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Rational Integrals of a Natural Mechanical System on the 2-Torus. / Agapov, S. V.

In: Siberian Mathematical Journal, Vol. 61, No. 2, 01.03.2020, p. 199-207.

Research output: Contribution to journal › Article › peer-review

Harvard

Agapov, SV 2020, 'Rational Integrals of a Natural Mechanical System on the 2-Torus', Siberian Mathematical Journal, vol. 61, no. 2, pp. 199-207. https://doi.org/10.1134/S0037446620020020

APA

Agapov, S. V. (2020). Rational Integrals of a Natural Mechanical System on the 2-Torus. Siberian Mathematical Journal, 61(2), 199-207. https://doi.org/10.1134/S0037446620020020

Vancouver

Agapov SV. Rational Integrals of a Natural Mechanical System on the 2-Torus. Siberian Mathematical Journal. 2020 Mar 1;61(2):199-207. doi: 10.1134/S0037446620020020

Author

Agapov, S. V. / Rational Integrals of a Natural Mechanical System on the 2-Torus. In: Siberian Mathematical Journal. 2020 ; Vol. 61, No. 2. pp. 199-207.

BibTeX

@article{b0d647a947524924a71161e7fc3ec996,
title = "Rational Integrals of a Natural Mechanical System on the 2-Torus",
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",
author = "Agapov, {S. V.}",
note = "Funding Information: The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-5913.2018.1). Acknowledgments Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = mar,
day = "1",
doi = "10.1134/S0037446620020020",
language = "English",
volume = "61",
pages = "199--207",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "2",

}

RIS

TY - JOUR

T1 - Rational Integrals of a Natural Mechanical System on the 2-Torus

AU - Agapov, S. V.

N1 - Funding Information: The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-5913.2018.1). Acknowledgments Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - natural mechanical system

KW - rational first integral

UR - http://www.scopus.com/inward/record.url?scp=85086326504&partnerID=8YFLogxK

U2 - 10.1134/S0037446620020020

DO - 10.1134/S0037446620020020

M3 - Article

AN - SCOPUS:85086326504

VL - 61

SP - 199

EP - 207

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 2

ER -

ID: 24503263