Dynamics of Gravitational System Satellite-Stabilizer on Circular and Elliptic Orbits
This paper studies the dynamics of a satellite with passive gravitational attitude control system in the plane of circular and elliptic orbits. At first it discusses small oscillations of the satellite-stabilizer system in the plane of a circular orbit in a vicinity of the more simple equilibrium position. The necessary and sufficient conditions for asymptotic stability of that equilibrium are obtained and the values of the parameters, where the maximal speed of response of the system is achieved, are analytically determined. The paper also studies the eccentricity oscillations in elliptic orbit. The forced solution of the system is determined and the minimal value for magnitude of the eccentricity oscillations amplitude of the satellite is determined.