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

Alexei Tsygvintsev (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Mots clés: dynamical systems; celestial mechanics; three-body problem; syzygies

Domaines: Mathématiques [math]; Physique [physics]

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