MASS CENTER AND RELATIVE MOTION VARIABLES IN THREEDIMENSIONAL SPACES WITH A TIME-DEPENDENT CURVATURE RADIUS

Abstract

Expressions for the variables of the mass center and the relative motion of two material particles in the three-dimensional Lobachevsky space and in the three-dimensional sphere with a time-dependent radius curvature are defined in terms of biquaternions. By using the action of the two particles in the above spaces, we have found that the problem of separation of the mass center and relative motion coordinates of this system reduces to the problem in the spaces of a completely constant curvature.