not discuss here the stability and oscillations of superfluid counterparts of the classical Roche binaries; their relative oscillation modes are derived in Ref. [@SW2000].

The general strategy for finding the equilibrium shapes of ellipsoidal figures and modes of their oscillations within the tensor virial method consist of (i) constructing moments of the hydrodynamic equations describing fluid motions in the rotating frame; (ii) computing Eulerian perturbations of the resulting virial equations; (iii) expressing these perturbations in terms of the virials of various order; these are defined as the moments of the Lagrangian displacement ${\mbox{\boldmath $\xi$}}_{\alpha,i}$ of fluid $\alpha$: $$\begin{aligned}
 V_{\alpha, i} &\equiv& \int_{V_{\alpha}}d^3 x\,\rho\, 
{\mbox{\boldmath $\xi$}}_{\alpha,i},
\quad ({\rm first ~order}) \\
 V_{\alpha, i;j} &\equiv& \int_{V_{\alpha}}d^3 x\,\rho\, 
{\mbox{\boldmath $\xi$}}_{\alpha,i} x_j,
\quad ({\rm second ~order}) \\
 V_{\alpha, i;jk} &\equiv& \int_{V_{\alpha}}d^3 x\,\rho\, 
{\mbox{\boldmath $\xi$}}_{\alpha,i} x_{j}x_{k},
\quad ({\rm third ~order}) \\
\dots\nonumber\end{aligned}$$ The advantage of using the homogeneous ellipsoidal approximation is that the perturbations of the gravitational energy tensor of an ellipsoid can be expressed in terms of the [*index symbols*]{} defined as (cf. EFE Chap. 3) $$\begin{aligned}
A_{ijk\dots}& =& a_1a_2a_3\int_0^{\infty}
\frac{du}{\Delta(a_i^2+u)(a_j^2+u)(a_k^2+u)\dots},\\
B_{ijk\dots}& =& a_1a_2a_3\int_0^{\infty}
\frac{udu}{\Delta(a_i^2+u)(a_j^2+u)(a_k^2+u)\dots},\end{aligned}$$ where $\Delta^2 = (a_1^2+u)(a_2^2+u)(a_3^2+u)$ and $a_1$, $a_2$, and $a_3$ are the semi-axis of the ellipsoid. This strategy is described 