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Abstract: In this paper, complex dynamic behaviors of the centrifugal flywheel governor systems are studied. We go deeper investigating the stability of the equilibrium points in the centrifugal flywheel governor system. These systems have a rich variety of non-linear behaviors, which are investigated here by numerically integrating the Lagrangian equations of motion. The routes to chaos are analyzed using Poincaré maps, which are found to be more complicated than those of non-linear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincaré sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. By studying numerical simulations, it is possible to provide reliable theory and effective numerical method for other systems. In addition, the methods and conclusions would be useful for rotational machines designers. [Copyright &y& Elsevier]

Abstract: Chaos and chaos synchronization of the centrifugal flywheel governor system are studied in this paper. By mechanics analyzing, the dynamical equation of the centrifugal flywheel governor system is established. Because of the non-linear terms of the system, the system exhibits both regular and chaotic motions. The characteristic of chaotic attractors of the system is presented by the phase portraits and power spectra. The evolution from Hopf bifurcation to chaos is shown by the bifurcation diagrams and a series of Poincaré sections under different sets of system parameters, and the bifurcation diagrams are verified by the related Lyapunov exponent spectra. This letter addresses control for the chaos synchronization of feedback control laws in two coupled non-autonomous chaotic systems with three different coupling terms, which is demonstrated and verified by Lyapunov exponent spectra and phase portraits. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme. [Copyright &y& Elsevier]