The only syzygy-free solution is Lagrange's
Dynamical Systems
2007-05-23 v1 Classical Analysis and ODEs
Abstract
A syzygy in the three-body problem is a collinear instant. We prove that with the exception of Lagrange's solution every solution to the zero angular momentum Newtonian three-body problem suffers syzygies. The proof works for all mass ratios.
Cite
@article{arxiv.math/0601269,
title = {The only syzygy-free solution is Lagrange's},
author = {Richard Montgomery},
journal= {arXiv preprint arXiv:math/0601269},
year = {2007}
}
Comments
12 pages. 1 figure