Simulating Spinning Rigid Bodies in 3D: Challenges and Solutions

[zarcon]

Hi all! I am having trouble understanding how to create a simulation of a spinning rigid body.

For each axis x, y, and z I have an angle and an angular velocity.
To rotate the object each axis is rotated independently - first the rotation about the x-axis followed by the rotation about the z- axis, then the rotation about the y-axis.

I really don't think this gives an accurate representation of the way the object would spin. for example - If the x and z angular velocities are equal and the y angular velocity is zero, I imagine that would result in a rotation about a diagonal axis in the xz plane. Instead the object essentially wobbles, never quite flipping over.

Is there a way to calculate an arbitrary axis of rotation from 3 anglular velocities? or even 2 angular velocities?

I hope i explained this okay, if anyone who has had experience doing this could offer some guidance, I would really apprectiate it.

Thanks!
Jonathan

 

[berkeman]

I think you will only get a stable resultant overall axis if each of the component rotational omegas is equal. If they are not equal, the resultant rotation vector (add the 3 component omega vectors) will change its direction as the object moves. Like, consider when Omega(x) is twice Omega(y), and think about how the resultant vector moves...

 

[arildno]

3-D rotations are NASTY.
Stay away from them!
If you are persistent, look up on Euler angles and the non-obvious manner in which the instantaneous angular velocity vector is related to them.
Goldstein's Classical Mechanics is a good start, but if you are to delve deeper into the computational issues involved, you're in it for life, I think.

As for the angular velocity vector, it is parallell to the normal of the plane of rotation at that moment.

As for the concept of "rotation axis", remember that if you go into anybody particle's rest frame, the body can be regarded as rotating about that particle with the same angular velocity as if you were in another body particle's rest frame.
But, the location of the rotation axis is in general different in the two cases.