Optimal stabilization of the equilibrium positions of a rigid body using rotors

In this work, the problem of optimal stabilization of the equilibrium positions of a rigid body using internal rotors is studied. The conditions for the optimal stabilization of the equilibrium positions are used to deduce a feedback control law as functions of the phase coordinates of the body and the parameters describing the equilibrium positions. The Lyapunov function is used to prove the asymptotic stability of these positions. Special cases and analysis of the obtained results are presented to assess the present method. Moreover, some of the results are compared with those obtained in the literature using other methods. In contrast to the usual methods in the literature, which stabilize some of the equilibrium positions of the rigid body, the present one has the advantage of stabilizing all the equilibrium positions with optimal control law.