Determining angular velocity radius and velocity of the center of rotation

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SUMMARY

The discussion centers on determining the angular velocity vector, radius (rra), and linear velocity (vr) of a rigid body given three points and their respective velocity vectors (va, vb, vc). The user has formulated nine equations based on the relationships between these vectors but struggles to find a definitive solution, even after attempting to solve it analytically and using MATLAB. The issue appears to stem from the non-uniqueness of the inverse of a cross product, leading to multiple potential solutions for the radius vector.

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  • Understanding of rigid body dynamics
  • Familiarity with vector mathematics, specifically cross products
  • Proficiency in MATLAB for numerical analysis
  • Knowledge of angular velocity concepts
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This discussion is beneficial for mechanical engineers, physicists, and students studying dynamics who are interested in analyzing rigid body motion and solving related vector equations.

Eve_mecheng
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Hey,

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.

Thanks.
 
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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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