“…In order to analyze the stability of the vortex reverse flow (21)- (23), which corresponds to the main rotation of the top (20), with account for (24), we rewrite Eq. (20) as a variational equation (25) Following [21,42,47] and taking the scalar product of the variational equation with and , with account for the scalar square derivative, the symmetry of inertia , the anti-symmetry of commutator , and the quasi-compactness of in the following equalities we obtain the energy identities .…”