Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2014, Volume 10, Number 4, Pages 447–464 (Mi nd456)  

This article is cited in 7 scientific papers (total in 7 papers)

Simplifying the structure of the third and fourth degree forms in the expansion of the Hamiltonian with a linear transformation

Anatoly P. Markeev

A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia
Full-text PDF (414 kB) Citations (7)
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Abstract: We consider the canonical differential equations describing the motion of a system with one degree of freedom. The origin of the phase space is assumed to be an equilibrium position of the system. It is supposed that in a sufficiently small neighborhood of the equilibrium Hamiltonian function can be represented by a convergent series. This series does not include terms of the second degree, and the terms of the third and fourth degrees are independent of time. Linear real canonical transformations leading the terms of the third and fourth degrees to the simplest forms are found. Classification of the systems in question being obtained on the basis of these forms is used in the discussion of the stability of the equilibrium position.
Keywords: Hamiltonian system, canonical transformation, stability.
Received: 04.11.2014
Revised: 20.11.2014
Document Type: Article
UDC: 531.36
Language: Russian
Citation: Anatoly P. Markeev, “Simplifying the structure of the third and fourth degree forms in the expansion of the Hamiltonian with a linear transformation”, Nelin. Dinam., 10:4 (2014), 447–464
Citation in format AMSBIB
\Bibitem{Mar14}
\by Anatoly~P.~Markeev
\paper Simplifying the structure of the third and fourth degree forms in the expansion of the Hamiltonian with a linear transformation
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 4
\pages 447--464
\mathnet{http://mi.mathnet.ru/nd456}
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  • https://www.mathnet.ru/eng/nd/v10/i4/p447
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Нелинейная динамика
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