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arXiv · 0811.3199

Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem

Ouyang Tiancheng·Duokui Yan
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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.

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Ouyang Tiancheng, Duokui Yan. 2008-11-19. Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem. https://arxiv.org/abs/0811.3199

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