Steady Motions of Rigid Body Satellites in a Central Gravitational Field

摘要

Numerous studies have been conducted on equilibrium orientations of objectsmoving under the influence of a central gravitational field. The results of many of these studies conclude that equilibrium conditions exist only when one of the principal axes coincides with the radius vector. Furthermore, these results assume that the center of force is located within the orbit plane, thereby tracing a great circle orbit. While these previous works have approximated the gravitational potential, this study examines relative equilibria obtained by retaining an exact expression for the potential of a spherical primary body, as shown in a recent paper by Wang, Maddocks, and Krishnaprasad. The exact dynamic equations for the motion of a finite rigid body in an inverse square gravitational force field are investigated. Only circular orbits for a specific satellite model consisting of six masses connected by three massless rigid rods are considered. The system dynamics are comprised of seven nonlinear equations, which were numerically solved on a Cray computer. The existence of equilibrium orientations which establish non-great circle orbits was verified and other interesting results were noted. The operational significance of these results was also examined. Equilibrium, Gravity-gradient, Continuation, Artificial satellites, AUTO, Gravitational fields, Satellite attitude, Numerical analysis, Newton-Raphson.