Stationary-platform Maneuvers Of Gyrostat Satellites

In this paper we present some novel results regarding the dynamics of gyrostats containing N axisymmetric rotors subject to control torques applied by the platform. The particular class of maneuvers we are interested in are termed "stationary-platform" maneuvers, because they are based on the notion of keeping the platform almost stationary throughout the maneuver. The basic idea behind this class of maneuvers is to control the rotors in such a way that the maneuver remains near a branch of equilibrium motions for which the platform angular velocity, w, is zero. Of course, u> is not actually zero, but it does remain small provided that the internal torques are small. We develop the equations of motion, and then discuss the stationary-platform conditions, which lead to the development of stationaryplatform control laws for the control torques. We give a simple proof that all stationary-platform equilibria are nonlinearly stable in the absence of energy dissipation. Numerical results are given which include the dissipative effects of a viscously damped rotor. The results confirm the effectiveness of the stationary-platform maneuver for a large-angle rotation with small angular velocity throughout the maneuver.