Periodic Solutions with Singularities in Two Dimensions in the $n$-body Problem
Dynamical Systems
2010-02-09 v3
Abstract
Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily extends to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated.
Cite
@article{arxiv.0811.0227,
title = {Periodic Solutions with Singularities in Two Dimensions in the $n$-body Problem},
author = {Tiancheng Ouyang and Skyler C. Simmons and Duokui Yan},
journal= {arXiv preprint arXiv:0811.0227},
year = {2010}
}