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2440.png"
 ALT="$\skew{5}\bar{\lambda}_0+n^{(0)} t$">|; 

$key = q/skew{5}bar{lambda}_0-varpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4782.png"
 ALT="$\skew{5}\bar{\lambda}_0-\varpi$">|; 

$key = q/skew{5}bar{lambda}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img754.png"
 ALT="$\skew{5}\bar{\lambda}_0$">|; 

$key = q/skew{5}bar{lambda}_0=varpi-n,tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img756.png"
 ALT="$\skew{5}\bar{\lambda}_0 = \varpi-n \tau$">|; 

$key = q/skew{5}bar{lambda}_{0,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2640.png"
 ALT="$\skew{5}\bar{\lambda}_{0 i}$">|; 

$key = q/skew{5}dot{mitOmega}_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4586.png"
 ALT="$\skew{5}\dot{\mit\Omega}_m$">|; 

$key = q/skew{5}dot{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1468.png"
 ALT="$\skew{5}\dot{\phi}$">|; 

$key = q/skew{5}dot{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1469.png"
 ALT="$\skew{5}\dot{\psi}$">|; 

$key = q/skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img978.png"
 ALT="$\skew{5}\dot{\theta}$">|; 

$key = q/skew{5}dot{theta}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1728.png"
 ALT="$\skew{5}\dot{\theta}=0$">|; 

$key = q/skew{5}dot{theta}=hslashr^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img977.png"
 ALT="$\skew{5}\dot{\theta} = h/r^{ 2}$">|; 

$key = q/sqrt{14,e},alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.33ex; " SRC="|."$dir".q|img1909.png"
 ALT="$\sqrt{14 e} \alpha$">|; 

$key = q/sqrt{2,e},alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.33ex; " SRC="|."$dir".q|img1908.png"
 ALT="$\sqrt{2 e} \alpha$">|; 

$key = q/sqrt{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.32ex; " SRC="|."$dir".q|img670.png"
 ALT="$\sqrt{2}$">|; 

$key = q/sqrt{R,g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.57ex; " SRC="|."$dir".q|img531.png"
 ALT="$\sqrt{R g}$">|; 

$key = q/ssimeq1+3,tauslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2029.png"
 ALT="$s\simeq 1+3 \tau/2$">|; 

$key = q/ssimeq2sqrt{sigma,tau};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.59ex; " SRC="|."$dir".q|img2031.png"
 ALT="$s\simeq 2\sqrt{\sigma \tau}$">|; 

$key = q/stackrel{displaystylerightarrow}{BA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.96ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1229.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{BA}$">|; 

$key = q/stackrel{displaystylerightarrow}{DA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.96ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1227.png"
 ALT="$\stackrel{\displaystyle \rightarrow}{DA}$">|; 

$key = q/t+deltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img610.png"
 ALT="$t+\delta t$">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img83.png"
 ALT="$t$">|; 

$key = q/t=-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img303.png"
 ALT="$t=-\infty$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img86.png"
 ALT="$t=0$">|; 

$key = q/t=T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img3728.png"
 ALT="$t=T$">|; 

$key = q/t=t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img308.png"
 ALT="$t=t_0$">|; 

$key = q/t=tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img674.png"
 ALT="$t=\tau$">|; 

$key = q/t>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img539.png"
 ALT="$t&gt;0$">|; 

$key = q/t_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img134.png"
 ALT="$t_1$">|; 

$key = q/t_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img136.png"
 ALT="$t_2$">|; 

$key = q/tan^{-1}left(1slash!sqrt{8}right)simeq19.5^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.23ex; vertical-align: -1.14ex; " SRC="|."$dir".q|img2079.png"
 ALT="$\tan^{-1}\left(1/\!\sqrt{8}\right)\simeq19.5^\circ$">|; 

$key = q/tau;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img279.png"
 ALT="$\tau$">|; 

$key = q/tau=6.3149times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2069.png"
 ALT="$\tau=6.3149\times 10^{-4}$">|; 

$key = q/tau>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1308.png"
 ALT="$\tau&gt;0$">|; 

$key = q/textbf{emI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1521.png"
 ALT="$\textbf{\em I}$">|; 

$key = q/theta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4172.png"
 ALT="$\theta'$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img12.png"
 ALT="$\theta $">|; 

$key = q/theta<alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1602.png"
 ALT="$\theta&lt;\alpha$">|; 

$key = q/theta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img673.png"
 ALT="$\theta=0$">|; 

$key = q/theta=23.44^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1703.png"
 ALT="$\theta = 23.44^\circ$">|; 

$key = q/theta=90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img512.png"
 ALT="$\theta = 90^\circ$">|; 

$key = q/theta=cos^{-1}(zslashr);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3976.png"
 ALT="$\theta = \cos^{-1}(z/r)$">|; 

$key = q/theta=delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1281.png"
 ALT="$\theta=\delta$">|; 

$key = q/theta=pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2339.png"
 ALT="$\theta=\pi$">|; 

$key = q/theta=pm23.9^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img2340.png"
 ALT="$\theta=\pm 23.9^\circ$">|; 

$key = q/theta=tan^{-1}(yslashx);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img584.png"
 ALT="$\theta=\tan^{-1}(y/x)$">|; 

$key = q/theta=theta(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img617.png"
 ALT="$\theta=\theta(t)$">|; 

$key = q/theta>alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1604.png"
 ALT="$\theta&gt;\alpha$">|; 

$key = q/theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img622.png"
 ALT="$\theta_0$">|; 

$key = q/theta_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img623.png"
 ALT="$\theta_0=0$">|; 

$key = q/theta_0=23.44^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1783.png"
 ALT="$\theta_0=23.44^\circ$">|; 

$key = q/thetarightarrowtheta+2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img735.png"
 ALT="$\theta\rightarrow
\theta+2\pi$">|; 

$key = q/thetasimeqalpha=0.2'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1656.png"
 ALT="$\theta\simeq \alpha = 0.2''$">|; 

$key = q/tilde{mu}'=G,m';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2423.png"
 ALT="$\tilde{\mu}'=G m'$">|; 

$key = q/tilde{mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1350.png"
 ALT="$\tilde{\mu}$">|; 

$key = q/tilde{mu}=G,m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2422.png"
 ALT="$\tilde{\mu} = G m$">|; 

$key = q/tilde{mu}simeq3.35;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1271.png"
 ALT="$\tilde{\mu}\simeq 3.35$">|; 

$key = q/tilde{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4532.png"
 ALT="$\tilde{\omega}$">|; 

$key = q/times(;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1099.png"
 ALT="$\times($">|; 

$key = q/times{bfR});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1100.png"
 ALT="$\times{\bf R})$">|; 

$key = q/times{bfp}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2074.png"
 ALT="$\times {\bf p}=0$">|; 

$key = q/times{bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1119.png"
 ALT="$\times{\bf r})$">|; 

$key = q/times{bfv}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1121.png"
 ALT="$\times{\bf v}'$">|; 

$key = q/trightarrowt+T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img732.png"
 ALT="$t\rightarrow t+T$">|; 

$key = q/tsimeq!sqrt{2,hslashg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.74ex; " SRC="|."$dir".q|img1133.png"
 ALT="$t\simeq \!\sqrt{2 h/g}$">|; 

$key = q/tsimeq12;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img2145.png"
 ALT="$t\simeq 12$">|; 

$key = q/u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img311.png"
 ALT="$u$">|; 

$key = q/u=(r_0,theta^{,2})^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img951.png"
 ALT="$u = (r_0 \theta^{ 2})^{-1}$">|; 

$key = q/u=r^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img653.png"
 ALT="$u=r^{ -1}$">|; 

$key = q/u=u(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img616.png"
 ALT="$u=u(\theta)$">|; 

$key = q/u_c=r_c^{,-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img654.png"
 ALT="$u_c = r_c^{ -1}$">|; 

$key = q/varphi_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1921.png"
 ALT="$\varphi_0$">|; 

$key = q/varpi';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2856.png"
 ALT="$\varpi'$">|; 

$key = q/varpi(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img761.png"
 ALT="$\varpi(^\circ)$">|; 

$key = q/varpi-{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4756.png"
 ALT="$\varpi-{\mit\Omega}$">|; 

$key = q/varpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img15.png"
 ALT="$\varpi $">|; 

$key = q/varpi=102.93^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img820.png"
 ALT="$\varpi=102.93^\circ$">|; 

$key = q/varpi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2549.png"
 ALT="$\varpi_i$">|; 

