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Journal Articles CRAS Compte Rendu Académie des Sciences Year : 2023

On the existence of generalised syzygies in the planar three-body problem

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Abstract

We consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurations. Our proof is elementary and uses only basic tools from the Sturm-Liouville theory.
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Dates and versions

ensl-03937024 , version 1 (13-01-2023)

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  • HAL Id : ensl-03937024 , version 1

Cite

Alexei Tsygvintsev. On the existence of generalised syzygies in the planar three-body problem. CRAS Compte Rendu Académie des Sciences, In press. ⟨ensl-03937024⟩
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