of total momentum for the combined fluids - it would be effective throughout the entire volume of fluids because the force is mediated by a macroscopically extended vortex lattice.

For isolated single-fluid ellipsoids the first harmonic oscillations are trivial, since they correspond to the motions of the center-of-mass of an ellipsoid and can be eliminated by a transformation to the reference frame whose origin is located at the center-of-mass of the ellipsoid. For two-fluid ellipsoids the fluid motions include the counter-phase (relative) oscillations of two fluids, which can not be eliminated by any transformation. These are the only new type of oscillations for the superfluid Maclaurin and Jacobi ellipsoids (the solitary ellipsoids with vanishing internal motions). In the case of ellipsoids in an external gravitational field (e.g. the Roche ellipsoids), the CM motions are not trivial any more, since the external (inhomogeneous by assumption) source of gravitational field breaks the translational symmetry of the problem. Hence, apart from the relative oscillations of two fluids, the CM oscillations become non-trivial.

Consider first the variation of the first order virial equation under the influence of perturbations. The variations of the inertial terms proceeds in full analogy to EFE. Here we concentrate on 