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Relative Equilibria in Curved Restricted 4-body Problems

Published online by Cambridge University Press:  20 November 2018

Sawsan Alhowaity ,
Florin Diacu  and
Ernesto Pérez-Chavela
Sawsan Alhowaity
Affiliation:
Department of Mathematics, Shaqra University, Saudi Arabia, e-mail : salhowaity@su.edu.sa Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia
Florin Diacu
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia Yangtze Center of Mathematics, Sichuan University, Chengdu, China Yale-NUS College, National University of Singapore, Singapore, e-mail : diacu@uvic.ca
Ernesto Pérez-Chavela
Affiliation:
Department of Mathematics, ITAM, México, e-mail : ernesto.perez@itam.mx
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Abstract

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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

70F1037N05N-body problemrelative equilibriacelestial mechanics
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 673 - 687
Copyright
Copyright © Canadian Mathematical Society 2018

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