Three body relative equilibria on \mathbbS²

2023/09/12 by Toshiaki Fujiwara, Fujiwara, Toshiaki, Ernesto Pérez-Chavela +1
Physics and Astronomy · #70F07 #70F10 #70F15 #Astro and Planetary Science #Classical Analysis and ODEs (math.CA) #Cosmology and Gravitation Theories #FOS: Mathematics #Nuclear physics research studies

paper · pdf · doi:10.48550/arxiv.2309.06603

openalex publication_date 2023/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study relative equilibria (RE in short) for three-body problem on \mathbbS², under the influence of a general potential which only depends on cosσ_ij where σ_ij are the mutual angles among the masses. Explicit conditions for masses m_k and cosσ_ij to form relative equilibrium are shown. Using the above conditions, we study the equal masses case under the cotangent potential. We show the existence of scalene and isosceles Euler RE, and isosceles and equilateral Lagrange RE.

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