RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2015, Volume 20, Issue 1, Pages 63–73 (Mi rcd61)  

This article is cited in 9 scientific papers (total in 9 papers)

On the Stability of a Planar Resonant Rotation of a Satellite in an Elliptic Orbit

Boris S. Bardin, Evgeniya A. Chekina, Alexander M. Chekin

Theoretical Mechanics Department, Faculty of Applied Mathematics and Physics, Moscow Aviation Institute, Volokolamskoe sh. 4, Moscow, 125871, Russia

Abstract: We study the Lyapunov stability problem of the resonant rotation of a rigid body satellite about its center of mass in an elliptical orbit. The resonant rotation is a planar motion such that the satellite completes one rotation in absolute space during two orbital revolutions of its center of mass. The stability analysis of the above resonance rotation was started in [4, 6]. In the present paper, rigorous stability conclusions in the previously unstudied range of parameter values are obtained. In particular, new intervals of stability are found for eccentricity values close to 1. In addition, some special cases are studied where the stability analysis should take into account terms of degree not less than six in the expansion of the Hamiltonian of the perturbed motion. Using the technique described in [7, 8], explicit formulae are obtained, allowing one to verify the stability criterion of a time-periodic Hamiltonian system with one degree of freedom in the special cases mentioned.

Keywords: Hamiltonian system, symplectic map, normal form, resonance, satellite, stability

Funding Agency Grant Number
Russian Science Foundation 14-21-00068
The work was carried out under the grant of the Russian Scientific Foundation (project No 14-21-00068) at the Moscow Aviation Institute (National Research University).


DOI: https://doi.org/10.1134/S1560354715010050

References: PDF file   HTML file

Bibliographic databases:

MSC: 34C15, 34C20, 34C23, 34C25
Received: 26.11.2014
Accepted:13.12.2014
Language:

Citation: Boris S. Bardin, Evgeniya A. Chekina, Alexander M. Chekin, “On the Stability of a Planar Resonant Rotation of a Satellite in an Elliptic Orbit”, Regul. Chaotic Dyn., 20:1 (2015), 63–73

Citation in format AMSBIB
\Bibitem{BarCheChe15}
\by Boris S. Bardin, Evgeniya A. Chekina, Alexander M. Chekin
\paper On the Stability of a Planar Resonant Rotation of a Satellite in an Elliptic Orbit
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 1
\pages 63--73
\mathnet{http://mi.mathnet.ru/rcd61}
\crossref{https://doi.org/10.1134/S1560354715010050}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3304938}
\zmath{https://zbmath.org/?q=an:1325.70032}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000349024900005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944180677}


Linking options:
  • http://mi.mathnet.ru/eng/rcd61
  • http://mi.mathnet.ru/eng/rcd/v20/i1/p63

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. B. S. Bardin, E. A. Chekina, “Ob ustoichivosti rezonansnogo vrascheniya sputnika na ellipticheskoi orbite”, Nelineinaya dinam., 12:4 (2016), 619–632  mathnet  crossref  elib
    2. Boris S. Bardin, Evgeniya A. Chekina, “On the Stability of Resonant Rotation of a Symmetric Satellite in an Elliptical Orbit”, Regul. Chaotic Dyn., 21:4 (2016), 377–389  mathnet  crossref
    3. 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
    4. Tatyana E. Churkina, Sergey Y. Stepanov, “On the Stability of Periodic Mercury-type Rotations”, Regul. Chaotic Dyn., 22:7 (2017), 851–864  mathnet  crossref
    5. J. Chu, Z. Liang, P. J. Torres, Zh. Zhou, “Existence and stability of periodic oscillations of a rigid Dumbbell satellite around its center of mass”, Discrete Contin. Dyn. Syst.-Ser. B, 22:7 (2017), 2669–2685  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. B. S. Bardin, A. N. Avdushkin, “Stability analysis of an equilibrium position in the photogravitational Sitnikov problem”, Eighth Polyakhov's Reading, AIP Conf. Proc., 1959, eds. E. Kustova, G. Leonov, N. Morosov, M. Yushkov, M. Mekhonoshina, Amer. Inst. Phys., 2018, 040002  crossref  isi  scopus
    8. B. S. Bardin, E. A. Chekina, “On orbital stability of planar oscillations of a satellite in a circular orbit on the boundary of the parametric resonance”, Eighth Polyakhov's Reading, AIP Conf. Proc., 1959, eds. E. Kustova, G. Leonov, N. Morosov, M. Yushkov, M. Mekhonoshina, Amer. Inst. Phys., 2018, 040003  crossref  isi  scopus
    9. Z. Liang, F. Liao, “Periodic solutions for a dumbbell satellite equation”, Nonlinear Dyn., 95:3 (2019), 2469–2476  crossref  zmath  isi  scopus
  • Number of views:
    This page:100
    References:31

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020