2021/12/13 by Yiyang Deng, Deng, Yiyang, Marshall Hampton +1
Engineering · Physics and Astronomy · #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.2112.06755
openalex publication_date 2021/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Central configurations and relative equilibria are an important facet of the study of the N-body problem, but become very difficult to rigorously analyze for N>3. In this paper we focus on a particular but interesting class of configurations of the 5-body problem: the equilateral pentagonal configurations, which have a cycle of five equal edges. We prove a variety of results concerning central configurations with this property, including a computer-assisted proof of the finiteness of such configurations for any positive five masses with a range of rational-exponent homogeneous potentials (including the Newtonian case and point-vortex model), some constraints on their shapes, and we determine some exact solutions for particular N-body potentials.