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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 593–609 (Mi nd687)  

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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 3.3858.2017/4.6
This work was carried out at the Moscow Aviation Institute (National Research University) within the framework of the state assignment (project No. 3.3858.2017/4.6).


DOI: https://doi.org/10.20537/nd190419

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MSC: 93B18, 93B52
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”, Nelin. Dinam., 15:4 (2019), 593–609

Citation in format AMSBIB
\Bibitem{Suk19}
\by E. A. Sukhov
\paper Bifurcation Analysis of Periodic Motions Originating from Regular Precessions of a Dynamically Symmetric Satellite
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 593--609
\mathnet{http://mi.mathnet.ru/nd687}
\crossref{https://doi.org/10.20537/nd190419}


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