16.2 : Inertia Tensor

The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.

The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least resistance to rotation. If there is a smaller moment of inertia value along a certain principal axis, it indicates that the object can rotate more freely around that specific axis. Conversely, the off-diagonal components in the inertia tensor matrix symbolize the product of inertia. This essentially illustrates the interplay between different axes.

It is possible to make the off-diagonal elements of the inertia tensor zero by choosing a unique orientation of the reference axes. This action results in the tensor being diagonalized. The modified tensor then only includes diagonal terms, and these are identified as the principal moments of inertia for the object. These are calculated in relation to the principal axes of inertia.