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Precession
Suppose that some position vector
precesses (i.e., rotates) about the
axis at the
angular velocity
. If
,
,
are the Cartesian components of
at time
then it follows from the analysis in the previous section that

(A.93) 
Hence, making use of the small angle approximations to the sine and cosine functions, we obtain

(A.94) 
which immediately implies that

(A.95) 
or
where
is the angular velocity of precession. Because vector
equations are coordinate independent, we deduce that the preceding expression is the general equation for the time evolution of
a position vector
that precesses at the angular velocity
.
Next: Curvilinear coordinates
Up: Useful mathematics
Previous: Rotational coordinate transformations
Richard Fitzpatrick
20160331