The stability of a "sleeping" Lagrante top with a vibrating suspension point

The motion of a Lagrange top, the suspension point of which performs vertic al harmonic oscillations of arbitrary frequency and amplitude, is considere d. The particular motion where the top rotates about a vertically positione d axis of symmetry at a constant angular velocity (a "sleeping" top) is inv estigated. The complete solution of the problem concerning the stability of such motion for all permissible values of the parameters of the problem is given. (C) 2001 Elsevier Science Ltd. All rights reserved.