Abstract
Complex dynamic behaviours of the centrifugal flywheel governor systems are studied. The centrifugal flywheel governor systems have a rich variety of non-linear behaviour, which are investigated here by numerically integrating the Lagrangian equations of motion. The routes to chaos are analysed using Poincare 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 Poincare sections, bifurcation diagrams, Lyapunov exponents. The chaotic motion of the system is effectively controlled based on NNC with the threshold function of the hyperbolic tangent function, that we obtain the steady periodic orbit of the system. 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.
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