Irrotational and zero angular momentum ellipsoids in the dirichlet problem

Two classes of new exact solutions are found in the Dirichlet problem of the oscillations of a self-gravitating fluid ellipsoidal mass with linear velocity field. These solutions describe irrotational ellipsoids and ellipsoids with zero angular momemtum. For ellipsoids with stationary boundary surface it is established that irrotational and zero angular momentum figures exist not only when the ellipsoids rotate around the central symetry axis, but also for an inclined position of the rotation axis