Quasi-periodic Almost-collision Orbits in the Spatial Three-Body Problem

2013/08/12 by Lei Zhao, Zhao, Lei · 1 citation
Engineering · Mathematics · Physics and Astronomy · #37N05 #70F15 #70F16 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Space Satellite Systems and Control #Spacecraft Dynamics and Control #math.DS #msc:37N05 #msc:70F15 #msc:70F16

paper · pdf · doi:10.48550/arxiv.1308.2484

25 pages, 2 figures

arxiv created 2013/08/12 · openalex publication_date 2013/08/12 · arxiv updated 2013/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a system of particles, quasi-periodic almost-collision orbits are collisionless orbits along which two bodies become arbitrarily close to each other -- the lower limit of their distance is zero but the upper limit is strictly positive -- and which are quasi-periodic in a regularized system up to a change of time. The existence of such orbits was shown in the restricted planar circular three-body problem by A. Chenciner and J. Llibre, and later, in the planar three-body problem by J. Féjoz. In the spatial three-body problem, the existence of a set of positive measure of such orbits was predicted by C. Marchal. In this article, we present a proof of this fact.

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• Consecutive collision orbits in the restricted three-body problem above the first critical energy value

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