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arXiv · 2506.13570

Partially rigid motions in the planar three-body problem

Richard Moeckel
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Abstract

A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibrium.

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Richard Moeckel. 2025-06-16. Partially rigid motions in the planar three-body problem. https://arxiv.org/abs/2506.13570

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