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

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 The n-Body Problem in Spaces of Constant Curvature. Part II: Singularities

2012 ◽  
Vol 22 (2) ◽  
pp. 267-275 ◽  
Author(s):  
Florin Diacu ◽  
Ernesto Pérez-Chavela ◽  
Manuele Santoprete
Keyword(s):  
Constant Curvature ◽  
Body Problem ◽  
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

Euler-type Relative Equilibria and their Stability in Spaces of Constant Curvature

2018 ◽  
Vol 70 (2) ◽  
pp. 426-450 ◽  
Author(s):  
Ernesto Pérez-Chavela ◽  
Juan Manuel Sánchez-Cerritos
Keyword(s):  
Constant Curvature ◽  
Algebraic Curve ◽  
Positive Measure ◽  
Relative Equilibrium ◽  
Relative Equilibria ◽  
Spectral Stability ◽  
Spaces Of Constant Curvature ◽  
Central Mass ◽  
Elliptic Case ◽  
The Masses

AbstractWe consider three point positivemasses moving onS2andH2. An Eulerian-relative equilibrium is a relative equilibrium where the three masses are on the same geodesic. In this paper we analyze the spectral stability of these kind of orbits where the mass at the middle is arbitrary and the masses at the ends are equal and located at the same distance from the central mass. For the case of S2, we found a positive measure set in the set of parameters where the relative equilibria are spectrally stable, and we give a complete classiûcation of the spectral stability of these solutions, in the sense that, except on an algebraic curve in the space of parameters, we can determine if the corresponding relative equilibriumis spectrally stable or unstable. OnH2, in the elliptic case, we prove that generically all Eulerian-relative equilibria are unstable; in the particular degenerate case when the two equal masses are negligible, we get that the corresponding solutions are spectrally stable. For the hyperbolic case we consider the system where the mass in the middle is negligible; in this case the Eulerian-relative equilibria are unstable.

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
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