On the control of programmed motion of a rigid body containing moving masses

Abstract

This paper is devoted to the study of the asymptotic stability of programmed motion of a rigid body, with the help of internal moving masses using the Lyapunov function. The adopted method is based on the choice of the programmed servo-control forces such that the rigid body performs the programmed motion, and the stabilizing servo-control forces of this motion. The equilibrium position of the rigid body which occurs at the principal axes of the body coincides with the inertial axes is proved to be asymptotically stable as a special case of the studied problem. The servo-control forces ensuring that it is btained. The advantages of this study are the exactness of the equations of motion and that the servo-control forces are derived as exactly non-linear functions of phase coordinates of the system and are not approximated as linear