A. P. Markeev, “On the Steklov case in rigid body dynamics”, Regul. Chaotic Dyn., 10:1 (2005), 81

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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)

DOI: https://doi.org/10.1070/RD2005v010n01ABEH000302

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 > 2 C

$B>A>2C$ or

2 B > A > B > C

$2B>A>B>C$ ,

A > 2 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}

Linking options:

https://www.mathnet.ru/eng/rcd698

https://www.mathnet.ru/eng/rcd/v10/i1/p81

This publication is cited in the following 8 articles:

Víctor Lanchares, Manuel Iñarrea, Ana Isabel Pascual, Antonio Elipe, “Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors”, Mathematics, 10:11 (2022), 1882
Ji-Huan He, T.S. Amer, H.F. El-Kafly, A.A. Galal, “Modelling of the rotational motion of 6-DOF rigid body according to the Bobylev-Steklov conditions”, Results in Physics, 35 (2022), 105391
Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520
Anatoly P. Markeev, “On the Stability of Periodic Motions of an Autonomous Hamiltonian System in a Critical Case of the Fourth-order Resonance”, Regul. Chaotic Dyn., 22:7 (2017), 773–781
Manuel Iñarrea, Víctor Lanchares, Ana I. Pascual, Antonio Elipe, “On the Stability of a Class of Permanent Rotations of a Heavy Asymmetric Gyrostat”, Regul. Chaotic Dyn., 22:7 (2017), 824–839
H. M. Yehia, S. Z. Hassan, M. E. Shaheen, “On the orbital stability of the motion of a rigid body in the case of Bobylev–Steklov”, Nonlinear Dyn, 80:3 (2015), 1173
Hamad M. Yehia, E. G. El-Hadidy, “On the Orbital Stability of Pendulum-like Vibrations of a Rigid Body Carrying a Rotor”, Regul. Chaotic Dyn., 18:5 (2013), 539–552
Andrzej J. Maciejewski, Maria Przybylska, “Integrable Variational Equations of Non-integrable Systems”, Regul. Chaotic Dyn., 17:3 (2012), 337–358

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

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