Random motion of a rigid body (Q677891)

The author studies the random motion of a rigid body with a fixed centre, using a stochastic differential equation on the special orthogonal group \(\text{SO}(d)\) of \(\mathbb{R}^d\), derived by the principle of the dynamics of rigid bodies. Problems discussed include (a) the stationary measure of the motion, (b) the meaning of angular velocity and momentum of the body, and (c) the stability of the rotating axis near the major and minor axes of the body.