The existence of periodic solutions in the problem of the motion of an axisymmetrical satellite relative to the center of mass in an evolutionary circular orbit is investigated. The motion of the satellite is described by canonical osculating Andoyer elements, referred to the mobile plane of the orbit. The analytical conditions for the existence of Poincare periodic solutions are obtained, the generating solutions of which are interpreted as generalized Cassini laws for bodies possessing an axis of dynamic symmetry. A qualitative and numerical investigation of the generating solutions is presented.
Department of Celestial Mechanics and Gravimetry
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