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# Relative Equilibria in Curved Restricted $4$-body Problems

Published:2018-05-30
Printed: Dec 2018
• Sawsan Alhowaity,
Department of Mathematics, Shaqra University, Saudi Arabia
• Florin Diacu,
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia
• Ernesto Pérez-Chavela,
Department of Mathematics, ITAM, México
 Format: LaTeX MathJax

## Abstract

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.
 Keywords: $N$-body problem, relative equilibria, celestial mechanics
 MSC Classifications: 70F10 - $n$-body problems 37N05 - Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]

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