[Paraview] [EXTERNAL] Re: Rotational velocities

[David Thompson]

> I've never done this, and maybe there is an existing established way to do it, but a simple Google search did not reveal it.

The proper Google search phrase to find mechanical engineering sites is "instant center of rotation". Most of them deal with 2-D though, as that's what's covered in undergraduate mechanics. If you find an advanced mechanics book (or an aerospace mechanics book), you should find the 3-D case.

> ... I'm guessing that he would probably be interested in rotations around the center of mass.

I think it's more likely for someone to be interested in the rotation about the instant center than the center of mass, but the angular velocity about the center of mass is also a useful thing to know. (It is also nice to know the moment of inertia about whatever axis you are dealing with because then you can estimate rotational kinetic energy as I\omega^2 and the linear kinetic energy as m*v^2 and compare the two.)

> An average of all the point coordinates might be a close enough approximation to the center of mass.

I would be nervous about using that approximation in a general-purpose tool because the angular velocities that result can vary significantly for small changes in the position of the center of mass when velocity is large.

You could use the mesh quality filter and cell-center filters to avoid bias from the mesh. Or do a least squares fit to the instant center of rotation and the angular velocity all at once.

> Next, find the translation of the rigid body by looking at the displacement at the center of mass. That displacement is the translation. Now subtract that translation vector from all the displacements to get what I will call the rotation displacement (a term I just made up).

If the body is deforming (or the element block contains independently-moving disjoint bodies), both the estimated displacement and your "rotation displacement" include variations due to non-rigid deflections.

> Now you can use any of these rotation displacements to find the rotation. Technically any one displacement will give you the rotation (because it is a rigid body), but you should pick one far away from the axis of rotation.

The problem I have with this is that -- assuming non-rigid deflections are significant -- the ones far from the axis of rotation are likely the ones most affected by non-rigid-body deflections.

	David