Nonlinear Phenomena in Complex Systems, 2016, Vol.19, No.4, pp.378

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2016, Vol.19, No.4, pp.378 - 386

On Separation of Variables into Relative and Center of Mass Motion for Two-Body System in Three–Dimensional Spaces of Constant Curvature
Yu. Kurochkin, Dz. Shoukavy, and I. Boyarina

Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three–dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of separation of the center mass and relative motion variables for action of two particles into biquaternionic form is formulated. We showed that the algebraic nature of these nonseparable variables follows from the fact that the algebra of biquaternions is noncommutative. Some special cases of separation of the center mass and relative motion variables are considered.

Key words: three–dimensional spaces of constant curvature, biquaternions, two-body system, separation of variables

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