Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem
Dynamical Systems
2008-11-20 v1
Abstract
This paper shows the existence of a periodic orbit with singularity in the symmetric collinear four body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proven by using the implicit function theorem and a continuity argument on differential equations of the regularized Hamiltonian.
Cite
@article{arxiv.0811.3199,
title = {Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem},
author = {Ouyang Tiancheng and Duokui Yan},
journal= {arXiv preprint arXiv:0811.3199},
year = {2008}
}
Comments
submitted, manuscripta mathematica