Response to “Comment on ‘Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2’ ” [J. Math. Phys. 46, 052702 (2005)]

2005 ◽  
Vol 46 (11) ◽  
pp. 114102 ◽  
Author(s):  
J. F. Cariñena ◽  
M. F. Ranada ◽  
M. Santander
Keyword(s):  
Constant Curvature ◽  
Hyperbolic Plane ◽  
Kepler Problem ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Spaces Of Constant Curvature ◽  
Math Phys

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.

scholarly journals A new integrable anisotropic oscillator on the two-dimensional sphere and the hyperbolic plane

2014 ◽  
Vol 47 (34) ◽  
pp. 345204 ◽  
Author(s):  
Ángel Ballesteros ◽  
Alfonso Blasco ◽  
Francisco J Herranz ◽  
Fabio Musso
Keyword(s):  
Hyperbolic Plane ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Anisotropic Oscillator
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