Periodic motions similar to hyperboloidal precession of a symmetric satellite in a circular orbit

Physics

Scientific paper

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Circular Orbits, Hyperbolic Trajectories, Precession, Satellite Orbits, Spacecraft Motion, Symmetrical Bodies, Celestial Mechanics, Center Of Mass, Differential Equations, Gravitational Fields, Hamiltonian Functions, Linear Equations, Moments Of Inertia

Scientific paper

The motion of a dynamically symmetric body (a satellite) relative to its center of mass in a circular orbit in a central Newtonian gravitational field is studied. A particular solution is obtained in which the satellite's axis of dynamic symmetry is perpendicular to the radius vector of its center of inertia and forms a constant angle with the velocity vector of the center of inertia (hyperboloidal precession). It is shown that there are two types of periodic motion for initial conditions not much different than those for hyperboloidal precession. The orbital stability of these periodic motions is analyzed in a rigorous nonlinear formulation for all admissible values of the relevant parameters.

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