(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Transforming angular velocity between different coordinate frames

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**