New relative equilibria of the N-body problem

1976 ◽  
Vol 1 (2) ◽  
pp. 119-123 ◽  
Author(s):  
Julian I. Palmore
Keyword(s):  
Body Problem ◽  
Relative Equilibria ◽  
N Body Problem

The n-Body Problem in Spaces of Constant Curvature. Part I: Relative Equilibria

2012 ◽  
Vol 22 (2) ◽  
pp. 247-266 ◽  
Author(s):  
Florin Diacu ◽  
Ernesto Pérez-Chavela ◽  
Manuele Santoprete
Keyword(s):  
Constant Curvature ◽  
Body Problem ◽  
Relative Equilibria ◽  
Spaces Of Constant Curvature ◽  
N Body Problem

scholarly journals Finiteness of relative equilibria in the planar generalized $N$-body problem with fixed subconfigurations

2015 ◽  
Vol 7 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Marshall Hampton ◽  
◽  
Anders Nedergaard Jensen ◽  
Keyword(s):  
Body Problem ◽  
Relative Equilibria ◽  
N Body Problem

scholarly journals Relative equilibria for the positive curved n–body problem

2020 ◽  
Vol 82 ◽  
pp. 104994
Author(s):  
Ernesto Pérez-Chavela ◽  
Juan Manuel Sánchez-Cerritos
Keyword(s):  
Body Problem ◽  
Relative Equilibria ◽  
N Body Problem

scholarly journals Continuation of relative equilibria in the n–body problem to spaces of constant curvature

2022 ◽  
Vol 307 ◽  
pp. 137-159
Author(s):  
A. Bengochea ◽  
C. García-Azpeitia ◽  
E. Pérez-Chavela ◽  
P. Roldan
Keyword(s):  
Constant Curvature ◽  
Body Problem ◽  
Relative Equilibria ◽  
Spaces Of Constant Curvature ◽  
N Body Problem

scholarly journals On the n -body problem in R4

2019 ◽  
Vol 377 (2158) ◽  
pp. 20190018
Author(s):  
Tanya Schmah ◽  
Cristina Stoica
Keyword(s):  
Invariant Manifold ◽  
Vortex Dynamics ◽  
Body Problem ◽  
Relative Equilibria ◽  
Geometric Mechanics ◽  
Theme Issue ◽  
N Body Problem ◽  
Set Up ◽  
The Masses ◽  
Force Problem

Using geometric mechanics methods, we examine aspects of the dynamics of n mass points in R 4 with a general pairwise potential. We investigate the central force problem, set up the n -body problem and discuss certain properties of relative equilibria. We describe regular n -gons in R 4 , and when the masses are equal we determine the invariant manifold of motions with regular n -gon configurations. In the case n  = 3, we reduce the dynamics to a 6 d.f. system and we show that for generic potentials and momenta, relative equilibria with equilateral configuration are unstable. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

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