Letand
be coordinate systems with the same origin
with system
rotating with angular velocity
with respect to
Let
be the position vector of a particle in
then
In the coordinate system s,are changing with time so
Sinceso
and
are perpendicular. Similarly for
and
and
and
Hence
(1)
(2)
,(3)
Differentiatinggives
(4)
Differentiatinggives
(5)
Differentiatinggives
(6)
Taking the dot product of (1) withgives
Taking the dot product of (2) withgives
Hence
Similarlyand
Hence
Letthen we can write
Then