Polygonal homographic orbits in spaces of constant curvature

2011/08/11 by Pieter Tibboel, Tibboel, Pieter
Engineering · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1108.2478

openalex publication_date 2011/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the geometry of the 2-dimensional n-body problem for spaces of constant curvature κ≠ 0, n≥ 3, does not allow for polygonal homographic solutions, provided that the corresponding orbits are irregular polygons of non-constant size.

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