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
Keyword(s):
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.