The bounded control gravitational stabilization problem for satellites with movable mass

We study the control plane motion of an axisymmetric satellite with a movable mass on its axis of symmetry in circular orbit under the influence of a gravity torque. The problem of the gravitational stabilization to in-plane perturbations of two diametrically opposite relative equilibrium positions of the satellite in a circular orbit using the swing-by technique is solved. A restricted law with continuous derivative for controlling the movable mass is proposed. We solve the problem of reorientation of the satellite by moving it from one stable equilibrium position to the other. The theoretical results are illustrated by graphical representation of the numerical simulation.