Lyapunov Stability and Solar Perturbations of a Passively Damped Gravity-Gradient Satellite

摘要

The rotational equations for a satellite and two gimballed damper booms connected at the center of mass are derived using Lagrange's general formulation. The complete motion is thus governed by five coupled equations where the translational orbital motion of the system is assumed not coupled with the rotational motion. Included are the conservative effects of both gravitational and gyroscopic torques. The latter results from the coupling between orbital angular velocity and the rotational motion in pitch-roll-yaw referenced to a local vertical frame. The motion occurs in the presence of small dynamic and instantaneous perturbations. The dynamic inputs are (1) interaction of solar radiation on extendible booms for varying moment of inertia parameters for gravity stabilization, and (2) periodic excitation due to eccentricity. The first yields time-dependent radiation torques and moment of inertia corrections caused by in- and out-of-plane bending due to thermal unbalance. The orbital eccentricity causes a once per orbit parametric excitation about each axis. Finally, the instantaneous perturbations, considered as step inputs, occur when the satellite emerges from the earth's shadow.