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<p>This paper addresses the spatial restricted elliptic problemof three bodies (material points) gravitating toward each other under Newton’s law ofgravitation. The eccentricity of the orbit of the main attracting bodies is assumed to besmall, and nonlinear oscillations ofa passively gravitating body near a Lagrangian triangular libration point are studied.It is assumed that in the limiting case of the circular problem the ratioof the frequency of rotation of the main bodies about their common center of massto the value of one of the frequencies of small linear oscillations of the passive bodyis exactly equal to three. A detailed analysis is made of two different particular cases ofinfluence of the three-dimensionality of theproblem on the characteristics of nonlinear oscillations of the passive body.</p>

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On Oscillations in a Neighborhood of Lagrangian Libration Points in One Resonance Case

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Anatoly P. Markeev

摘要

This paper addresses the spatial restricted elliptic problemof three bodies (material points) gravitating toward each other under Newton’s law ofgravitation. The eccentricity of the orbit of the main attracting bodies is assumed to besmall, and nonlinear oscillations ofa passively gravitating body near a Lagrangian triangular libration point are studied.It is assumed that in the limiting case of the circular problem the ratioof the frequency of rotation of the main bodies about their common center of massto the value of one of the frequencies of small linear oscillations of the passive bodyis exactly equal to three. A detailed analysis is made of two different particular cases ofinfluence of the three-dimensionality of theproblem on the characteristics of nonlinear oscillations of the passive body.