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

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 theor em. The optimal control moments which stabilize this motion are obtained us ing the conditions of ensuring the optimal asymptotic stability as non-line ar functions of phase coordinates of the system. These moments stabilize as ymptotically one type of the rotational motions of the rigid body. The othe r rotational motions are unstable in the Lyapunov sense. As a particular ca se of our problem, the equilibrium position of the rigid body, which occurs when the principal axes of inertia coincide with the inertial axes, is pro ved to be asymptotically stable. This study is characterized by that non-li near equations of motion which are used to prove the asymptotic stability a nd derivation of the control moments. (C) 1999 Elsevier Science Ltd. All ri ghts reserved.