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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 4-5, Pages 690–706
DOI: https://doi.org/10.1134/S1560354723040111
(Mi rcd1228)
 

This article is cited in 3 scientific papers (total in 3 papers)

Special Issue: On the 80th birthday of professor A. Chenciner

Three-Body Relative Equilibria on S2

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
Citations (3)
References:
Abstract: We study relative equilibria (RE) for the three-body problem on S2, under the influence of a general potential which only depends on cosσij where σij are the mutual angles among the masses. Explicit conditions for masses mk and cosσij 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 i<jmimjU(cosσij) with any mass ratios.
Keywords: relative equilibria, Euler and Lagrange configurations.
Funding agency Grant number
CONACYT - Consejo Nacional de Ciencia y Tecnología A1S10112
The second author (EPC) has been partially supported by Asociación Mexicana de Cultura A.C. and Conacyt-México Project A1S10112.
Received: 16.03.2023
Accepted: 29.08.2023
Document Type: Article
MSC: 70F07, 70F10, 70F15
Language: English
Citation: Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Three-Body Relative Equilibria on S2”, Regul. Chaotic Dyn., 28:4-5 (2023), 690–706
Citation in format AMSBIB
\Bibitem{FujPer23}
\by Toshiaki Fujiwara, Ernesto P\'erez-Chavela
\paper Three-Body Relative Equilibria on $\mathbb{S}^2$
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 690--706
\mathnet{http://mi.mathnet.ru/rcd1228}
\crossref{https://doi.org/10.1134/S1560354723040111}
Linking options:
  • https://www.mathnet.ru/eng/rcd1228
  • https://www.mathnet.ru/eng/rcd/v28/i4/p690
  • This publication is cited in the following 3 articles:
    1. Philip Arathoon, “Relative equilibria of mechanical systems with rotational symmetry”, Nonlinearity, 37:9 (2024), 095001  crossref
    2. Toshiaki Fujiwara, Ernesto Pérez-Chavela, “Continuations and Bifurcations of Relative Equilibria for the Positively Curved Three-Body Problem”, Regul. Chaotic Dyn., 29:6 (2024), 803–824  mathnet  crossref
    3. Shuqiang Zhu, “The Schubart Orbits in the Curved Three-Body Problem with Two Equal Masses”, J Nonlinear Sci, 34:6 (2024)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:78
    References:34
     
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