This chapter considers a mathematical model for rotational motions of a body with a cavity containing an ideal fluid. Harmonic oscillations of a fluid in a cavity were studied in [34, 148, 299]. In [148, 299], only cavities of special shape were considered. In [34], no constraints on the shape of cavities were imposed, but it was assumed that the natural vibrations of the fluid in the cavity in a rotating body were already damped out, and only the forced motion of the fluid was considered.