Instability of sleeping asymmetric tops under dissipative perturbations

In this work we study the instability of the relative equilibria of the Ham iltonian system corresponding to asymmetric sleeping tops when a viscous di ssipative perturbation is added. To do this, we consider, for the unperturb ed problem, the classes of asymmetric sleeping tops for which the relative equilibria of the linearized Hamiltonian system are spectrally stable at a range of angular velocities. For these classes we determine the movement of the eigenvalues of the underlying Hamiltonian system which is initially on the imaginary axis. (C) 2001 Elsevier Science Ltd. All rights reserved.