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Nelin. Dinam., 2016, Volume 12, Number 4, Pages 619–632 (Mi nd542)  

This article is cited in 3 scientific papers (total in 3 papers)

Original papers

On the stability of a resonant rotation of a satellite in an elliptic orbit

B. S. Bardin, E. A. Chekina

Moscow Aviation institute, Volokolamskoe sh. 4, Moscow, 125871, Russia

Abstract: We deal with the problem of stability for a resonant rotation of a satellite. It is supposed that the satellite is a rigid body whose center of mass moves in an elliptic orbit. The resonant rotation is a planar motion such that the body completes one rotation in absolute space during two orbital revolutions of its center of mass. The stability analysis of the resonant rotation with respect to planar perturbations has been performed in detail earlier. In this paper we investigate the stability of the resonant rotation with respect to both planar and spatial perturbations for a nonsymmetric satellite. For small values of the eccentricity we have obtained boundaries of instability domains (parametric resonance domains) in an analytic form. For arbitrary eccentricity values we numerically construct domains of stability in linear approximation. Outside the above stability domains the resonant rotation is unstable in the sense of Lyapunov.

Keywords: Hamiltonian system, resonant periodic motion, parametric resonance, satellite, stability

Funding Agency Grant Number
Russian Science Foundation 14-21-00068


DOI: https://doi.org/10.20537/nd1604006

Full text: PDF file (346 kB)
References: PDF file   HTML file

UDC: 531.36, 531.352
MSC: 34C15, 34C20, 34C25
Received: 28.09.2016
Accepted:07.11.2016

Citation: B. S. Bardin, E. A. Chekina, “On the stability of a resonant rotation of a satellite in an elliptic orbit”, Nelin. Dinam., 12:4 (2016), 619–632

Citation in format AMSBIB
\Bibitem{BarChe16}
\by B.~S.~Bardin, E. A. Chekina
\paper On the stability of a resonant rotation of a satellite in an elliptic orbit
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 4
\pages 619--632
\mathnet{http://mi.mathnet.ru/nd542}
\crossref{https://doi.org/10.20537/nd1604006}
\elib{http://elibrary.ru/item.asp?id=27715767}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Boris S. Bardin, Evgeniya A. Chekina, “On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Second-order Resonance Case”, Regul. Chaotic Dyn., 22:7 (2017), 808–823  mathnet  crossref
    2. Tatyana E. Churkina, Sergey Y. Stepanov, “On the Stability of Periodic Mercury-type Rotations”, Regul. Chaotic Dyn., 22:7 (2017), 851–864  mathnet  crossref
    3. B. S. Bardin, E. A. Chekina, “On the constructive algorithm for stability investigation of an equilibrium point of a periodic Hamiltonian system with two degrees of freedom in first-order resonance case”, Mech. Sol., 53:2 (2018), S15–S25  crossref  mathscinet  isi  scopus
  • Нелинейная динамика
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