Existence of prograde double-double orbits in the equal-mass four-body problem

2017/10/27 by Wentian Kuang, Kuang, Wentian, Duokui Yan +1
Engineering · Physics and Astronomy · #Astro and Planetary Science #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1710.09960

openalex publication_date 2017/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle θ∈ (0, π/7] in the equal-mass four-body problem. A new geometric argument is introduced to show that for any θ∈ (0, π/2), the action of the minimizer corresponding to the prograde double-double orbit is strictly greater than the action of the minimizer corresponding to the retrograde double-double orbit. This geometric argument can also be applied to study orbits in the planar three-body problem, such as the retrograde orbits, the prograde orbits, the Schubart orbit and the Hénon orbit.

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