Two-body problem on spaces of constant curvature: II. Spectral properties of the Hamiltonian

2000 ◽  
Vol 124 (3) ◽  
pp. 1265-1272 ◽  
Author(s):  
I. É. Stepanova ◽  
A. V. Shchepetilov
Keyword(s):  
Constant Curvature ◽  
Spectral Properties ◽  
Body Problem ◽  
Spaces Of Constant Curvature ◽  
Two 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 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 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

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Sign in / Sign up

Export Citation Format

Share Document