Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite

E. A. Sukhov

Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 593-609

Résumé

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.

Détail

Keywords: Hamiltonian mechanics, satellite dynamics, periodic motions, orbital stability.
Mots-clés : bifurcations