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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 2, Pages 255–265
DOI: https://doi.org/10.33048/smzh.2020.61.202 (Mi smj5979) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Rational integrals of a natural mechanical system on the 2-torus

S. V. Agapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (395 kB) Citations (8)
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DOI: https://doi.org/10.33048/smzh.2020.61.202
Abstract: Under study are the problems of existence of the first integrals rational in momenta for a natural mechanical system on the 2-torus. We prove that a rational integral with a linear numerator and denominator reduces to a linear integral. Considering the case of a quadratic numerator and linear denominator, we obtain an analogous result under some additional assumptions on the coefficients of the first integral.
Keywords: natural mechanical system, rational first integral.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-5913.2018.1
The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-5913.2018.1).
Received: 16.08.2019
Revised: 16.08.2019
Accepted: 25.12.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 2, Pages 199–207
DOI: https://doi.org/10.1134/S0037446620020020
Bibliographic databases:
Document Type: Article
UDC: 513.938
MSC: 35R30
Language: Russian
Citation: S. V. Agapov, “Rational integrals of a natural mechanical system on the 2-torus”, Sibirsk. Mat. Zh., 61:2 (2020), 255–265; Siberian Math. J., 61:2 (2020), 199–207
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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