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I am trying to solve the following problem:

**v**=

_{a}**v**+

_{r}**ω**×

**r**

_{ra}**v**=

_{b}**v**+

_{r}**ω**×(

**r**+

_{ra}**r**)

_{ab}**v**=

_{c}**v**+

_{r}**ω**× (

**r**)

_{ra}+r_{ac}I know the vectors

**va**,

**vb**,

**vc**,

**r**and

_{ab}**r**and I want to know the angular velocity vector, the radius

_{ac}**r**and the velocity

_{ra}**v**. 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.

_{r}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.