Regular and chaotic dynamics of a simplified fly-ball governor

Abstract

The dynamics of a simplified model of a fly-ball speed governor undergoing a harmonic variation about its rotational speed is studied in this paper. This system is a non-linear damped system subjected to parametric excitation. The harmonic balance method is applied to analyse the stability of period attractors and the behaviour of bifurcations. The time evolutions of the response of the non-linear dynamic system are described by time history, phase portraits and Poincaré maps. The regular and chaotic behaviour is observed by various numerical techniques such as power spectra, Lyapunov exponents and Lyapunov dimension. Finally, the domains of attraction of periodic and stranger attractors of the system are located by applying the interpolated cell mapping (ICM) method.