In non-relativistic mechanics the center of mass of an isolated system is
easily separated out from the relative variables. For a N-body system these
latter are usually described by a set of Jacobi normal coordinates, based on
the clustering of the centers of mass of sub-clusters. The Jacobi variables are
then the starting point for separating {\it orientational} variables, connected
with the angular momentum constants of motion, from {\it shape} (or {\it
vibrational}) variables. Jacobi variables, however, cannot be extended to
special relativity. We show by group-theoretical methods that two new sets of
relative variables can be defined in terms of a {\it clustering of the angular
momenta of sub-clusters} and directly related to the so-called {\it dynamical
body frames} and {\it canonical spin bases}. The underlying group-theoretical
structure allows a direct extension of such notions from a non-relativistic to
a special- relativistic context if one exploits the {\it rest-frame instant
form of dynamics}. The various known definitions of relativistic center of mass
are recovered. The separation of suitable relative variables from the so-called
{\it canonical internal} center of mass leads to the correct kinematical
framework for the relativistic theory of the orbits for a N-body system with
action -at-a-distance interactions. The rest-frame instant form is also shown
to be the correct kinematical framework for introducing the Dixon multi-poles
for closed and open N-body systems, as well as for continuous systems,
exemplified here by the configurations of the Klein-Gordon field that are
compatible with the previous notions of center of mass.Comment: Latex, p.75, Invited contribution for the book {\it Atomic and
Molecular Clusters: New Research} (Nova Science
