English

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