Gravitational stabilization of a satellite using a movable mass

The plane motion of an axisymmetric satellite with a small movable mass on its axis of symmetry is examined, and the equation of the motion of this system in an elliptical orbit is derived. Problems regarding the gravitational stabilization of two diametrically opposite relative equilibrium positions of the satellite in a circular orbit to in-plane perturbations are investigated. A continuous law for controlling the movable mass, which ensures stabilization of the axis of symmetry of the satellite to the local vertical and reorientation of the satellite by moving it from one stable equilibrium position to the other, is constructed using the swing-by technique. A solution is obtained by using the second method of classical stability theory and constructing the corresponding Lyapunov functions. The asymptotic convergence of the solutions with the control obtained is confirmed by the results of numerical simulation of the motion of the system. (C) 2012 Elsevier Ltd. All rights reserved.