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Russian Journal of Nonlinear Dynamics, 2021, Volume 17, Number 4, Pages 453–464
DOI: https://doi.org/10.20537/nd210407 (Mi nd770) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Nonlinear physics and mechanics

On the Orbital Stability of Pendulum-like Oscillations of a Heavy Rigid Body with a Fixed Point in the Bobylev – Steklov Case

B. S. Bardinabc, E. A. Chekinaa

a Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia
b Mechanical Engineering Research Institute of the Russian Academy of Sciences, M. Kharitonyevskiy per. 4, Moscow, 101990 Russia
c Moscow Automobile and Road Construction State Technical University (MADI), Leningradsky pr. 64, Moscow, 125319 Russia
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DOI: https://doi.org/10.20537/nd210407
Abstract: The orbital stability of pendulum-like oscillations of a heavy rigid body with a fixed point in the Bobylev – Steklov case is investigated. In particular, a nonlinear study of the orbital stability is performed for the so-called case of degeneracy, where it is necessary to take into account terms of order six in the Hamiltonian expansion in a neighborhood of the unperturbed periodic orbit.
Keywords: rigid body, rotations, oscillations, orbital stability, Hamiltonian system, local coordinates, normal form.
Funding agency Grant number
Russian Science Foundation 19-11-00116
This work was supported by the grant of the Russian Scientific Foundation (project No. 19-11-00116) at the Moscow Aviation Institute (National Research University).
Received: 07.12.2021
Accepted: 15.12.2021
Bibliographic databases:
Document Type: Article
MSC: 34D20, 37J40, 70K30, 70K45, 37N05
Language: english
Citation: B. S. Bardin, E. A. Chekina, “On the Orbital Stability of Pendulum-like Oscillations of a Heavy Rigid Body with a Fixed Point in the Bobylev – Steklov Case”, Rus. J. Nonlin. Dyn., 17:4 (2021), 453–464
Citation in format AMSBIB
\Bibitem{BarChe21}
\by B. S. Bardin, E. A. Chekina
\paper On the Orbital Stability of Pendulum-like Oscillations
of a Heavy Rigid Body with a Fixed Point in the
Bobylev – Steklov Case
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 4
\pages 453--464
\mathnet{http://mi.mathnet.ru/nd770}
\crossref{https://doi.org/10.20537/nd210407}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123557535}
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