A Determine Mass moment of inertia about any axis given Ixx..

Tags:
1. Jul 26, 2017

Mohsen Diraneyya

Hello,

I am analyzing human motion. for each body segment, I have measured values for Ixx, Iyy, and Izz in local coordinate system. I want to transfer all body properties from one coordinate system to another using a transformation matrix.

My question is that
, is there a way to calculate mass moment or inertia about any known axis, given the mass moment of inertia about the three primary axes? Ixx, Iyy ans Izz

Thanks.

2. Jul 26, 2017

Orodruin

Staff Emeritus
Yes, the moment of inertia is a symmetric rank two tensor. Given the principal directions and their corresponding moments uniquely defines this tensor.

3. Jul 26, 2017

Mohsen Diraneyya

Does that mean I can simply use rotational transformation matrix as any other vector to get new moments of inertia ?

4. Jul 26, 2017

Orodruin

Staff Emeritus
No, it is a rank 2 tensor, not a vector. You marked this thread "A" so I assumed you were familiar with tensors. Written in matrix form, the components of a rank 2 tensor transform according to
$$I' = A I A^T,$$
where $I$ contains the components of the moment of inertia tensor in old system, $I'$ its components in the new system, and $A$ is the rotation matrix connecting the systems.

5. Jul 26, 2017