In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass. Three notions of { \it external} relativistic center of mass can be defined only in terms of the { \it external} Poincar\'e group realization. Inside the Wigner hyperplane, an { \it internal} unfaithful realization of the Poincar\'e group is defined. The three concepts of { \it internal} center of mass weakly { \it coincide} and are eliminated by the rest-frame conditions. An adapted canonical basis of relative variables is found. The invariant mass is the Hamiltonian for the relative motions. In this framework we can introduce the same { \it dynamical body frames}, { \it orientation-shape} variables, { \it spin frame} and { \it canonical spin bases} for the rotational kinematics developed for the non-relativistic N-body problem.
Categories: hep-th astro-ph gr-qc nucl-th