On the Impossibility of Global Stabilization of the Lagrange Top

Abstract

It is shown that the problem of the asymptotic stabilization of a given position of the Lagrange top for any control from a sufficiently wide class does not permit the existence of a single uniformly asymptotically stable equilibrium, even with possible impacts of the top against the horizontal plane; i.e., the global stabilization of the system is impossible. In particular, we show that it is impossible to globally stabilize the top by moving its pivot point along the horizontal plane.