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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.