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<p>In this paper, we prove the integrability of some classes of odd-order dynamical systems (namely, systems of order three, five, seven, and nine), which are homogeneous in some variables and contain a&#xa0;system on the tangent bundle of a&#xa0;smooth manifolds. In this case, we separate force fields into internal (conservative) and external, which has sign-alternating dissipation. External fields are introduced by using some unimodular transformations and generalize fields considered earlier.</p>

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INTEGRABLE DYNAMICAL SYSTEMS OF ODD ORDER WITH SIGN-ALTERNATING DISSIPATION

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • M. V. Shamolin

摘要

In this paper, we prove the integrability of some classes of odd-order dynamical systems (namely, systems of order three, five, seven, and nine), which are homogeneous in some variables and contain a system on the tangent bundle of a smooth manifolds. In this case, we separate force fields into internal (conservative) and external, which has sign-alternating dissipation. External fields are introduced by using some unimodular transformations and generalize fields considered earlier.