Relative Equilibria in Curved Restricted 4-body Problems

Alhowaity, Sawsan ; Diacu, Florin ; Pérez-Chavela, Ernesto

Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 673-687

Résumé

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.

Détail

DOI : 10.4153/CMB-2018-019-9

Mots-clés : 70F10, 37N05, N-body problem, relative equilibria, celestial mechanics

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