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Determining angular velocity radius and velocity of the center of rotation

  1. Sep 6, 2012 #1

    I am trying to solve the following problem:

    va=vr+ ω × rra
    vb=vr+ ω ×(rra+rab)
    vc=vr+ ω × (rra+rac)

    I know the vectors va, vb, vc, rab and rac and I want to know the angular velocity vector, the radius rra and the velocity vr. Physically it means that I know 3 points on a rigid body and I want to decompose their velocities in an angular and linear component by determing around which point they rotate.

    So there are 9 equations and 9 unkowns. But if I try to solve this problem analytically I can not come to any answer. I also put it in MATLAB but this also gives weird results.
    My first attempt was subtracting the vectors which eventually gave me a solution for omega. But than I still could not solve the problem.

    Does anyone know why this is the case? Is it something with the outer product which I don't understand? Are there infinite number of solution to this problem? Or do I just do something wrong?

    Any help would be appreciated since I am already trying things for some days.

  2. jcsd
  3. Sep 7, 2012 #2
    Does it have something to do with the fact that the inverse of a cross product does not have an unique solution? So if for v= ω x r I would know v and ω than there are infinite solutions for r.
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