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Regular and Chaotic Dynamics, 2005, Volume 10, Issue 1, Pages 81–93
DOI: https://doi.org/10.1070/RD2005v010n01ABEH000302
(Mi rcd698)
 

This article is cited in 8 scientific papers (total in 8 papers)

On the Steklov case in rigid body dynamics

A. P. Markeev

Institute of Problems in Mechanics, Russian Academy of Sciences, 101, Vernadsky av., 119526 Moscow, Russia
Citations (8)
Abstract: We study the motion of a heavy rigid body with a fixed point. The center of mass is located on mean or minor axis of the ellipsoid of inertia, with the moments of inertia satisfying the conditions $B>A>2C$ or $2B>A>B>C$, $A>2C$ as well as the usual triangle inequalities. Under these circumstances the Euler–Poisson equations have the particular periodic solutions mentioned by V. A. Steklov. We examine the problem of the orbital stability of the periodic motions of a rigid body, which correspond to the Steklov solutions.
Keywords: rigid body dynamics, Euler–Poisson equations, Steklov solutions, orbital stability of the periodic motions.
Received: 21.09.2004
Accepted: 26.01.2005
Bibliographic databases:
Document Type: Article
MSC: 70E17, 70E50
Language: English
Citation: A. P. Markeev, “On the Steklov case in rigid body dynamics”, Regul. Chaotic Dyn., 10:1 (2005), 81–93
Citation in format AMSBIB
\Bibitem{Mar05}
\by A. P. Markeev
\paper On the Steklov case in rigid body dynamics
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 1
\pages 81--93
\mathnet{http://mi.mathnet.ru/rcd698}
\crossref{https://doi.org/10.1070/RD2005v010n01ABEH000302}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2136832}
\zmath{https://zbmath.org/?q=an:1120.70007}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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