The fast-superfast transition is a particular movement of eigenvalues found by Lewis et al. when studying the family of sleeping equilibria in the Lagrange top. Although this behaviour of eigenvalues typically suggests a change in stability or a bifurcation, in this case there is no particular change in the qualitative dynamical properties of the system. Using modern methods, based on the singularities of symmetry groups for Hamiltonian systems, we clarify the appearance of this transition.
