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 -