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

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