Velocity Syzygies and Bounding Syzygy Moments in the Planar Three-Body Problem
Year: 2024
Type: article
Abstract: We consider the Newtonian planar three-body problem, defining a syzygy (velocity syzygy) as a configuration where the positions (velocities) of the three bodies become collinear. We demonstrate that if the total energy is negative, every collision-free solution has an infinite number of velocity syzygies. Specifically, the velocities of the three bodies become parallel within every interval of time containing three consecutive syzygies. Using comparison theory for matrix Riccati equations, we derive new upper and lower bounds on the moments when syzygies occur.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.683
Author: Alexei Tsygvintsev
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404695124