$key = q/vartheta'=varpi'+theta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4958.png"
 ALT="$\vartheta'=\varpi'+\theta'$">|; 

$key = q/vartheta-vartheta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4969.png"
 ALT="$\vartheta-\vartheta'$">|; 

$key = q/vartheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img2894.png"
 ALT="$\vartheta$">|; 

$key = q/vartheta=cos^{-1}(Zslashr);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2683.png"
 ALT="$\vartheta=\cos^{-1}(Z/r)$">|; 

$key = q/vartheta=varpi+theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img4957.png"
 ALT="$\vartheta = \varpi+\theta$">|; 

$key = q/varv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img312.png"
 ALT="$\varv$">|; 

$key = q/varv=dxslashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img217.png"
 ALT="$\varv=dx/dt$">|; 

$key = q/varv^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img197.png"
 ALT="$\varv^{ 2}$">|; 

$key = q/varv^{,2}=skew{3}dot{x}^{,2}+skew{3}dot{y}^{,2}+skew{3}dot{z}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2173.png"
 ALT="$\varv^{ 2}=\skew{3}\dot{x}^{ 2}+\skew{3}\dot{y}^{ 2}+\skew{3}\dot{z}^{ 2}$">|; 

$key = q/varv^{,2}=sum_{l=1,3}dot{X}_l^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img4705.png"
 ALT="$\varv^{ 2}=\sum_{l=1,3}\dot{X}_l^{ 2}$">|; 

$key = q/varv_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img304.png"
 ALT="$\varv_0$">|; 

$key = q/varv_c=sqrt{G,Mslashr_a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img663.png"
 ALT="$\varv_c=\sqrt{G M/r_a}$">|; 

$key = q/varv_c=sqrt{G,Mslashr_p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.73ex; vertical-align: -0.83ex; " SRC="|."$dir".q|img661.png"
 ALT="$\varv_c=\sqrt{G M/r_p}$">|; 

$key = q/varv_t=r,skew{5}dot{theta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img660.png"
 ALT="$\varv_t=r \skew{5}\dot{\theta}$">|; 

$key = q/varv_{rmesc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img562.png"
 ALT="$\varv_{\rm esc}$">|; 

$key = q/vslashc;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2794.png"
 ALT="$v/c$">|; 

$key = q/vslashcll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2791.png"
 ALT="$v/c\ll 1$">|; 

$key = q/x''';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1614.png"
 ALT="$x'''$">|; 

$key = q/x'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1606.png"
 ALT="$x''$">|; 

$key = q/x',y',z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4710.png"
 ALT="$x', y', z'$">|; 

$key = q/x';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img1105.png"
 ALT="$x'$">|; 

$key = q/x'=r,sintheta,cosphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4448.png"
 ALT="$x'=r \sin\theta \cos\phi$">|; 

$key = q/x'simeq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1131.png"
 ALT="$x'\simeq 0$">|; 

$key = q/x(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3962.png"
 ALT="$x(t)$">|; 

$key = q/x(t=0)=x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img219.png"
 ALT="$x(t=0)=x_0$">|; 

$key = q/x,,y,,z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2146.png"
 ALT="$x, y, z$">|; 

$key = q/x-x_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img209.png"
 ALT="$x-x_0&gt;0$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img49.png"
 ALT="$x$">|; 

$key = q/x=-2,e,a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img4012.png"
 ALT="$x=-2 e a$">|; 

$key = q/x=-mu_2+rho_1=mu_1+rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2197.png"
 ALT="$x = -\mu_2+\rho_1=\mu_1+\rho_2$">|; 

$key = q/x=-mu_2+rho_1=mu_1-rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2189.png"
 ALT="$x = -\mu_2+\rho_1=\mu_1-\rho_2$">|; 

$key = q/x=-mu_2-rho_1=mu_1-rho_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2204.png"
 ALT="$x = -\mu_2-\rho_1=\mu_1-\rho_2$">|; 

$key = q/x=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img229.png"
 ALT="$x=0$">|; 

$key = q/x=a,(1pme^{,2})slashe;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4013.png"
 ALT="$x=a (1\pm e^{ 2})/e$">|; 

$key = q/x=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img291.png"
 ALT="$x=a$">|; 

$key = q/x=d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3994.png"
 ALT="$x=d$">|; 

$key = q/x=pma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.23ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img226.png"
 ALT="$x=\pm a$">|; 

$key = q/x=r,cosbeta,coslambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3167.png"
 ALT="$x=r \cos\beta \cos\lambda$">|; 

$key = q/x=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img741.png"
 ALT="$x=r \cos \theta$">|; 

$key = q/x=x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img205.png"
 ALT="$x=x_0$">|; 

$key = q/x=x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img206.png"
 ALT="$x=x_1$">|; 

$key = q/x=x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img207.png"
 ALT="$x=x_2$">|; 

$key = q/x=y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img905.png"
 ALT="$x=y=0$">|; 

$key = q/x^{,2}+y^{,2}=xi^{,2}+eta^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2323.png"
 ALT="$x^{ 2}+y^{ 2}=\xi^{ 2}+\eta^{ 2}$">|; 

$key = q/x^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.11ex; " SRC="|."$dir".q|img325.png"
 ALT="$x^{ 2}$">|; 

$key = q/x_0=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img221.png"
 ALT="$x_0=0$">|; 

$key = q/x_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3052.png"
 ALT="$x_1'$">|; 

$key = q/x_1,x_2,x_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1375.png"
 ALT="$x_1, x_2, x_3$">|; 

$key = q/x_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3049.png"
 ALT="$x_1$">|; 

$key = q/x_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3582.png"
 ALT="$x_2$">|; 

$key = q/x_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3628.png"
 ALT="$x_3$">|; 

$key = q/x_4,x_5,x_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1376.png"
 ALT="$x_4, x_5, x_6$">|; 

$key = q/x_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3371.png"
 ALT="$x_4$">|; 

$key = q/x_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3460.png"
 ALT="$x_5$">|; 

$key = q/x_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3378.png"
 ALT="$x_6$">|; 

$key = q/x_7;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img3583.png"
 ALT="$x_7$">|; 

$key = q/x_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3382.png"
 ALT="$x_8$">|; 

$key = q/x_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3491.png"
 ALT="$x_9$">|; 

$key = q/x_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4011.png"
 ALT="$x_c$">|; 

$key = q/x_c=r_cslash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4015.png"
 ALT="$x_c = r_c/2$">|; 

$key = q/x_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img540.png"
 ALT="$x_i$">|; 

$key = q/x_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1373.png"
 ALT="$x_j$">|; 

$key = q/x_j=x_j(q_1,q_2,cdots,q_{calF},t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1396.png"
 ALT="$x_j=x_j(q_1,q_2,\cdots, q_{\cal F},t)$">|; 

$key = q/x_{01};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3459.png"
 ALT="$x_{01}$">|; 

$key = q/x_{02};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3581.png"
 ALT="$x_{02}$">|; 

$key = q/x_{03};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3627.png"
 ALT="$x_{03}$">|; 

$key = q/x_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3492.png"
 ALT="$x_{10}$">|; 

$key = q/x_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3386.png"
 ALT="$x_{11}$">|; 

$key = q/x_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3518.png"
 ALT="$x_{12}$">|; 

$key = q/xi,,eta,,zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2090.png"
 ALT="$\xi, \eta, \zeta$">|; 

$key = q/xi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2091.png"
 ALT="$\xi$">|; 

$key = q/xi_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4300.png"
 ALT="$\xi_i$">|; 

$key = q/xslashr_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img963.png"
 ALT="$x/r_c$">|; 

$key = q/xy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1514.png"
 ALT="$xy$">|; 

$key = q/y''';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1615.png"
 ALT="$y'''$">|; 

$key = q/y'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1607.png"
 ALT="$y''$">|; 

$key = q/y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1106.png"
 ALT="$y'$">|; 

$key = q/y'=r,sintheta,sinphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4449.png"
 ALT="$y'=r \sin\theta \sin\phi$">|; 

$key = q/y(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2356.png"
 ALT="$y(t)$">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img50.png"
 ALT="$y$">|; 

$key = q/y=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2188.png"
 ALT="$y=0$">|; 

$key = q/y=r,cosbeta,sinlambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3168.png"
 ALT="$y=r \cos\beta \sin\lambda$">|; 

$key = q/y=r,sintheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img742.png"
 ALT="$y=r \sin \theta$">|; 

