  A general algorithm to construct particle trajectories in 1+1 dimensional
canonical relativistic models is presented. The method is a generalization of
the construction used in Ruijsenaars-Schneider models and provides a simple
proof of the fact that the latter satisfies the world-line conditions granting
proper physical Poincare invariance. The 2-particle case for the rational
Ruijsenaars-Schneider model is worked out explicitly. It is shown that the
particle coordinates do not Poisson commute, as required by the no-interaction
theorem of Currie, Jordan and Sudarshan.
