Bifurcation analysis of periodic motions originating from regular precessions of a dynamically symmetric satellite. (English) Zbl 1470.70027
Summary: We deal with motions of a dynamically symmetric rigid-body satellite about its center of mass in a central Newtonian gravitational field. In this case the equations of motion possess particular solutions representing the so-called regular precessions: cylindrical, conical and hyperboloidal precession. If a regular precession is stable there exist two types of periodic motions in its neighborhood: short-periodic motions with a period close to \(2\pi / \omega_2\) and long-periodic motions with a period close to \(2 \pi / \omega_1\) where \(\omega_2\) and \(\omega_1\) are the frequencies of the linearized system \(( \omega_2 > \omega_1)\).In this work we obtain analytically and numerically families of short-periodic motions arising from regular precessions of a symmetric satellite in a nonresonant case and long-periodic motions arising from hyperboloidal precession in cases of third- and fourth-order resonances. We investigate the bifurcation problem for these families of periodic motions and present the results in the form of bifurcation diagrams and Poincaré maps.
Keywords:
Hamiltonian mechanics; satellite dynamics; bifurcations; periodic motions; orbital stabilityReferences:
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