English

The Binary Returns!

Dynamical Systems 2016-10-25 v3 Classical Analysis and ODEs

Abstract

Consider the spatial Newtonian three body problem at fixed negative energy and fixed angular momentum. The moment of inertia II provides a measure of the overall size of a three-body system. We will prove that there is a positive number I0I_0 depending on the energy and angular momentum levels as well as the masses such that every solution at these levels passes through II0I\leq I_0 at some instant of time. Motivation for this result comes from trying to prove the impossibility of realizing a certain syzygy sequence in the zero angular momentum problem.

Keywords

Cite

@article{arxiv.1512.01852,
  title  = {The Binary Returns!},
  author = {Connor Jackman},
  journal= {arXiv preprint arXiv:1512.01852},
  year   = {2016}
}

Comments

16 pages, 4 figures

R2 v1 2026-06-22T12:02:42.428Z