  The center of mass and spin for isolated sources of gravitational radiation
that move at relativistic speeds are defined. As a first step, we also present
these definitions in flat space. This contradicts some general wisdom given in
textbooks claiming that such definitions are not covariant and thus, have no
physical meaning. We then generalize the definitions to asymptotically flat
spacetimes giving their equations of motion when gravitational radiation is
emitted by the isolated sources. The resulting construction has some
similarities with the Mathisson-Papapetrou equations which describes the motion
of the particle in an external field. We analyze the relationship between the
center of mass velocity and the Bondi linear momentum and show they are not
proportional to each other. A similar situation happens between the total and
intrinsic angular momentum when the Bondi momentum vanishes. We claim that
extra terms should be added in other approaches to adequately describe the time
evolution of isolated sources of gravitational radiation.
