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arXiv · 1801.02126

Relative Equilibria in curved restricted 4-body problems

Florin Diacu·Sawsan Alhowaity
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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 configu- rations 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.

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Florin Diacu, Sawsan Alhowaity. 2018-01-07. Relative Equilibria in curved restricted 4-body problems. https://doi.org/10.4153/cmb-2018-019-9

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