The Kepler Problem and the Laplace–Runge–Lenz Vector on Spaces of Constant Curvature and Arbitrary Signature

2008 ◽  
Vol 7 (1) ◽  
pp. 87-99 ◽  
Author(s):  
José F. Cariñena ◽  
Manuel F. Rañada ◽  
Mariano Santander
Keyword(s):  
Constant Curvature ◽  
Kepler Problem ◽  
Spaces Of Constant Curvature ◽  
Arbitrary Signature

scholarly journals Lambert's theorem and projective dynamics

2019 ◽  
Vol 377 (2158) ◽  
pp. 20180417
Author(s):  
Alain Albouy ◽  
Lei Zhao
Keyword(s):  
Constant Curvature ◽  
Vortex Dynamics ◽  
Kepler Problem ◽  
Keplerian Orbit ◽  
Theme Issue ◽  
Spaces Of Constant Curvature ◽  
Elapsed Time ◽  
Space Of Constant Curvature

We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We prove that the Hooke problem has a property similar to Lambert's theorem, which also extends to the spaces of constant curvature. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

scholarly journals The classical Kepler problem and geodesic motion on spaces of constant curvature

2000 ◽  
Vol 41 (12) ◽  
pp. 8108-8116 ◽  
Author(s):  
Aidan J. Keane ◽  
Richard K. Barrett ◽  
John F. L. Simmons
Keyword(s):  
Constant Curvature ◽  
Kepler Problem ◽  
Geodesic Motion ◽  
Spaces Of Constant Curvature

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.

Simplexes in spaces of constant curvature

1991 ◽  
Vol 38 (1) ◽  
Author(s):  
B.V. Dekster ◽  
J.B. Wilker
Keyword(s):  
Constant Curvature ◽  
Spaces Of Constant Curvature
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