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Abstract <p> We present a brief overview of our results on new integrable cases in Hamiltonian mechanics. The paper is devoted to a description of quadratic Hamiltonians that have an additional integral of motion in the cases of linear Poisson brackets <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2627_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak{e}(3)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2627_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak{so}(4)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2627_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathfrak{so}(3,1)\)</EquationSource> </InlineEquation>. </p>

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Integrable Hamiltonians related to the \(\mathfrak{e}(3)\), \(\mathfrak{so}(4)\), and \(\mathfrak{so}(3,1)\) Poisson brackets

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • V. V. Sokolov

摘要

Abstract

We present a brief overview of our results on new integrable cases in Hamiltonian mechanics. The paper is devoted to a description of quadratic Hamiltonians that have an additional integral of motion in the cases of linear Poisson brackets \(\mathfrak{e}(3)\) , \(\mathfrak{so}(4)\) and \(\mathfrak{so}(3,1)\) .