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.(adsbygoogle = window.adsbygoogle || []).push({});

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 matrixAwhich I can use to convert any vectorr'in the x-y-z system to a vectorrin the X-Y-Z system.

I am trying to find out how I can express the angular velocity,ωof my rigid body using this information. I know thatrxω=dr/dt for any position vectorrdescribing the position of a point on the rigid body (correct?).

I also know thatr=Ar', so thatr=dA/dt*r'(sincer'is constant, the point stationary in the x-y-z frame).

I cannot "solve" forωin therxω=dr/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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Angular velocity of a 3D rigid body with Eulerian Angles

**Physics Forums | Science Articles, Homework Help, Discussion**