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<b>Abstract</b>— <p>The general three-body problem is considered in shape space. Solutions to the problem in such a space have a number of remarkable properties. The paper presents the equations of motion of the three-body problem in shape space, the integrals of the problem are investigated. As it turns out, Sundman’s inequality is a simple consequence of the energy integral in the shape space. The periodic solutions obtained of the three-body problem are considered in shape space, and their properties are studied.</p>

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The Three-Body Problem in Shape Space

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • V. B. Titov

摘要

Abstract—

The general three-body problem is considered in shape space. Solutions to the problem in such a space have a number of remarkable properties. The paper presents the equations of motion of the three-body problem in shape space, the integrals of the problem are investigated. As it turns out, Sundman’s inequality is a simple consequence of the energy integral in the shape space. The periodic solutions obtained of the three-body problem are considered in shape space, and their properties are studied.