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<p>We study natural mechanical systems on the two-dimensional plane in a magnetic fieldthat admit an additional first integral which is rational in momenta.In this article,we construct new integrable examples of such systems and also studythe problem of existence of rational integrals in the absence of a&#xa0;magnetic&#xa0;field.</p>

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Rational Integrals of Natural Systems in a Magnetic Field

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • S. V. Agapov,
  • D. V. Solov’ev

摘要

We study natural mechanical systems on the two-dimensional plane in a magnetic fieldthat admit an additional first integral which is rational in momenta.In this article,we construct new integrable examples of such systems and also studythe problem of existence of rational integrals in the absence of a magnetic field.