Euler's Equations of Motion for Rotation of Rigid Body

Theorem
Let a rigid body $B$ rotate about an axis $\AA$ which is fixed in relation to $B$ and parallel to the principal axis of inertia of $B$.

Then the rotation of $B$ about $\AA$ is described by:


 * $\mathbf I \cdot \dot {\boldsymbol \omega} + \boldsymbol \omega \times \paren {\mathbf I \cdot \boldsymbol\omega} = \mathbf M$

where:
 * $\mathbf M$ is the applied torque applied to $B$ about $\AA$
 * $\mathbf I$ is the moment of inertia of $B$ with respect to $\AA$
 * $\boldsymbol \omega$ is the angular velocity about $\AA$.