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In the Wigner-covariant rest-frame instant form of dynamics it is possible todevelop a relativistic kinematics for the N-body problem. The Wignerhyperplanes define the intrinsic rest frame and realize the separation of thecenter-of-mass. Three notions of {\it external} relativistic center of mass canbe defined only in terms of the {\it external} Poincar\'e group realization.Inside the Wigner hyperplane, an {\it internal} unfaithful realization of thePoincar\'e group is defined. The three concepts of {\it internal} center ofmass weakly {\it coincide} and are eliminated by the rest-frame conditions. Anadapted canonical basis of relative variables is found. The invariant mass isthe Hamiltonian for the relative motions. In this framework we can introducethe same {\it dynamical body frames}, {\it orientation-shape} variables, {\itspin frame} and {\it canonical spin bases} for the rotational kinematicsdeveloped for the non-relativistic N-body problem.Comment: 78 pages, revtex fil

Centers of mass and rotational kinematics for the relativistic N-body problem in the rest-frame instant form