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Abstract <p>A particular case of a local integral, published by Shamshiev in2024, leads asymptotically to a potential with almost sphericalsymmetry at large distances <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11755_2025_5252_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> <!--ASPBull2560004Shamshiev-m1--> </InlineEquation>. The <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11755_2025_5252_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="126" /> </InlineMediaObject> <EquationSource Format="TEX">\(L(x,y,z)=\textrm{const}\)</EquationSource> <!--ASPBull2560004Shamshiev-m2--> </InlineEquation> surfaces, which give the boundaries of the area ofmotion and are close to spheres, are found.</p>

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Cases of Further Integrability of the Equation of Motion in the Presence of the Local Integral in the Space Model. II

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • F. T. Shamshiev

摘要

Abstract

A particular case of a local integral, published by Shamshiev in2024, leads asymptotically to a potential with almost sphericalsymmetry at large distances \(r\) . The \(L(x,y,z)=\textrm{const}\) surfaces, which give the boundaries of the area ofmotion and are close to spheres, are found.