Optimal stabilization of rotational motion of a rigid body around its center of gravity

The present work considers the optimal stabilization problem in rotational motion of a rigid body around its center of gravity. The case of the Euler rotational motion of a rigid body around a fixed point is considered. The optimal stabilization problem of the considered motion is assumed and solved. Input controls are introduced in the direction of the generalized coordinates, full controllability of linear approximation of the system is checked. Besides the optimal stabilization problem of the system on classical sense is solved, optimal Lyapunov function, optimal controls and value of functional are obtained.