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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
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
Аннотация:
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.
Ключевые слова:
relative equilibria, Euler and Lagrange configurations.
Поступила в редакцию: 16.03.2023 Принята в печать: 29.08.2023
Образец цитирования:
Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Three-Body Relative Equilibria on $\mathbb{S}^2$”, Regul. Chaotic Dyn., 28:4-5 (2023), 690–706
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1228 https://www.mathnet.ru/rus/rcd/v28/i4/p690
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