Equilibria stability of the satellite as a system with a countable number of degrees of freedom

The satellite that is considered as a hybrid dynamical system, consists of a rigid body and an isotropic elastic element of an arbitrary shape, and moves in a field of central Newtonian force about an attracting center so that its instantaneous center of mass rotates in a circular orbit with a constant angular velocity. Nonlinear stability tin Lyapunov sense) of the satellite's relative equilibria in its motion about the center of mass is investigated with the help of the Routh-Lyapunov theorem under discretization of the problem by means of a series representation (without truncation) of the infinitesimal elastic displacements in terms of some set of pre-assigned functions and some other assumptions. As presented in the paper, sufficient stability conditions contain a finite number of inequalities imposed on the system's parameters. An illustrative trample of a satellite with an elastic beam is considered. (C) 2001 Elsevier Science Ltd. All rights reserved.