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
.