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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 496, Pages 5–9
DOI: https://doi.org/10.31857/S268695432101015X (Mi danma144) 		 
This article is cited in 10 scientific papers (total in 10 papers)

MATHEMATICS

Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases

V. V. Vedyushkina, A. T. Fomenko

Lomonosov Moscow State University
Full-text PDF (954 kB) Citations (10)
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DOI: https://doi.org/10.31857/S268695432101015X
Abstract: A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).
Keywords: integrable system, billiard, billiard book, Liouville equivalence, Fomenko–Zieschang invariant, evolutionary force billiards, rigid body dynamics.
Funding agency Grant number
19-01-00775-a
This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00775-a.
Received: 23.01.2021
Revised: 23.01.2021
Accepted: 26.01.2021
English version:
Doklady Mathematics, 2021, Volume 103, Issue 1, Pages 1–4
DOI: https://doi.org/10.1134/S1064562421010154
Bibliographic databases:
Document Type: Article
UDC: 517.938.5
Language: Russian
Citation: V. V. Vedyushkina, A. T. Fomenko, “Force evolutionary billiards and billiard equivalence of the Euler and Lagrange cases”, Dokl. RAN. Math. Inf. Proc. Upr., 496 (2021), 5–9; Dokl. Math., 103:1 (2021), 1–4
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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