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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 6, Pages 878–887
DOI: https://doi.org/10.1134/S1560354723060059 (Mi rcd1239) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom

Boris S. Bardin

Department of Mechatronic and Theoretical Mechanics, Institute of Computer Science and Applied Mathematics, Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, 125993 Moscow, Russia
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DOI: https://doi.org/10.1134/S1560354723060059
Abstract: A general method is presented for constructing a nonlinear canonical transformation, which makes it possible to introduce local variables in a neighborhood of periodic motions of an autonomous Hamiltonian system with two degrees of freedom. This method can be used for investigating the behavior of the Hamiltonian system in the vicinity of its periodic trajectories. In particular, it can be applied to solve the problem of orbital stability of periodic motions.
Keywords: normal form, KAM theory, orbital stability, periodic orbit, Hamiltonian system, canonical transformation.
Funding agency Grant number
Russian Science Foundation 22-21-00729
This research was supported by the grant of the Russian Science Foundation (project 22-21-00729) and was carried out at the Moscow Aviation Institute (National Research University).
Received: 11.12.2022
Accepted: 01.11.2023
Document Type: Article
MSC: 34D20, 37J40, 70K30, 70K45, 37N05
Language: English
Citation: Boris S. Bardin, “On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom”, Regul. Chaotic Dyn., 28:6 (2023), 878–887
Citation in format AMSBIB
\Bibitem{Bar23}
\by Boris S. Bardin
\paper On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 6
\pages 878--887
\mathnet{http://mi.mathnet.ru/rcd1239}
\crossref{https://doi.org/10.1134/S1560354723060059}
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