  In this paper, it is the first time to construct a complete post-Newtonian
(PN) model of a rigid body by means of a new constraint on the mass current
density and mass density. In our PN rigid body model most of relations, such as
spin vector proportional to the angular velocity, the definition on the moment
of inertia tensor, the key relation between the mass quadrupole moment and the
moment of inertia tensor, rigid rotating formulae of mass quadrupole moment and
the moment of inertia tensor, are just the extension of the main relations in
Newtonian rigid body model. When all of $1/c^2$ terms are neglected, the PN
rigid body model and the corresponding formulae reduce to Newtonian version.
The key relation is obtained in this paper for the first time, which might be
very useful in the future application to problems in geodynamics and astronomy.
