Calculate moment of inertia about arbitrary axis from Ixx, Iyy, Izz

[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.

 

[Orodruin]

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

 

[Mohsen Diraneyya]

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

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

 

[Orodruin]

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

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.

 

[Mohsen Diraneyya]

My bad. Thanks A lot