$key = q/y_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3053.png"
 ALT="$y_1'$">|; 

$key = q/y_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3050.png"
 ALT="$y_1$">|; 

$key = q/y_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3584.png"
 ALT="$y_2$">|; 

$key = q/y_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3629.png"
 ALT="$y_3$">|; 

$key = q/y_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3372.png"
 ALT="$y_4$">|; 

$key = q/y_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3461.png"
 ALT="$y_5$">|; 

$key = q/y_6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3379.png"
 ALT="$y_6$">|; 

$key = q/y_8;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3493.png"
 ALT="$y_8$">|; 

$key = q/y_9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3494.png"
 ALT="$y_9$">|; 

$key = q/y_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img548.png"
 ALT="$y_i$">|; 

$key = q/y_{10};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3495.png"
 ALT="$y_{10}$">|; 

$key = q/y_{11};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3387.png"
 ALT="$y_{11}$">|; 

$key = q/y_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3519.png"
 ALT="$y_{12}$">|; 

$key = q/y_{7};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3585.png"
 ALT="$y_{7}$">|; 

$key = q/yz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1516.png"
 ALT="$yz$">|; 

$key = q/z''';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1616.png"
 ALT="$z'''$">|; 

$key = q/z'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1608.png"
 ALT="$z''$">|; 

$key = q/z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1104.png"
 ALT="$z'$">|; 

$key = q/z'=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img4450.png"
 ALT="$z'=r \cos\theta$">|; 

$key = q/z(-t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2361.png"
 ALT="$z(-t)]$">|; 

$key = q/z(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3963.png"
 ALT="$z(t)$">|; 

$key = q/z(t)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2357.png"
 ALT="$z(t)]$">|; 

$key = q/z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1677.png"
 ALT="$z)$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.17ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img80.png"
 ALT="$z$">|; 

$key = q/z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img743.png"
 ALT="$z=0$">|; 

$key = q/z=R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1322.png"
 ALT="$z=R$">|; 

$key = q/z=r,costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.27ex; " SRC="|."$dir".q|img1220.png"
 ALT="$z=r \cos\theta$">|; 

$key = q/z=r,sinbeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3169.png"
 ALT="$z=r \sin\beta$">|; 

$key = q/z_1';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.77ex; " SRC="|."$dir".q|img3054.png"
 ALT="$z_1'$">|; 

$key = q/z_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3051.png"
 ALT="$z_1$">|; 

$key = q/z_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3630.png"
 ALT="$z_2$">|; 

$key = q/z_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3631.png"
 ALT="$z_3$">|; 

$key = q/z_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.28ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img3390.png"
 ALT="$z_4$">|; 

$key = q/z_5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3612.png"
 ALT="$z_5$">|; 

$key = q/z_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.34ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img549.png"
 ALT="$z_i$">|; 

$key = q/zeta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4959.png"
 ALT="$\zeta'$">|; 

$key = q/zeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1164.png"
 ALT="$\zeta$">|; 

$key = q/zeta<zeta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1184.png"
 ALT="$\zeta&lt;\zeta_c$">|; 

$key = q/zeta=-2.55times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1261.png"
 ALT="$\zeta=-2.55\times 10^{-8}$">|; 

$key = q/zeta=-5.62times10^{-8};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1272.png"
 ALT="$\zeta=-5.62\times 10^{-8}$">|; 

$key = q/zeta>zeta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1188.png"
 ALT="$\zeta&gt;\zeta_c$">|; 

$key = q/zeta^{,3slash2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3695.png"
 ALT="$\zeta^{ 3/2}$">|; 

$key = q/zetall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1161.png"
 ALT="$\zeta\ll 1$">|; 

$key = q/{bf1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4076.png"
 ALT="${\bf 1}$">|; 

$key = q/{bfA}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3942.png"
 ALT="${\bf A}({\bf r})$">|; 

$key = q/{bfA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img3944.png"
 ALT="${\bf A}$">|; 

$key = q/{bfA}=nablaV;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img3945.png"
 ALT="${\bf A} = \nabla V$">|; 

$key = q/{bfA}^T,{bfA}={bf1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2319.png"
 ALT="${\bf A}^T {\bf A} = {\bf 1}$">|; 

$key = q/{bfA}^T={bfA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4072.png"
 ALT="${\bf A}^T = {\bf A}$">|; 

$key = q/{bfA}^ast={bfA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img4071.png"
 ALT="${\bf A}^\ast = {\bf A}$">|; 

$key = q/{bfF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img288.png"
 ALT="${\bf F}$">|; 

$key = q/{bfF}=F_r,{bfe}_r+F_theta,{bfe}_theta+F_z,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2821.png"
 ALT="${\bf F} = F_r {\bf e}_r+F_\theta {\bf e}_\theta+F_z {\bf e}_z$">|; 

$key = q/{bfF}=sum_{i=1,N}{bfF}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img1488.png"
 ALT="${\bf F} = \sum_{i=1,N} {\bf F}_i$">|; 

$key = q/{bfF}={bfF}_1+{bfF}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img287.png"
 ALT="${\bf F} = {\bf F}_1+{\bf F}_2$">|; 

$key = q/{bfF}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img285.png"
 ALT="${\bf F}_1$">|; 

$key = q/{bfF}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img286.png"
 ALT="${\bf F}_2$">|; 

$key = q/{bfF}_A+{bfF}_B+{bfF}_C={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img290.png"
 ALT="${\bf F}_A+{\bf F}_B+{\bf F}_C = {\bf0}$">|; 

$key = q/{bfF}_C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img289.png"
 ALT="${\bf F}_C$">|; 

$key = q/{bfF}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img182.png"
 ALT="${\bf F}_i$">|; 

$key = q/{bfF}_{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img282.png"
 ALT="${\bf F}_{A}$">|; 

$key = q/{bfF}_{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img283.png"
 ALT="${\bf F}_{B}$">|; 

$key = q/{bfF}_{B}=-{bfF}_{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img284.png"
 ALT="${\bf F}_{B}= -{\bf F}_{A}$">|; 

$key = q/{bfF}_{rmPR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img2820.png"
 ALT="${\bf F}_{\rm PR}$">|; 

$key = q/{bfF}_{rmrad};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2819.png"
 ALT="${\bf F}_{\rm rad}$">|; 

$key = q/{bfL};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img32.png"
 ALT="${\bf L}$">|; 

$key = q/{bfL}=sum_{i=1,N}m_i,{bfr}_itimesd{bfr}_islashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img1489.png"
 ALT="${\bf L}=\sum_{i=1,N} m_i {\bf r}_i\times d{\bf r}_i/dt$">|; 

$key = q/{bfL}=textbf{emI},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1550.png"
 ALT="${\bf L} = \textbf{\em I} $">|; 

$key = q/{bfP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img168.png"
 ALT="${\bf P}$">|; 

$key = q/{bfP}_{rmabs}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img2798.png"
 ALT="${\bf P}_{\rm abs}'$">|; 

$key = q/{bfP}_{rmem}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.12ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2800.png"
 ALT="${\bf P}_{\rm em}'$">|; 

$key = q/{bfR}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2398.png"
 ALT="${\bf R}'$">|; 

$key = q/{bfR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1095.png"
 ALT="${\bf R}$">|; 

$key = q/{bfR}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2397.png"
 ALT="${\bf R}_s$">|; 

$key = q/{bfa}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img105.png"
 ALT="${\bf a}'$">|; 

$key = q/{bfa}'=d^{,2}{bfr}slashdt'^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1083.png"
 ALT="${\bf a}'= d^{ 2}{\bf r}/dt'^{ 2}$">|; 

$key = q/{bfa}'={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img114.png"
 ALT="${\bf a}'= {\bf0}$">|; 

$key = q/{bfa}'neq{bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.21ex; " SRC="|."$dir".q|img117.png"
 ALT="${\bf a}'\neq{\bf0}$">|; 

$key = q/{bfa};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1228.png"
 ALT="${\bf a}$">|; 

$key = q/{bfa}=a_x,{bfe}_x+a_y,{bfe}_y+a_x,{bfe}_z=(a_x,,a_y,,a_z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3922.png"
 ALT="${\bf a} = a_x {\bf e}_x+a_y {\bf e}_y+a_x {\bf e}_z= (a_x, a_y, a_z)$">|; 

$key = q/{bfa}=d^{,2}{bfr}slashdt^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1082.png"
 ALT="${\bf a}= d^{ 2}{\bf r}/dt^{ 2}$">|; 

