1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
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

  1. Sep 5, 2010 #1
    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.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted