Nonlinear Phenomena in Complex Systems, 2020, Vol.23, No.3, pp.306

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2020, Vol.23, No.3, pp.306 - 311

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere
Yu. Kurochkin, Dz. Shoukavy, and I. Boyarina

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.

Key words: two particle problem, biquaternion, spaces of constant curvature

DOI: https://doi.org/10.33581/1561-4085-2020-23-3-306-311

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