Constructing Examples in Relativistic Classical Particle Mechanics

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Abstract
A new method is proposed for constructing examples in relativistic classical particle mechanics, starting with the Poincaré group and space reflections as transformations of position and velocity variables for two free particles and deriving equations for Lorentz covariant position variables for two interacting particles. The advantages are that the equations do not couple the position variables of the two particles, and solutions yield the particle world lines directly. Solutions are obtained for a special case.