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.

Original languageEnglish
Pages (from-to)199-207
Number of pages9
JournalSiberian Mathematical Journal
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • natural mechanical system
  • rational first integral

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.01.PQ MATHEMATICS

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