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## Main Question or Discussion Point

Say I have an odd shaped rigid body in pure rotation. I fix an orthogonal x-y-z coordinate system to the body, and coincide the origin of this coordinate system to the origin of my global coordinate system X-Y-Z.

I have 3 Eulerian angles (as functions of time) which I can use to describe the orientation of my rigid body at any instant. I also have a transformation matrix

I am trying to find out how I can express the angular velocity,

I also know that

I cannot "solve" for

It's probably a very easy question but I'd appreciate any help. Thanks.

I have 3 Eulerian angles (as functions of time) which I can use to describe the orientation of my rigid body at any instant. I also have a transformation matrix

**A**which I can use to convert any vector**r'**in the x-y-z system to a vector**r**in the X-Y-Z system.I am trying to find out how I can express the angular velocity,

**ω**of my rigid body using this information. I know that**r**x**ω**=d**r**/dt for any position vector**r**describing the position of a point on the rigid body (correct?).I also know that

**r**=**Ar'**, so that**r**=d**A**/dt***r'**(since**r'**is constant, the point stationary in the x-y-z frame).I cannot "solve" for

**ω**in the**r**x**ω**=d**r**/dt since there are infinitely many possibilities (it yields a skew-symmetric 3x3 matrix). It seems like if I have the position vector of a point on the body as a function of time, I should be able to express the angular velocity but I'm stuck.It's probably a very easy question but I'd appreciate any help. Thanks.