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Nelin. Dinam., 2016, Volume 12, Number 1, Pages 75–90 (Mi nd513)  

This article is cited in 3 scientific papers (total in 3 papers)

Original papers

On the stability of the two-link trajectory of the parabolic Birkhoff billiards

A. P. Markeev

A.Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: We study the inertial motion of a material point in a planar domain bounded by two coaxial parabolas. Inside the domain the point moves along a straight line, the collisions with the boundary curves are assumed to be perfectly elastic. There is a two-link periodic trajectory, for which the point alternately collides with the boundary parabolas at their vertices, and in the intervals between collisions it moves along the common axis of the parabolas. We study the nonlinear problem of stability of the two-link trajectory of the point.

Keywords: map, canonical transformations, Hamilton system, stability

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00380_а


Full text: PDF file (371 kB)
References: PDF file   HTML file
UDC: 531.01, 531.36
MSC: 70H05, 70H15, 70E50
Received: 10.02.2016
Revised: 22.02.2016

Citation: A. P. Markeev, “On the stability of the two-link trajectory of the parabolic Birkhoff billiards”, Nelin. Dinam., 12:1 (2016), 75–90

Citation in format AMSBIB
\Bibitem{Mar16}
\by A.~P.~Markeev
\paper On the stability of the two-link trajectory of the parabolic Birkhoff billiards
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 1
\pages 75--90
\mathnet{http://mi.mathnet.ru/nd513}


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    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, “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
    2. Anatoly P. Markeev, “On the Stability of Periodic Motions of an Autonomous Hamiltonian System in a Critical Case of the Fourth-order Resonance”, Regul. Chaotic Dyn., 22:7 (2017), 773–781  mathnet  crossref
    3. A. N. Kirillov, R. V. Alkin, “Ustoichivost periodicheskikh bilyardnykh traektorii v treugolnike”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:1 (2018), 25–39  mathnet  crossref  elib
  • Нелинейная динамика
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