Physics - Inertia Tensor open forum discussion

By: Richard - redeyes2003
Inertia Tensor, How to use  
2004-07-14 02:45

I have never use the inertia tensor before, but I need to now. I did some background reading on it, but I still don't understand how to use it.

If you have the inertia tensor for a body, I, where I is a matrix, what operations would you carry out on it to
(1) rotate body about an axis
(2) rotate body again about a different axis.

For the first part, from previous knowledge, it seems as if I need the scalar inertia about that axis, but I do not know (I do not know anything about how to use it).

By: Martin Baker - martinbaker
RE: Inertia Tensor, How to use  
2004-07-14 08:48

Inertia Tensor relates angular acceleration to torque in the same way that mass relates acceleration to force.

For linear motion: F=m a
For angular motion T=[I] a

I suppose the linear version could be written in matrix form:

Fx = [ m 0 0 ] ax
Fy = [ 0 m 0 ] ay
Fz = [ 0 0 m ] az

So in the linear case only the leading diagonal is non-zero, so a force in the x-direction will only produce an acceleration in the x-direction and not in the y and z direction.

However, this in not the case for rotations, a torque about the x axis may produce an acceleration about the y and z axis, so we need all the terms in the matrix. It is only if the object is symmetrical about the rotation that we get a leading diagonal matrix. We can find the axis of symmetry by calculating the eigenvectors of the matrix.

What I find makes this complicated is that the inertia tensor is defined in the local coordinates of the object, if we are working in global coordinates, then the terms of the inertia tensor will be continually varying.

Martin

By: Richard - redeyes2003
RE: Inertia Tensor, How to use  
2004-07-14 14:09

It does not seem so difficult now. I just have to be careful what frame I am working in. Thanks for your expertise, Martin.

less confused Richard.