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            \title{Relativistic equations of motion of celestial bodies}
\author{Michel H. Soffel}

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\maketitle

Recently, Damour, Soffel and Xu (DSX) have introduced a new formalism
of relativistic celestial mechanics of systems of N arbitrarily
composed and shaped, weakly self-gravitating, rotating, deformable
bodies. This formalism is aiming at yielding a complete description, at
the first post-Newtonian approximation, of the global dynamics of such
N-body systems, the local gravitional structure of each body and
provides a new theory of Relativistic astronomical reference frames.
The DSX-formalism will be introduced and the Relativistic equations of
motion will be discussed for massive bodies and for Earth's orbiting
satellites. Special attention will be given to the problem of
rotational motion; attempts to define quasi-rigid bodies and concepts
like angular velocity or moments of inertia will be discussed.


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