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as you know, the attitude of a robot is represented using many ways, euler angles, quaternion, rodriquez parameters, and so on. I should use rodriquez representation in a problem formulated same as a robotic problem.

the kinematic based on rodriquez parameters are defined as below:

enter image description here

I want to have $\omega$ formulation based on $\dot{p}$. is there any way to calculate it analytically?

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  • $\begingroup$ I don't know the answer to your question, but matrix inversion formula for sum of matrices may be of interest if you don't get an answer. 1, 2. $\endgroup$
    – AJN
    Jul 11 at 1:22
  • $\begingroup$ Can you tell us the use case of inverting this formula. Perhaps there is a work around (numerical or analytic) that would suit your application. $\endgroup$
    – AJN
    Jul 11 at 13:23
  • $\begingroup$ thank you @AJN, actually I want it to use it in designing closed loop control law. about the quaternion, Fibonatic has helped me in this post, but unity property of quaternion can not be satisfied in control law design. so I switched to MRP. $\endgroup$
    – King
    Jul 12 at 6:02
  • $\begingroup$ 1 I don't know why unity property of quaternion can not be satisfied in control law. There are published results which use quaternion based control laws AFAIK. 2 In the practical application, there will be a device which converts / integrates angular velocity to the Rodrigues parameters using the above formula. So the control system designer wanting to reconstruct $\omega$ from $\dot{p}, p$ is surprising. Please add a good description of the various parts of your control system / plant. 3 In case you don't get an answer here, ask the moderators to migrate this to math.SE. $\endgroup$
    – AJN
    Jul 12 at 12:21

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