Geodesic
Relative Equilibria in Curved Restricted 4-body Problems
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 673-687

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DOI

We consider the curved $4$ -body problems on spheres and hyperbolic spheres. After obtaining a criterion for the existence of quadrilateral configurations on the equator of the sphere, we study two restricted $4$ -body problems, one in which two masses are negligible and another in which only one mass is negligible. In the former, we prove the evidence square-like relative equilibria, whereas in the latter we discuss the existence of kite-shaped relative equilibria.
DOI : 10.4153/CMB-2018-019-9
Mots-clés : 70F10, 37N05, N-body problem, relative equilibria, celestial mechanics 
Alhowaity, Sawsan; Diacu, Florin; Pérez-Chavela, Ernesto. Relative Equilibria in Curved Restricted 4-body Problems. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 673-687. doi: 10.4153/CMB-2018-019-9
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     author = {Alhowaity, Sawsan and Diacu, Florin and P\'erez-Chavela, Ernesto},
     title = {Relative {Equilibria} in {Curved} {Restricted} 4-body {Problems}},
     journal = {Canadian mathematical bulletin},
     pages = {673--687},
     year = {2018},
     volume = {61},
     number = {4},
     doi = {10.4153/CMB-2018-019-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-019-9/}
}
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%J Canadian mathematical bulletin
%D 2018
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