  We consider the motion of a rigid body immersed in an incompressible perfect
fluid which occupies a three-dimensional bounded domain. For such a system the
Cauchy problem is well-posed locally in time if the initial velocity of the
fluid is in the Holder space C^{1,r}. In this paper we prove that the
smoothness of the motion of the rigid body may be only limited by the
smoothness of the boundaries (of the body and of the domain). In particular for
analytic boundaries the motion of the rigid body is analytic (till the
classical solution exists and till the solid does not hit the boundary).
Moreover in this case this motion depends smoothly on the initial data.
