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
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.
Hamiltonian mechanics, satellite dynamics, bifurcations, periodic motions, orbital stability
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MSC: 93B18, 93B52
E. A. Sukhov, “Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite”, Nelin. Dinam., 15:4 (2019), 593–609
Citation in format AMSBIB
\by E. A. Sukhov
\paper Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite
\jour Nelin. Dinam.
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