# Homework Help: Transforming angular velocity between different coordinate frames

1. Sep 5, 2010

### wajih0008

1. The problem statement, all variables and given/known data
There are two coordinate frames i.e. frame A and frame B. The relationship between them is that frame A is rotated w.r.t to frame B . This relationship remains fixed i.e. rigid body. This rigid body relationship is given by rotation matrix R_BA which transforms the vector in frame A to a vector in frame B. Now i have a 3D angular velocity describing rotation of frame Ai.e. w_A. I want to calculate 3D angular velocity of frame B i.e w_B. How can i do this . I have two solutions(given below) which don't agree with each other.

2. Relevant equations

R_BA rotation from frame A to frame B
R_AB rotation from frame B to frame A. This is the transpose of R_BA
Delta R_B delta rotation in frame B
Delta R_A delta rotation in frame A
w_A 3D angular velocity in frame A
w_B 3D angular velocity in frame B

3. The attempt at a solution
Solution One
I can convert this angular velocity w_A into rotation matrix i.e. Delta R_A, then do the following
Delta R_A= R_BA*Delta R_A *R_AB

Now i can convert Delta R_A back to angular velocity w_B.

Solution two

w_B= R_BA * w_A

Now these two solution don't agree. In solution one i converted the angular velocity to delta rotation, applied the transformation and converted the rotation back to angular velocity.

In the second i directly applied the the rotation.