Spherical vectors and rotation of axes

[meteo student]

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 ?

 

[andrewkirk]

What does this mean:

The north pole of this sphere is rotated and I have a new north pole

Are you just wanting to find the coordinates of the velocity vector in a new spherical coordinate system that arises from a rotation of the axes of the original spherical coordinate system around a line through the origin of the original system?

 

[meteo student]

Yes exactly.

I have velocities in the unrotated frame with respect to a geographical north pole of the earth. I have also been given the position of a point in the unrotated frame as well the origin of the rotated north pole.

I have defined theta the rotation angle in terms of the coordinates of a position in the unrotated frame and rotated frame using law of cosines/sines. Now all I need to do is construct the rotation matrix and multiply the velocities ?