$key = q/{bfa}=d{bfv}slashdtequiv(dvarv_xslashdt,,dvarv_yslashdt,,dvarv_zslashdt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img104.png"
 ALT="${\bf a} = d{\bf v}/dt \equiv (d\varv_x/dt, d\varv_y/dt, d\varv_z/dt)$">|; 

$key = q/{bfa}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img113.png"
 ALT="${\bf a}={\bf0}$">|; 

$key = q/{bfb};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3919.png"
 ALT="${\bf b}$">|; 

$key = q/{bfc};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3920.png"
 ALT="${\bf c}$">|; 

$key = q/{bfd};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3921.png"
 ALT="${\bf d}$">|; 

$key = q/{bfe};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img874.png"
 ALT="${\bf e}$">|; 

$key = q/{bfe}=e,{bfe}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4148.png"
 ALT="${\bf e}= e {\bf e}_x$">|; 

$key = q/{bfe}_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3980.png"
 ALT="${\bf e}_\phi$">|; 

$key = q/{bfe}_phi=nablaphislash|nablaphi|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img3979.png"
 ALT="${\bf e}_\phi = \nabla\phi/\vert\nabla\phi\vert$">|; 

$key = q/{bfe}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img587.png"
 ALT="${\bf e}_r$">|; 

$key = q/{bfe}_r=(costheta,,sintheta,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5083.png"
 ALT="${\bf e}_r=(\cos\theta, \sin\theta, 0)$">|; 

$key = q/{bfe}_r=nablarslash|nablar|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3969.png"
 ALT="${\bf e}_r=\nabla r/\vert\nabla r\vert$">|; 

$key = q/{bfe}_requiv{bfr}slashr;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img585.png"
 ALT="${\bf e}_r\equiv {\bf r}/r$">|; 

$key = q/{bfe}_theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img588.png"
 ALT="${\bf e}_\theta$">|; 

$key = q/{bfe}_theta=(-sintheta,,costheta,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img5084.png"
 ALT="${\bf e}_\theta = (-\sin\theta, \cos\theta, 0)$">|; 

$key = q/{bfe}_theta=nablathetaslash|nablatheta|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3970.png"
 ALT="${\bf e}_\theta = \nabla\theta/\vert\nabla\theta\vert$">|; 

$key = q/{bfe}_thetaequiv{bfe}_ztimes{bfe}_r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img586.png"
 ALT="${\bf e}_\theta\equiv {\bf e}_z\times {\bf e}_r$">|; 

$key = q/{bfe}_x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1545.png"
 ALT="${\bf e}_x$">|; 

$key = q/{bfe}_y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1546.png"
 ALT="${\bf e}_y$">|; 

$key = q/{bfe}_z!cdot!{bfe}_{z'}=costheta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1631.png"
 ALT="${\bf e}_z\!\cdot\!{\bf e}_{z'} =\cos\theta$">|; 

$key = q/{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1547.png"
 ALT="${\bf e}_z$">|; 

$key = q/{bfe}_{x'''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1617.png"
 ALT="${\bf e}_{x'''}$">|; 

$key = q/{bfe}_{x''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1609.png"
 ALT="${\bf e}_{x''}$">|; 

$key = q/{bfe}_{x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1622.png"
 ALT="${\bf e}_{x'}$">|; 

$key = q/{bfe}_{y'''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1618.png"
 ALT="${\bf e}_{y'''}$">|; 

$key = q/{bfe}_{y''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1610.png"
 ALT="${\bf e}_{y''}$">|; 

$key = q/{bfe}_{y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1623.png"
 ALT="${\bf e}_{y'}$">|; 

$key = q/{bfe}_{z'''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1619.png"
 ALT="${\bf e}_{z'''}$">|; 

$key = q/{bfe}_{z'''}={bfe}_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1625.png"
 ALT="${\bf e}_{z'''}={\bf e}_{z'}$">|; 

$key = q/{bfe}_{z''};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1611.png"
 ALT="${\bf e}_{z''}$">|; 

$key = q/{bfe}_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img31.png"
 ALT="${\bf e}_{z'}$">|; 

$key = q/{bfe}_{z'}cdot{bfL}times;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1600.png"
 ALT="${\bf e}_{z'}\cdot{\bf L}\times$">|; 

$key = q/{bff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img121.png"
 ALT="${\bf f}$">|; 

$key = q/{bff}=-nablaU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img335.png"
 ALT="${\bf f}=-\nabla U$">|; 

$key = q/{bff}=m,{bfg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1092.png"
 ALT="${\bf f}= m {\bf g}$">|; 

$key = q/{bff}={bff}_1+{bff}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img128.png"
 ALT="${\bf f} = {\bf f}_1+{\bf f}_2$">|; 

$key = q/{bff}={bff}_{21};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img264.png"
 ALT="${\bf f} = {\bf f}_{21}$">|; 

$key = q/{bff}_1+{bff}_2={bff};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img129.png"
 ALT="${\bf f}_1+{\bf f}_2={\bf f}$">|; 

$key = q/{bff}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img126.png"
 ALT="${\bf f}_1$">|; 

$key = q/{bff}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img127.png"
 ALT="${\bf f}_2$">|; 

$key = q/{bff}_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img340.png"
 ALT="${\bf f}_{12}$">|; 

$key = q/{bff}_{12}=-{bff}_{21};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img259.png"
 ALT="${\bf f}_{12} = -{\bf f}_{21}$">|; 

$key = q/{bff}_{21};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img258.png"
 ALT="${\bf f}_{21}$">|; 

$key = q/{bff}_{21}=-{bff}_{12};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img342.png"
 ALT="${\bf f}_{21}=-{\bf f}_{12}$">|; 

$key = q/{bff}_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img155.png"
 ALT="${\bf f}_{ij}$">|; 

$key = q/{bff}_{ij}=-{bff}_{ji};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1486.png"
 ALT="${\bf f}_{ij} = - {\bf f}_{ji}$">|; 

$key = q/{bff}_{ji};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img153.png"
 ALT="${\bf f}_{ji}$">|; 

$key = q/{bff}propto{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img338.png"
 ALT="${\bf f}\propto {\bf r}$">|; 

$key = q/{bfg};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img347.png"
 ALT="${\bf g}$">|; 

$key = q/{bfg}={bfg}_g+{bfg}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1149.png"
 ALT="${\bf g} = {\bf g}_g + {\bf g}_c$">|; 

$key = q/{bfg}_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1151.png"
 ALT="${\bf g}_c$">|; 

$key = q/{bfg}_c=-nablachi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1155.png"
 ALT="${\bf g}_c = - \nabla\chi$">|; 

$key = q/{bfg}_g=-nabla{mitPhi}(r,theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1150.png"
 ALT="${\bf g}_g=-\nabla{\mit\Phi}(r,\theta)$">|; 

$key = q/{bfh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img581.png"
 ALT="${\bf h}$">|; 

$key = q/{bfh}=h,{bfe}_z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4147.png"
 ALT="${\bf h} = h {\bf e}_z$">|; 

$key = q/{bfh}={bfr}timesdot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img871.png"
 ALT="${\bf h} = {\bf r}\times \dot{\bf r}$">|; 

$key = q/{bfh}={bfr}timesskew{2}dot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img4140.png"
 ALT="${\bf h} = {\bf r}\times\skew{2}\dot{\bf r}$">|; 

$key = q/{bfh}equiv{bfr}timesdot{bfr}={bf0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img868.png"
 ALT="${\bf h}\equiv {\bf r}\times\dot{\bf r}={\bf0}$">|; 

$key = q/{bfp}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2785.png"
 ALT="${\bf p}'$">|; 

$key = q/{bfp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img123.png"
 ALT="${\bf p}$">|; 

$key = q/{bfp}_i=m_i,d{bfr}_islashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img166.png"
 ALT="${\bf p}_i = m_i d{\bf r}_i/dt$">|; 

$key = q/{bfr}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img346.png"
 ALT="${\bf r}'$">|; 

$key = q/{bfr}'=(x',,y',,z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img351.png"
 ALT="${\bf r}' = (x', y', z')$">|; 

$key = q/{bfr}'={bfR}'-{bfR}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2401.png"
 ALT="${\bf r}'={\bf R}'-{\bf R}_s$">|; 

$key = q/{bfr}'equiv(x',,y',,z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img87.png"
 ALT="${\bf r}'\equiv (x', y', z')$">|; 

