  We study the motion of the system, S, constituted by a rigid body, B,
containing in its interior a viscous compressible fluid, and moving in absence
of external forces. Our main objective is to characterize the long time
behavior of the coupled system body-fluid. Under suitable assumptions on the
"mass distribution" of S, and for sufficiently "small" Mach number and initial
data, we show that every corresponding motion (in a suitable regularity class)
must tend to a steady state where the fluid is at rest with respect to B.
Moreover, S, as a whole, performs a uniform rotation around an axis parallel to
the (constant) angular momentum of S, and passing through its center of mass.
