I have a velocity vector as a function of a latitude and longitude on the surface of a sphere. Let us assume I have a point V(lambda, phi) where V is the velocity. The north pole of this sphere is rotated and I have a new north pole and I have a point V'(lambda, phi) in the new system. I have the transformation matrix between the unrotated system and rotated system in terms of a position defined in terms of lambda and phi. Rather than just multiplying the rotation matrix by this transformation matrix I must differentiate the components of the transformation matrix with respect to time and multiply that result by the column vector containing the velocities. Is that correct ?