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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 7 scientific papers (total in 7 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 (7)
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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 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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