|
This article is cited in 1 scientific paper (total in 1 paper)
Special Issue: On the 80th birthday of professor A. Chenciner
Three-Body Relative Equilibria on $\mathbb{S}^2$
Toshiaki Fujiwaraa, Ernesto Pérez-Chavelab a College of Liberal Arts and Sciences, Kitasato University,
1-15-1 Kitasato, Sagamihara, 252-0329 Kanagawa, Japan
b Department of Mathematics, ITAM,
Río Hondo 1, Col. Progreso Tizapán, 01080 México, México
Abstract:
We study relative equilibria ($RE$) for the three-body problem
on $\mathbb{S}^2$,
under the influence of a general potential which only depends on
$\cos\sigma_{ij}$ where $\sigma_{ij}$ are the mutual angles
among the masses.
Explicit conditions for
masses $m_k$ and $\cos\sigma_{ij}$
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, isosceles, and equilateral Euler $RE$, and isosceles
and equilateral Lagrange $RE$.
We also show that
the equilateral Euler $RE$ on a rotating meridian
exists for general potential $\sum_{i<j}m_i m_j U(\cos\sigma_{ij})$
with any mass ratios.
Keywords:
relative equilibria, Euler and Lagrange configurations.
Received: 16.03.2023 Accepted: 29.08.2023
Citation:
Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Three-Body Relative Equilibria on $\mathbb{S}^2$”, Regul. Chaotic Dyn., 28:4-5 (2023), 690–706
Linking options:
https://www.mathnet.ru/eng/rcd1228 https://www.mathnet.ru/eng/rcd/v28/i4/p690
|
Statistics & downloads: |
Abstract page: | 32 | References: | 15 |
|