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Regular and Chaotic Dynamics, 2003, Volume 8, Issue 3, Pages 297–304
DOI: https://doi.org/10.1070/RD2003v008n03ABEH000245 (Mi rcd783) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On stability of regular precessions of a non-symmetric gyroscope

A. P. Markeev

Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow 119526, Vernadsky ave. 101, Russia
Citations (5)
DOI: https://doi.org/10.1070/RD2003v008n03ABEH000245
Abstract: We consider the motion of a rigid body around a fixed point in homogeneous gravity field. The body is not dynamically symmetric and the center of gravity is situated on the straight line passing through the fixed point perpendicular to circular cross-sections of inertia ellipsoid. In 1947, G.Grioli proved that the body with such geometry of mass can be in a state of regular precession around of a nonvertical axis. In this paper we study the stability of this precession.
Received: 05.05.2003
Bibliographic databases:
Document Type: Article
MSC: 34K20, 70E17
Language: English
Citation: A. P. Markeev, “On stability of regular precessions of a non-symmetric gyroscope”, Regul. Chaotic Dyn., 8:3 (2003), 297–304
Citation in format AMSBIB
\Bibitem{Mar03}
\by A. P. Markeev
\paper On stability of regular precessions of a non-symmetric gyroscope
\jour Regul. Chaotic Dyn.
\yr 2003
\vol 8
\issue 3
\pages 297--304
\mathnet{http://mi.mathnet.ru/rcd783}
\crossref{https://doi.org/10.1070/RD2003v008n03ABEH000245}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2020845}
\zmath{https://zbmath.org/?q=an:1150.70311}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003RCD.....8..297M}
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  • https://www.mathnet.ru/eng/rcd783
  • https://www.mathnet.ru/eng/rcd/v8/i3/p297
    • This publication is cited in the following 5 articles:
    1. 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  crossref
    2. 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  mathnet  crossref
    3. 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  mathnet  crossref
    4. 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  crossref
    5. 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  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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