$key = q/{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img140.png"
 ALT="${\bf r}$">|; 

$key = q/{bfr}=(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img350.png"
 ALT="${\bf r}=(x,  y,  z)$">|; 

$key = q/{bfr}=(xi,,eta,,zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2105.png"
 ALT="${\bf r} = (\xi, \eta, \zeta)$">|; 

$key = q/{bfr}={bfR}-{bfR}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2400.png"
 ALT="${\bf r} = {\bf R}-{\bf R}_s$">|; 

$key = q/{bfr}={bfr}_2-{bfr}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img271.png"
 ALT="${\bf r}= {\bf r}_2-{\bf r}_1$">|; 

$key = q/{bfr}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img256.png"
 ALT="${\bf r}_1$">|; 

$key = q/{bfr}_1=(-mu_2,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2147.png"
 ALT="${\bf r}_1=(-\mu_2, 0, 0)$">|; 

$key = q/{bfr}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.39ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img257.png"
 ALT="${\bf r}_2$">|; 

$key = q/{bfr}_2=(mu_1,,0,,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2148.png"
 ALT="${\bf r}_2=(\mu_1, 0, 0)$">|; 

$key = q/{bfr}_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img373.png"
 ALT="${\bf r}_3$">|; 

$key = q/{bfr}_i-{bfr}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img178.png"
 ALT="${\bf r}_i-{\bf r}_j$">|; 

$key = q/{bfr}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img152.png"
 ALT="${\bf r}_i$">|; 

$key = q/{bfr}_itimes;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img187.png"
 ALT="${\bf r}_i\times$">|; 

$key = q/{bfr}_itimes{bff}_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img175.png"
 ALT="${\bf r}_i\times {\bf f}_{ij}$">|; 

$key = q/{bfr}_jtimes{bff}_{ji};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img176.png"
 ALT="${\bf r}_j\times {\bf f}_{ji}$">|; 

$key = q/{bfr}_m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1745.png"
 ALT="${\bf r}_m$">|; 

$key = q/{bfr}_s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1708.png"
 ALT="${\bf r}_s$">|; 

$key = q/{bfr}_{cm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img163.png"
 ALT="${\bf r}_{cm}$">|; 

$key = q/{bfr}equiv(x,,y,,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img82.png"
 ALT="${\bf r}\equiv (x, y, z)$">|; 

$key = q/{bfr}equiv(x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1676.png"
 ALT="${\bf r}\equiv (x$">|; 

$key = q/{bfr}simeq{bfR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1096.png"
 ALT="${\bf r}\simeq {\bf R}$">|; 

$key = q/{bfu}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img116.png"
 ALT="${\bf u}(t)$">|; 

$key = q/{bfu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img84.png"
 ALT="${\bf u}$">|; 

$key = q/{bfu}equiv(u,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img85.png"
 ALT="${\bf u} \equiv (u,0,0)$">|; 

$key = q/{bfv}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img96.png"
 ALT="${\bf v}'$">|; 

$key = q/{bfv}'=d{bfr}slashdt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1076.png"
 ALT="${\bf v}' = d{\bf r}/dt'$">|; 

$key = q/{bfv};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img124.png"
 ALT="${\bf v}$">|; 

$key = q/{bfv}=dot{bfr};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img942.png"
 ALT="${\bf v}=\dot{\bf r}$">|; 

$key = q/{bfv}=d{bfr}slashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img138.png"
 ALT="${\bf v} = d{\bf r}/dt$">|; 

$key = q/{bfv}=d{bfr}slashdtequiv(dxslashdt,,dyslashdt,,dzslashdt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img95.png"
 ALT="${\bf v} = d{\bf r}/dt \equiv (dx/dt, dy/dt, dz/dt)$">|; 

$key = q/{bfv}_i=d{bfr}_islashdt;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img1494.png"
 ALT="${\bf v}_i = d{\bf r}_i/dt$">|; 

$key = q/{bfw};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.12ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1973.png"
 ALT="${\bf w}$">|; 

$key = q/{bfx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.06ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2317.png"
 ALT="${\bf x}$">|; 

$key = q/{bfx}^T,{bfx}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img2321.png"
 ALT="${\bf x}^T {\bf x}=$">|; 

$key = q/{bfx}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.45ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4081.png"
 ALT="${\bf x}_i$">|; 

$key = q/{bfx}_i^T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img4095.png"
 ALT="${\bf x}_i^T$">|; 

$key = q/{bfx}_i^T{bfx}_j=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img4100.png"
 ALT="${\bf x}_i^T{\bf x}_j = 0$">|; 

$key = q/{bfx}_i^{,ast}cdot{bfx}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img4088.png"
 ALT="${\bf x}_i^{ \ast}\cdot{\bf x}_i$">|; 

$key = q/{bfx}_i^{ast,T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img4082.png"
 ALT="${\bf x}_i^{\ast T}$">|; 

$key = q/{bfx}_i^{ast,T}{bfx}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img4087.png"
 ALT="${\bf x}_i^{\ast T}{\bf x}_i$">|; 

$key = q/{bfx}_icdot{bfx}_j=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4101.png"
 ALT="${\bf x}_i \cdot{\bf x}_j=0$">|; 

$key = q/{bfx}_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4094.png"
 ALT="${\bf x}_j$">|; 

$key = q/{calC};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4428.png"
 ALT="${\cal C}$">|; 

$key = q/{calC}=0.25;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4437.png"
 ALT="${\cal C} = 0.25$">|; 

$key = q/{calC}=0.331;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4429.png"
 ALT="${\cal C} = 0.331$">|; 

$key = q/{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img35.png"
 ALT="${\cal E}$">|; 

$key = q/{calE}<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1900.png"
 ALT="${\cal E}&lt;1$">|; 

$key = q/{calE}=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1901.png"
 ALT="${\cal E}=-1$">|; 

$key = q/{calE}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1898.png"
 ALT="${\cal E}=1$">|; 

$key = q/{calE}=G,M,(e-1)slash(2,r_p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img678.png"
 ALT="${\cal E} = G M (e-1)/(2 r_p)$">|; 

$key = q/{calE}>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.13ex; " SRC="|."$dir".q|img1899.png"
 ALT="${\cal E}&gt;1$">|; 

$key = q/{calE}_{rmabs}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.81ex; " SRC="|."$dir".q|img2797.png"
 ALT="${\cal E}_{\rm abs}'$">|; 

$key = q/{calE}_{rmem}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.66ex; " SRC="|."$dir".q|img2799.png"
 ALT="${\cal E}_{\rm em}'$">|; 

$key = q/{calF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.24ex; " SRC="|."$dir".q|img1371.png"
 ALT="${\cal F}$">|; 

$key = q/{calF}=3,N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.73ex; vertical-align: -0.24ex; " SRC="|."$dir".q|img1372.png"
 ALT="${\cal F}= 3 N$">|; 

$key = q/{calI};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img553.png"
 ALT="${\cal I}$">|; 

$key = q/{calI}=sum_{i=1,N}m_i,r_i^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img551.png"
 ALT="${\cal I}=\sum_{i=1,N} m_i  r_i^{ 2}$">|; 

$key = q/{calI}=summ_i,r_i^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.51ex; vertical-align: -0.76ex; " SRC="|."$dir".q|img565.png"
 ALT="${\cal I}=\sum m_i r_i^{ 2}$">|; 

$key = q/{calI}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img569.png"
 ALT="${\cal I}_0$">|; 

$key = q/{calI}_0=(2slash5),M,R^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1661.png"
 ALT="${\cal I}_0 = (2/5) M R^{ 2}$">|; 

$key = q/{calI}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1288.png"
 ALT="${\cal I}_\parallel$">|; 

$key = q/{calI}_parallel<{calI}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1646.png"
 ALT="${\cal I}_\parallel&lt;{\cal I}_\perp$">|; 

$key = q/{calI}_parallel=(2slash5),m,R^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1289.png"
 ALT="${\cal I}_\parallel=(2/5) m R^{ 2}$">|; 

$key = q/{calI}_parallelslash(M,R^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img4608.png"
 ALT="${\cal I}_\parallel/(M R^{ 2})$">|; 

$key = q/{calI}_parallelslashM,R^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.40ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img4606.png"
 ALT="${\cal I}_\parallel/M R^{ 2}$">|; 

$key = q/{calI}_parallelslash{calI}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img2078.png"
 ALT="${\cal I}_\parallel/{\cal I}_\perp$">|; 

