RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Nelin. Dinam., 2014, Volume 10, Number 4, Pages 447–464 (Mi nd456)  

This article is cited in 5 scientific papers (total in 5 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

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.

Full text: PDF file (414 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 531.36
MSC: 70H05,70H15,70E50
Received: 04.11.2014
Revised: 20.11.2014

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}


Linking options:
  • http://mi.mathnet.ru/eng/nd456
  • http://mi.mathnet.ru/eng/nd/v10/i4/p447

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. P. Markeev, “Ob ustoichivosti nepodvizhnykh tochek otobrazhenii, sokhranyayuschikh ploschad”, Nelineinaya dinam., 11:3 (2015), 503–545  mathnet
    2. Anatoly P. Markeev, “On the Birkhoff Transformation in the Case of Complete Degeneracy of the Quadratic Part of the Hamiltonian”, Regul. Chaotic Dyn., 20:3 (2015), 309–316  mathnet  crossref  mathscinet  zmath  adsnasa
    3. Boris S. Bardin, Victor Lanchares, “On the Stability of Periodic Hamiltonian Systems with One Degree of Freedom in the Case of Degeneracy”, Regul. Chaotic Dyn., 20:6 (2015), 627–648  mathnet  crossref  mathscinet  adsnasa
    4. A. P. Markeev, “On the stability of periodic trajectories of a planar Birkhoff billiard”, Proc. Steklov Inst. Math., 295 (2016), 190–201  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Rodrigo Gutierrez, Claudio Vidal, “Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case”, Regul. Chaotic Dyn., 22:7 (2017), 880–892  mathnet  crossref
  • Нелинейная динамика
    Number of views:
    This page:177
    Full text:73
    References:41

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019