This Chapter is devoted to models describing rotational motions of a solid body with a cavity, one part of which is filled with an ideal fluid and the other part, with a gas at constant pressure.

Section 1 contains the setting of the problem of a rotating rigid body with a cavity filled with an ideal fluid with free surface. It is shown that, under the unperturbed motion, the free surface has cylindrical shape, provided that the problem is isoperimetric.