$key = q/{calI}_parallelslash{calI}_perp=1slash(1-skew{3}tilde{epsilon})=1.003284;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1652.png"
 ALT="${\cal I}_\parallel/{\cal I}_\perp=1/(1-\skew{3}\tilde{\epsilon})=1.003284$">|; 

$key = q/{calI}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.43ex; " SRC="|."$dir".q|img1467.png"
 ALT="${\cal I}_\perp$">|; 

$key = q/{calI}_perp<{calI}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1603.png"
 ALT="${\cal I}_\perp&lt; {\cal I}_\parallel$">|; 

$key = q/{calI}_perp>{calI}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1605.png"
 ALT="${\cal I}_\perp&gt;{\cal I}_\parallel$">|; 

$key = q/{calI}_perpneq{calI}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1572.png"
 ALT="${\cal I}_\perp\neq {\cal I}_\parallel$">|; 

$key = q/{calI}_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1517.png"
 ALT="${\cal I}_{ij}$">|; 

$key = q/{calI}_{ij}^{,ast}={calI}_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -1.06ex; " SRC="|."$dir".q|img1522.png"
 ALT="${\cal I}_{ij}^{ \ast} = {\cal I}_{ij}$">|; 

$key = q/{calI}_{ji}={calI}_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1523.png"
 ALT="${\cal I}_{ji} = {\cal I}_{ij}$">|; 

$key = q/{calI}_{x'x'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1560.png"
 ALT="${\cal I}_{x'x'}$">|; 

$key = q/{calI}_{x'x'}={calI}_{y'y'}={calI}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1570.png"
 ALT="${\cal I}_{x'x'} = {\cal I}_{y'y'} = {\cal I}_\perp$">|; 

$key = q/{calI}_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img1511.png"
 ALT="${\cal I}_{xx}$">|; 

$key = q/{calI}_{xx}={calI}_{yy}={calI}_perp;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1695.png"
 ALT="${\cal I}_{xx}={\cal I}_{yy}={\cal I}_\perp$">|; 

$key = q/{calI}_{xy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1513.png"
 ALT="${\cal I}_{xy}$">|; 

$key = q/{calI}_{y'y'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1561.png"
 ALT="${\cal I}_{y'y'}$">|; 

$key = q/{calI}_{yy};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1512.png"
 ALT="${\cal I}_{yy}$">|; 

$key = q/{calI}_{yy}>{calI}_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1904.png"
 ALT="${\cal I}_{yy}&gt;{\cal I}_{xx}$">|; 

$key = q/{calI}_{yz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1515.png"
 ALT="${\cal I}_{yz}$">|; 

$key = q/{calI}_{z'z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1562.png"
 ALT="${\cal I}_{z'z'}$">|; 

$key = q/{calI}_{z'z'}={calI}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1571.png"
 ALT="${\cal I}_{z'z'} = {\cal I}_\parallel$">|; 

$key = q/{calI}_{zz};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1548.png"
 ALT="${\cal I}_{zz}$">|; 

$key = q/{calI}_{zz}={calI}_parallel;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1696.png"
 ALT="${\cal I}_{zz}= {\cal I}_\parallel$">|; 

$key = q/{calI}_{zz}>{calI}_{yy}>{calI}_{xx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1821.png"
 ALT="${\cal I}_{zz}&gt;{\cal I}_{yy}&gt;{\cal I}_{xx}$">|; 

$key = q/{calL};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.28ex; " SRC="|."$dir".q|img1413.png"
 ALT="${\cal L}$">|; 

$key = q/{calL}=K-U;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.28ex; " SRC="|."$dir".q|img1440.png"
 ALT="${\cal L}=K-U$">|; 

$key = q/{calM}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4194.png"
 ALT="${\cal M}'$">|; 

$key = q/{calM}'=0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img3500.png"
 ALT="${\cal M}'=0^\circ$">|; 

$key = q/{calM}'=90^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img3499.png"
 ALT="${\cal M}'=90^\circ$">|; 

$key = q/{calM};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img1860.png"
 ALT="${\cal M}$">|; 

$key = q/{calM}=(G,Mslash2,r_p^{,3})^{1slash2},(t-tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.68ex; vertical-align: -0.95ex; " SRC="|."$dir".q|img902.png"
 ALT="${\cal M} = (G M/2 r_p^{ 3})^{1/2} (t-\tau)$">|; 

$key = q/{calM}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img695.png"
 ALT="${\cal M}=0$">|; 

$key = q/{calM}=n,(t-tau);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2691.png"
 ALT="${\cal M} = n (t-\tau)$">|; 

$key = q/{calM}=pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img696.png"
 ALT="${\cal M} = \pi$">|; 

$key = q/{calM}=skew{5}bar{lambda}-varpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img4877.png"
 ALT="${\cal M} = \skew{5}\bar{\lambda}-\varpi$">|; 

$key = q/{calM}=skew{5}bar{lambda}_0-varpi+n,t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4762.png"
 ALT="${\cal M}=\skew{5}\bar{\lambda}_0-\varpi+ n t$">|; 

$key = q/{calM}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img2752.png"
 ALT="${\cal M}_0$">|; 

$key = q/{calM}_0={calM}(t)-int_0^tn(t'),dt';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 3.18ex; vertical-align: -1.02ex; " SRC="|."$dir".q|img5151.png"
 ALT="${\cal M}_0 = {\cal M}(t) -\int_0^t n(t') dt'$">|; 

$key = q/{calM}rightarrow{calM}+2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.67ex; vertical-align: -0.20ex; " SRC="|."$dir".q|img733.png"
 ALT="${\cal M}\rightarrow {\cal M}+2\pi$">|; 

$key = q/{calO}(1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img506.png"
 ALT="${\cal O}(1)$">|; 

$key = q/{calO}(I^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3634.png"
 ALT="${\cal O}(I^{ 2})$">|; 

$key = q/{calO}(e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4930.png"
 ALT="${\cal O}(e)$">|; 

$key = q/{calO}(e,I);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3635.png"
 ALT="${\cal O}(e I)$">|; 

$key = q/{calO}(e^n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4935.png"
 ALT="${\cal O}(e^n)$">|; 

$key = q/{calO}(e^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img1865.png"
 ALT="${\cal O}(e^{ 2})$">|; 

$key = q/{calO}(e^{,n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4927.png"
 ALT="${\cal O}(e^{ n})$">|; 

$key = q/{calO}(epsilon',e,n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2511.png"
 ALT="${\cal O}(\epsilon' e n)$">|; 

$key = q/{calO}(epsilon,e,n');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2534.png"
 ALT="${\cal O}(\epsilon e n')$">|; 

$key = q/{calO}(m);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3366.png"
 ALT="${\cal O}(m)$">|; 

$key = q/{calO}(m^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3367.png"
 ALT="${\cal O}(m^{ 2})$">|; 

$key = q/{calO}(m^{,2},I);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3615.png"
 ALT="${\cal O}(m^{ 2} I)$">|; 

$key = q/{calO}(m^{,2},aslasha');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3522.png"
 ALT="${\cal O}(m^{ 2} a/a')$">|; 

$key = q/{calO}(m^{,2},e');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3498.png"
 ALT="${\cal O}(m^{ 2} e')$">|; 

$key = q/{calO}(m^{,2},e);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3590.png"
 ALT="${\cal O}(m^{ 2} e)$">|; 

$key = q/{calO}(m^{,4});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3464.png"
 ALT="${\cal O}(m^{ 4})$">|; 

$key = q/{calR}'({bfr},{bfr}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2425.png"
 ALT="${\cal R}'({\bf r}, {\bf r}')$">|; 

$key = q/{calR}(r,vartheta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2690.png"
 ALT="${\cal R}(r,\vartheta)$">|; 

$key = q/{calR}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4627.png"
 ALT="${\cal R}({\bf r})$">|; 

$key = q/{calR}({bfr},{bfr}');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2424.png"
 ALT="${\cal R}({\bf r},{\bf r}')$">|; 

$key = q/{calR};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img2707.png"
 ALT="${\cal R}$">|; 

$key = q/{calR}_n(r,theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4213.png"
 ALT="${\cal R}_n(r,\theta,\phi)$">|; 

$key = q/{calS}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img4932.png"
 ALT="${\cal S}'$">|; 

$key = q/{calS}'={calS}_0'+{calS}_1'+{calS}_2';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.79ex; " SRC="|."$dir".q|img5075.png"
 ALT="${\cal S}'={\cal S}_0'+{\cal S}_1'+{\cal S}_2'$">|; 

