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This article is cited in 1 scientific paper (total in 1 paper)
Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite
E. A. Sukhov Moscow aviation institute (National Research University),
Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia
Abstract:
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 stability.
Received: 20.06.2019 Accepted: 20.10.2019
Citation:
E. A. Sukhov, “Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite”, Rus. J. Nonlin. Dyn., 15:4 (2019), 593–609
Linking options:
https://www.mathnet.ru/eng/nd687 https://www.mathnet.ru/eng/nd/v15/i4/p593
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