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Abstract <p> We present new cases of integrable ninth-order dynamical systems that are homogeneousin part of the variables and in which a system on the cotangent bundle of a four-dimensionalmanifold can be isolated. Here the force field splits into an internal (conservative) field andan external field; the latter may have dissipation of either sign. The external field is introducedwith the use of some unimodular transformation and generalizes the earlier-considered fields.Complete sets of first integrals as well as of invariant differential forms are given.</p>

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Integrable Ninth-Order Dynamical Systems with Dissipation

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • M. V. Shamolin

摘要

Abstract

We present new cases of integrable ninth-order dynamical systems that are homogeneousin part of the variables and in which a system on the cotangent bundle of a four-dimensionalmanifold can be isolated. Here the force field splits into an internal (conservative) field andan external field; the latter may have dissipation of either sign. The external field is introducedwith the use of some unimodular transformation and generalizes the earlier-considered fields.Complete sets of first integrals as well as of invariant differential forms are given.