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On some collinear configurations in the planar three-body problem

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Abstract

We study the planar Newtonian three-body problem and analyse the configurations in which the three bodies or their velocities are collinear. The existence of such configurations, also called generalised syzygies, was previously investigated by the author in [4] for bounded solutions. In this paper we generalise our result to the case of negative energy and provide a more simple proof. We also study periodic solutions admitting a particular geometric rigidity and show that they always suffer syzygies i.e. collinear in positions configurations.

Dates and versions

ensl-03937025 , version 1 (13-01-2023)

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Alexei Tsygvintsev. On some collinear configurations in the planar three-body problem. 2023. ⟨ensl-03937025⟩
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