This paper is devoted to the study of the asymptotic stability of programme
d 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 progra
mmed servo-control forces such that the rigid body performs the programmed
motion, and the stabilizing servo-control forces of this motion. The equili
brium 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 ensurin
g 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 exact
ly non-linear functions of phase coordinates of the system and are not appr
oximated as linear. (C) 1999 Elsevier Science Science Ltd. All rights reser
ved.