Dissipation-induced heteroclinic orbits in tippe tops

Abstract

This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top axe determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell-Bloch equations. A standard linear analysis reveals that the modified Maxwell-Bloch equations describe the spectral instability of the noninverted state and Lyapunov stability of the inverted state. Standard nonlinear analysis based on the energy momentum method gives necessary and sufficient conditions for the existence of a dissipation-induced connecting orbit between these relative equilibria. © 2008 Society for Industrial and Applied Mathematics.