Action minimizers under topological constraints in the planar equal-mass four-body problem

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

paper · pdf · doi:10.48550/arxiv.1710.09959

openalex publication_date 2017/10/27 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

It is shown that in the planar equal-mass four-body problem, there exist two sets of new action minimizers connecting two planar boundary configurations with fixed symmetry axes and specific order constraints on the four bodies: a double isosceles configuration and an isosceles trapezoid configuration. By applying the level estimate method, these minimizers are shown to be collision-free and they can be extended to two new sets of periodic or quasi-periodic orbits.

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