2022/03/28 by Toshiaki Fujiwara, Fujiwara, Toshiaki, Ernesto Pérez-Chavela +1
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #70F07 #70F15 #Astro and Planetary Science #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geophysics and Gravity Measurements #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.2203.14930
openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Relative equilibria on a rotating meridian on \mathbbS2 in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles, including equilateral, can form a relative equilibrium, except for the two equal arc angles θ= π/2. For θ∈ (0,2π/3)∖ \π/2\, the mid mass must be on the rotation axis, in our case, at the north or south pole of \mathbbS2. For θ∈ (2π/3,π), the mid mass must be on the equator. For θ=2π/3, we obtain the equilateral triangle, where the position of the masses is arbitrary. When the largest arc angle a_ℓ is in a_ℓ∈ (π/2,ac), with ac=1.8124..., two scalene configurations exist for given a_ℓ.