Bifurcation and chaos of a non-autonomous rotational machine systems

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.