Optimal stabilization of the rotational motion of a rigid body with the help of rotors

Abstract

Abstract Optimal stabilization of the rotational motion of a symmetrical rigid body with the help of internal rotors is studied. In such a study the asymptotic stability of this motion is proved by using Barbachen and Krasovskii theorem. The optimal control moments which stabilize this motion are obtained using the conditions of ensuring the optimal asymptotic stability as non-linear functions of phase coordinates of the system. These moments stabilize asymptotically one type of the rotational motions of the rigid body. The other rotational motions are unstable in the Lyapunov sense. As a particular case of our problem, the equilibrium position of the rigid body, which occurs when the principal axes of inertia coincide with the inertial axes, is proved to be asymptotically stable. This study is characterized by that non-linear equations of motion which are used to prove the asymptotic stability and derivation of the control moments.