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Expressions for variables of the center of mass and relative motions fortwo-body system with different and equal masses in three-dimensional spaces ofconstant curvature are introduced in the terms of biquaternions. The problem ofthe separation of center mass and relative motion variables for action of twoparticles into biquaternionic form is formulated. We showed that the algebraicnature of these nonseparable variables follows from the fact that algebra ofbiquaternions is noncommutative. Some special cases of separation of centermass and relative motion variables are considered.

On the separation of variables into relative and center of mass motion for two-body system in three-dimensional spaces of constant curvature