  After a short review of the history and problems of relativistic Hamiltonian
mechanics with action-at-a-distance inter-particle potentials, we study
isolated two-body systems in the rest-frame instant form of dynamics. We give
explicit expressions of the relevant relativistic notions of center of mass, we
determine the generators of the Poincare' group in presence of interactions and
we show how to do the reconstruction of particles' orbits from the relative
motion and the canonical non-covariant center of mass. In the case of a simple
Coulomb-like potential model, it is possible to integrate explicitly the
relative motion and show the two dynamical trajectories.
