Regular and Chaotic Dynamics
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Regular and Chaotic Dynamics, 2012, том 17, выпуск 3-4, страницы 243–257
DOI: https://doi.org/10.1134/S1560354712030033
(Mi rcd401)
 

Эта публикация цитируется в 19 научных статьях (всего в 19 статьях)

On the Orbital Stability of Pendulum-like Oscillations and Rotations of a Symmetric Rigid Body with a Fixed Point

Boris S. Bardin, Alexander A. Savin

Moscow Aviation Institute, Volokolamskoe sh. 4, Moscow, 125993, Russia
Аннотация: We deal with the problem of orbital stability of planar periodic motions of a dynamically symmetric heavy rigid body with a fixed point. We suppose that the center of mass of the body lies in the equatorial plane of the ellipsoid of inertia. Unperturbed periodic motions are planar pendulum-like oscillations or rotations of the body around a principal axis keeping a fixed horizontal position.
Local coordinates are introduced in a neighborhood of the unperturbed periodic motion and equations of the perturbed motion are obtained in Hamiltonian form. Regions of orbital instability are established by means of linear analysis. Outside the above-mentioned regions, nonlinear analysis is performed taking into account terms up to degree 4 in the expansion of the Hamiltonian in a neighborhood of unperturbed motion. The nonlinear problem of orbital stability is reduced to analysis of stability of a fixed point of the symplectic map generated by the equations of the perturbed motion. The coefficients of the symplectic map are determined numerically. Rigorous results on the orbital stability or instability of unperturbed motion are obtained by analyzing these coefficients. The orbital stability is investigated analytically in two limiting cases: small amplitude oscillations and rotations with large angular velocities when a small parameter can be introduced.
Ключевые слова: Hamiltonian system, periodic motions, normal form, resonance, action–angle variables, orbital stability.
Финансовая поддержка Номер гранта
Российский фонд фундаментальных исследований 11-01-00322
Министерство образования и науки Российской Федерации NSh-4149.2012.1
11.G34.31.0039
This research was supported by the Russian Foundation for Basic Research (11-01-00322), the State Program for Support of Leading Scientific Schools (NSh-4149.2012.1) and by the Grant of the Government of the Russian Federation for state support of scientific research conducted under supervision of leading scientists at Russian institutions of higher professional education (Contract No 11.G34.31.0039).
Поступила в редакцию: 27.01.2012
Принята в печать: 08.05.2012
Реферативные базы данных:
Тип публикации: Статья
Язык публикации: английский
Образец цитирования: Boris S. Bardin, Alexander A. Savin, “On the Orbital Stability of Pendulum-like Oscillations and Rotations of a Symmetric Rigid Body with a Fixed Point”, Regul. Chaotic Dyn., 17:3-4 (2012), 243–257
Цитирование в формате AMSBIB
\RBibitem{BarSav12}
\by Boris S. Bardin, Alexander A. Savin
\paper On the Orbital Stability of Pendulum-like Oscillations and Rotations of a Symmetric Rigid Body with a Fixed Point
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 3-4
\pages 243--257
\mathnet{http://mi.mathnet.ru/rcd401}
\crossref{https://doi.org/10.1134/S1560354712030033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2956221}
\zmath{https://zbmath.org/?q=an:1253.70009}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..243B}
Образцы ссылок на эту страницу:
  • https://www.mathnet.ru/rus/rcd401
  • https://www.mathnet.ru/rus/rcd/v17/i3/p243
  • Эта публикация цитируется в следующих 19 статьяx:
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