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Rigid body dynamics question

  1. May 19, 2008 #1
    I have been working on a rigid body subject quite a long. But till now there is an unresolved question for me. When we calculating the torque acting on the rigid body we use the following definition of the torque: t = r X f, X - is a cross product. So if I calculate the torque in a body-fixed system I use r in the body-fixed system too, but for force f - I am not sure. In which coordinate system should it be expressed - in the body-fixed or in space-fixed. Are this forces different in both systems? Sorry, for probably stupid questions. Thanks
  2. jcsd
  3. May 19, 2008 #2
    Sorry, I've found - we really need to do all in the same coordinate system.

    But now, I have some other question - probably, more interesting. The torque acting on the rigid body (expressed in the body-fixed frame) is given by: t = -0.5*S(q)*(dU/dq), gde U - potential, q - is a quaternion, ans S(q) - is a matrix such that: dq/dt = 0.5*S(q)w, where w - is a 4-dimensional angular velocity. Can anybody explain how to get that formula for the torque?
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