16.2 : 慣性テンソル

The inertia tensor is used to describe the distribution of mass and rotational inertia of a rigid body.

The inertia tensor is represented using a 3×3 matrix. Each element of the matrix corresponds to different moments of inertia about specific axes.

The diagonal elements of the inertia tensor matrix represent the moments of inertia about the principal axes of the body. These principal axes are the axes around which the body rotates most easily.

A smaller moment of inertia value along a particular principal axis implies that the body can be easily rotated around that axis.

Additionally, the off-diagonal elements of the inertia tensor matrix represent the product of inertia, which describes the coupling between different axes.

By choosing a unique inclination of the reference axes, the off-diagonal terms of the inertia tensor can be made zero, and the tensor is diagonalized.

The modified tensor then has only diagonal terms and are termed as the principal moments of inertia for the body computed with respect to the principal axes of inertia.