The Fast-Superfast Transition in the Sleeping Lagrange Top

TL;DR

This paper investigates the fast-superfast eigenvalue transition in the sleeping Lagrange top, clarifying its nature using modern symmetry group methods, and shows it does not imply a stability change.

Contribution

It applies advanced symmetry group analysis to explain the eigenvalue transition in the Lagrange top without indicating a stability bifurcation.

Findings

Eigenvalue transition does not correspond to stability change.

Modern symmetry methods clarify the transition's nature.

The transition is explained through singularities of symmetry groups.

Abstract

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.