  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.
