scholarly journals On the central configurations of the n-body problem

2017 ◽  
Vol 2 (2) ◽  
pp. 509-518 ◽  
Author(s):  
Jaume Llibre
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Regular Polyhedra ◽  
Satellite Problem ◽  
N Body Problem

AbstractWe present a brief survey on some classes of central configurations of then-body problem. We put special emphasis on the central configurations of the 1+n-body problem also called the coorbital satellite problem, and on the nested central configurations formed by either regularn-gons, or regular polyhedra. We also present some conjectures.

scholarly journals Central configurations in planar n-body problem with equal masses for $$n=5,6,7$$

2019 ◽  
Vol 131 (10) ◽  
Author(s):  
Małgorzata Moczurad ◽  
Piotr Zgliczyński
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Central Configuration ◽  
Newtonian Potential ◽  
Computer Assisted ◽  
Computer Assisted Proof ◽  
N Body Problem ◽  
Reflective Symmetry

Abstract We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for $$n=5,6,7$$ n = 5 , 6 , 7 with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For $$n=8,9,10$$ n = 8 , 9 , 10 , we establish the existence of central configurations without any reflectional symmetry.

Sign in / Sign up

Export Citation Format

Share Document