$$\require{cancel}$$
In Chapter 5, we studied the rotation of rigid bodies about an axis of symmetry. For these cases, we have $$\boldsymbol{L} = I \boldsymbol{\omega}$$, where I is the moment of inertia with respect to the rotation axis. In this section, we’ll derive the more general form, in which the number I is replaced by a 2-tensor, i.e., a map from a vector space (here $$\mathbb{R}^{3}$$) into itself, represented by a 3×3 matrix.