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Let
![$\displaystyle X$](img2388.png) |
![$\displaystyle = -\frac{\cos\theta}{\sin\theta}\,\frac{\partial{\mit\Phi}_r}{\partial \phi},$](img4832.png) |
(12.249) |
![$\displaystyle Y$](img2390.png) |
![$\displaystyle = \cos\theta\,\frac{\partial{\mit\Phi}_r}{\partial\theta},$](img4833.png) |
(12.250) |
![$\displaystyle P$](img4834.png) |
![$\displaystyle ={\mit\Phi}_r',$](img4835.png) |
(12.251) |
![$\displaystyle Q$](img3678.png) |
![$\displaystyle = {\mit\Psi}_r''$](img4836.png) |
(12.252) |
in Equations (12.191)-(12.196). It follows that
and
as well as
Let
![$\displaystyle X$](img2388.png) |
![$\displaystyle = \cos\theta\,\frac{\partial{\mit\Psi}_r}{\partial \theta},$](img4847.png) |
(12.259) |
![$\displaystyle Y$](img2390.png) |
![$\displaystyle = \frac{\cos\theta}{\sin\theta}\,\frac{\partial{\mit\Psi}_r}{\partial\phi},$](img4848.png) |
(12.260) |
![$\displaystyle P$](img4834.png) |
![$\displaystyle ={\mit\Phi}_r'',$](img4849.png) |
(12.261) |
![$\displaystyle Q$](img3678.png) |
![$\displaystyle = {\mit\Psi}_r'$](img4850.png) |
(12.262) |
in Equations (12.191)-(12.196). It follows that
and
as well as
Next: Gyroscopic Coefficients
Up: Terrestrial Ocean Tides
Previous: Basis Eigenfunctions
Richard Fitzpatrick
2016-01-22