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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
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