$key = q/{calS};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.15ex; " SRC="|."$dir".q|img4884.png"
 ALT="${\cal S}$">|; 

$key = q/{calS}={calS}_0+{calS}_1+{calS}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img5068.png"
 ALT="${\cal S}={\cal S}_0+{\cal S}_1+{\cal S}_2$">|; 

$key = q/{calS}_n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.65ex; " SRC="|."$dir".q|img4934.png"
 ALT="${\cal S}_n'$">|; 

$key = q/{calS}_n(theta,phi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4208.png"
 ALT="${\cal S}_n(\theta,\phi)$">|; 

$key = q/{calS}_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img4926.png"
 ALT="${\cal S}_n$">|; 

$key = q/{calT}_J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img52.png"
 ALT="${\cal T}_J$">|; 

$key = q/{cal}O(e'^{,2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img3036.png"
 ALT="${\cal }O(e'^{ 2})$">|; 

$key = q/{displaymath}alpha_{ij}=left{{array}{ccc}a_islasha_j&mbox{hspace{1cm}}&a_j>a_i[0.5ex]a_jslasha_i&&a_j<a_i{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; " SRC="|."$dir".q|img2556.png"
 ALT="\begin{displaymath}\alpha_{ij} =\left\{
\begin{array}{ccc}
a_i/a_j&amp;\mbox{\hspace{1cm}}&amp;a_j&gt;a_i\ [0.5ex]
a_j/a_i&amp;&amp;a_j&lt;a_i
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}alpha_{i}=left{{array}{ccc}aslasha_i&mbox{hspace{1cm}}&a_i>a[0.5ex]a_islasha&&a_i<a{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img2641.png"
 ALT="\begin{displaymath}\alpha_{i} =\left\{
\begin{array}{ccc}
a/a_i&amp;\mbox{\hspace{1cm}}&amp;a_i&gt;a\ [0.5ex]
a_i/a&amp;&amp;a_i&lt;a
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}bar{alpha}_{ij}=left{{array}{ccc}a_islasha_j&mbox{hspace{1cm}}&a_j>a_i[0.5ex]1&&a_j<a_i{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.52ex; " SRC="|."$dir".q|img2557.png"
 ALT="\begin{displaymath}\bar{\alpha}_{ij} =\left\{
\begin{array}{ccc}
a_i/a_j&amp;\mbox{\hspace{1cm}}&amp;a_j&gt;a_i\ [0.5ex]
1&amp;&amp;a_j&lt;a_i
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}bar{alpha}_{i}=left{{array}{ccc}aslasha_i&mbox{hspace{1cm}}&a_i>a[0.5ex]1&&a_i<a{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img2642.png"
 ALT="\begin{displaymath}\bar{\alpha}_{i} =\left\{
\begin{array}{ccc}
a/a_i&amp;\mbox{\hspace{1cm}}&amp;a_i&gt;a\ [0.5ex]
1&amp;&amp;a_i&lt;a
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}nabla^{,2}{mitPhi}_0simeqleft{{array}{lll}4pi,G,rho&mbox{hspace{0.5cm}}&rleqa[0.5ex]0r>a{array}right.,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img4234.png"
 ALT="\begin{displaymath}\nabla^{ 2}{\mit\Phi}_0 \simeq\left\{
\begin{array}{lll} 4\p...
...mbox{\hspace{0.5cm}}&amp;r\leq a\ [0.5ex]
0r&gt;a
\end{array}\right.,\end{displaymath}">|; 

$key = q/{displaymath}rho_0(r)=left{{array}{lll}gamma&mbox{hspace{0.5cm}}&rleqR[0.5ex]0&&r>R{array}right..{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 5.46ex; " SRC="|."$dir".q|img4444.png"
 ALT="\begin{displaymath}\rho_0(r)=\left\{
\begin{array}{lll}
\gamma&amp;\mbox{\hspace{0.5cm}}&amp;r\leq R\ [0.5ex]
0&amp;&amp;r&gt;R
\end{array}\right. .\end{displaymath}">|; 

$key = q/{mitDelta}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3561.png"
 ALT="${\mit\Delta}=0$">|; 

$key = q/{mitDelta}R=0.24,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1349.png"
 ALT="${\mit\Delta} R = 0.24 {\rm m}$">|; 

$key = q/{mitDelta}R=0.54,{rmm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1348.png"
 ALT="${\mit\Delta} R =0.54 {\rm m}$">|; 

$key = q/{mitDelta}beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3736.png"
 ALT="${\mit\Delta}\beta$">|; 

$key = q/{mitDelta}beta=-0.1^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3735.png"
 ALT="${\mit\Delta}\beta=-0.1^\circ$">|; 

$key = q/{mitDelta}lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img71.png"
 ALT="${\mit \Delta }\lambda $">|; 

$key = q/{mitDelta}lambda=-0.3^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img3734.png"
 ALT="${\mit\Delta}\lambda = -0.3^\circ$">|; 

$key = q/{mitDelta}lambda={mitDelta}beta=0^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img3723.png"
 ALT="${\mit\Delta}\lambda={\mit\Delta}\beta=0^\circ$">|; 

$key = q/{mitDelta}skew{5}bar{lambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.84ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img809.png"
 ALT="${\mit\Delta}\skew{5}\bar{\lambda}$">|; 

$key = q/{mitDelta}skew{5}bar{lambda}slash360^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img808.png"
 ALT="${\mit\Delta}\skew{5}\bar{\lambda}/360^\circ$">|; 

$key = q/{mitDelta}t=2pislashn';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3650.png"
 ALT="${\mit\Delta} t=2\pi/n'$">|; 

$key = q/{mitGamma}=gamma^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2292.png"
 ALT="${\mit\Gamma}=\gamma^{ 2}$">|; 

$key = q/{mitOmega}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1311.png"
 ALT="${\mit\Omega}'$">|; 

$key = q/{mitOmega}'=2,omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.62ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1315.png"
 ALT="${\mit\Omega}'=2 \omega$">|; 

$key = q/{mitOmega}(^circ);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img762.png"
 ALT="${\mit\Omega}(^\circ)$">|; 

$key = q/{mitOmega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img16.png"
 ALT="${\mit \Omega }$">|; 

$key = q/{mitOmega}=({calI}_{parallel}slash{calI}_perp-1),omega_{z'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.67ex; " SRC="|."$dir".q|img1579.png"
 ALT="${\mit\Omega}= ({\cal I}_{\parallel}/{\cal I}_\perp-1) \omega_{z'}$">|; 

$key = q/{mitOmega}=1.76times10^{-4},{rmrad.,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1201.png"
 ALT="${\mit\Omega}= 1.76\times 10^{-4} {\rm rad. s}^{-1}$">|; 

$key = q/{mitOmega}=7.29times10^{-5},{rmrad.,s}^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.14ex; " SRC="|."$dir".q|img1189.png"
 ALT="${\mit\Omega} = 7.29\times 10^{-5} {\rm rad. s}^{-1}$">|; 

$key = q/{mitOmega}=7.29times10^{-5},{rmrad.slashs};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4514.png"
 ALT="${\mit\Omega}=7.29\times 10^{-5} {\rm rad./s}$">|; 

$key = q/{mitOmega}>omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.56ex; vertical-align: -0.12ex; " SRC="|."$dir".q|img1277.png"
 ALT="${\mit\Omega}&gt;\omega$">|; 

$key = q/{mitOmega}^{,2},rho={mitOmega}^{,2},R,coslambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1101.png"
 ALT="${\mit\Omega}^{ 2} \rho = {\mit\Omega}^{ 2} R \cos\lambda$">|; 

$key = q/{mitOmega}^{,2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.78ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1130.png"
 ALT="${\mit\Omega}^{ 2}$">|; 

$key = q/{mitOmega}_5=gamma_5=107.5^circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.06ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2604.png"
 ALT="${\mit\Omega}_5=\gamma_5=107.5^\circ$">|; 

$key = q/{mitOmega}_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.44ex; " SRC="|."$dir".q|img2551.png"
 ALT="${\mit\Omega}_i$">|; 

$key = q/{mitOmega}_ngg{mitOmega}_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1801.png"
 ALT="${\mit\Omega}_n\gg {\mit\Omega}_\phi$">|; 

$key = q/{mitOmega}_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4565.png"
 ALT="${\mit\Omega}_\phi$">|; 

$key = q/{mitPhi}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1235.png"
 ALT="${\mit\Phi}'$">|; 

$key = q/{mitPhi}(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img511.png"
 ALT="${\mit\Phi}(r)$">|; 

$key = q/{mitPhi}(r,theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img390.png"
 ALT="${\mit\Phi}(r,\theta)$">|; 

$key = q/{mitPhi}(r,theta)={mitPhi}_0(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img459.png"
 ALT="${\mit\Phi}(r,\theta) = {\mit\Phi}_0(r)$">|; 

$key = q/{mitPhi}({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img365.png"
 ALT="${\mit\Phi}({\bf r})$">|; 

$key = q/{mitPhi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img1152.png"
 ALT="${\mit\Phi}$">|; 

$key = q/{mitPhi}=c,r^{,2}slash6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4246.png"
 ALT="${\mit\Phi}=c r^{ 2}/6$">|; 

$key = q/{mitPhi}_2({bfr});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4256.png"
 ALT="${\mit\Phi}_2({\bf r})$">|; 

$key = q/{mitPhi}_n(r)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img454.png"
 ALT="${\mit\Phi}_n(r)=0$">|; 

$key = q/{mitPi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.51ex; vertical-align: -0.09ex; " SRC="|."$dir".q|img6.png"
 ALT="${\mit \Pi }$">|; 

$key = q/{muskipz@5mudividemuskipz@tw@mkernmuskipz@mathaccentV{bar}016{mkern-muskipz@{lambda}mkernmuskipz@}mkern-muskipz@}{}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img13.png"
 ALT="${\muskip \z@ 5mu\divide \muskip \z@ \tw@ \mkern \muskip \z@ \mathaccentV {bar}016{\mkern -\muskip \z@ {\lambda }\mkern \muskip \z@ }\mkern -\muskip \z@ }{}_0$">|; 

$key = q/|X_0-1|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3138.png"
 ALT="$\vert X_0-1\vert$">|; 

$key = q/|X|<sigma_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1179.png"
 ALT="$\vert X\vert&lt;\sigma_c$">|; 

$key = q/|cdots|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4078.png"
 ALT="$\vert\cdots\vert$">|; 

$key = q/|deltaX|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3139.png"
 ALT="$\vert\delta X\vert$">|; 

$key = q/|deltaY|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3140.png"
 ALT="$\vert\delta Y\vert$">|; 

$key = q/|deltaZ|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img3141.png"
 ALT="$\vert\delta Z\vert\ll 1$">|; 

$key = q/|delta_2|lla;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4230.png"
 ALT="$\vert\delta_2\vert\ll a$">|; 

$key = q/|deltaphi_1|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4572.png"
 ALT="$\vert\delta\phi_1\vert$">|; 

$key = q/|deltaphi_2|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img4573.png"
 ALT="$\vert\delta\phi_2\vert\ll 1$">|; 

$key = q/|deltatheta_1|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4570.png"
 ALT="$\vert\delta\theta_1\vert$">|; 

$key = q/|deltatheta_2|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4571.png"
 ALT="$\vert\delta\theta_2\vert$">|; 

$key = q/|deltax|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2370.png"
 ALT="$\vert\delta x\vert$">|; 

$key = q/|deltay|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img2371.png"
 ALT="$\vert\delta y\vert\ll 1$">|; 

$key = q/|delta|llR;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4441.png"
 ALT="$\vert\delta\vert\ll R$">|; 

$key = q/|e_y|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1969.png"
 ALT="$\vert e_y\vert$">|; 

$key = q/|e_z|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1970.png"
 ALT="$\vert e_z\vert\ll 1$">|; 

$key = q/|epsilon|(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img4377.png"
 ALT="$\vert\epsilon\vert(a)$">|; 

$key = q/|epsilon|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4334.png"
 ALT="$\vert\epsilon\vert$">|; 

$key = q/|epsilon|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img468.png"
 ALT="$\vert\epsilon\vert\ll 1$">|; 

$key = q/|gamma|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1917.png"
 ALT="$\vert\gamma\vert\ll 1$">|; 

$key = q/|l|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.95ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4452.png"
 ALT="$\vert l\vert$">|; 

$key = q/|m|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img4453.png"
 ALT="$\vert m\vert\ll 1$">|; 

$key = q/|nu_x|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1964.png"
 ALT="$\vert\nu_x\vert$">|; 

$key = q/|nu_y|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1965.png"
 ALT="$\vert\nu_y\vert$">|; 

$key = q/|omega_{x'}|,|omega_{y'}|llomega_{z'}=omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1724.png"
 ALT="$\vert\omega_{x'}\vert, \vert\omega_{y'}\vert\ll \omega_{z'}= \omega$">|; 

$key = q/|p_x|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1966.png"
 ALT="$\vert p_x\vert$">|; 

$key = q/|p_y|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1967.png"
 ALT="$\vert p_y\vert\ll 1$">|; 

$key = q/|sigma|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1986.png"
 ALT="$\vert\sigma\vert$">|; 

$key = q/|sinI|<!sqrt{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2725.png"
 ALT="$\vert\sin I\vert&lt;\! \sqrt{2/3}$">|; 

$key = q/|sinI|=!sqrt{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2727.png"
 ALT="$\vert\sin I\vert=\!\sqrt{2/3}$">|; 

$key = q/|sinI|>!sqrt{2slash3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.49ex; " SRC="|."$dir".q|img2726.png"
 ALT="$\vert\sin I\vert&gt; \!\sqrt{2/3}$">|; 

$key = q/|skew{5}dot{mitOmega}|gg{mitOmega}_phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.57ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img4574.png"
 ALT="$\vert\skew{5}\dot{\mit\Omega}\vert\gg {\mit\Omega}_\phi$">|; 

$key = q/|skew{5}dot{phi}|,|skew{5}dot{theta}|llskew{5}dot{psi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.34ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1725.png"
 ALT="$\vert\skew{5}\dot{\phi}\vert, \vert\skew{5}\dot{\theta}\vert\ll \skew{5}\dot{\psi}$">|; 

$key = q/|skew{5}dot{phi}|llomega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1731.png"
 ALT="$\vert\skew{5}\dot{\phi}\vert\ll \omega$">|; 

$key = q/|tau|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2028.png"
 ALT="$\vert\tau\vert$">|; 

$key = q/|tau|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1987.png"
 ALT="$\vert\tau\vert\ll 1$">|; 

$key = q/|t|<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2997.png"
 ALT="$\vert t\vert&lt;1$">|; 

$key = q/|w_x|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1975.png"
 ALT="$\vert w_x\vert$">|; 

$key = q/|w_y|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.17ex; vertical-align: -0.73ex; " SRC="|."$dir".q|img1976.png"
 ALT="$\vert w_y\vert\ll 1$">|; 

$key = q/|x|;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img237.png"
 ALT="$\vert x\vert$">|; 

$key = q/|x|<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img2996.png"
 ALT="$\vert x\vert&lt;1$">|; 

$key = q/|x|slashall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img1342.png"
 ALT="$\vert x\vert/a\ll 1$">|; 

$key = q/|y|slashall1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1343.png"
 ALT="$\vert y\vert/a\ll 1$">|; 

$key = q/|zeta|<zeta_csimeq9times10^{-4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.29ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1243.png"
 ALT="$\vert\zeta\vert&lt;\zeta_c\simeq 9\times 10^{-4}$">|; 

$key = q/|zeta|>zeta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1244.png"
 ALT="$\vert\zeta\vert&gt;\zeta_c$">|; 

$key = q/|zeta|ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1242.png"
 ALT="$\vert\zeta\vert\ll 1$">|; 

$key = q/|zeta|llzeta_c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.01ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img1250.png"
 ALT="$\vert\zeta\vert\ll \zeta_c$">|; 

$key = q/|{bfh}|>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.90ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img579.png"
 ALT="$\vert{\bf h}\vert&gt;0$">|; 

$key = q/|{bfr}'-{bfr}|^{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 2.23ex; vertical-align: -0.46ex; " SRC="|."$dir".q|img402.png"
 ALT="$\vert{\bf r}'-{\bf r}\vert^{-1}$">|; 

$key = q/~^T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 1.00ex; vertical-align: 0.71ex; " SRC="|."$dir".q|img1538.png"
 ALT="$&nbsp;^T$">|; 

$key = q/~^ast;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 STYLE="height: 0.61ex; vertical-align: 0.76ex; " SRC="|."$dir".q|img4073.png"
 ALT="$&nbsp;^\ast$">|; 

1;

