My final project for the course was a study of the bifurcations of the whirling planar pendulum. This system demonstrates some really interesting nonlinear dynamics. Plus, the whirling planar pendulum is a component of Watt's regulator which is inherently cool because it is an example of mechanical feedback control. Bifurcations of the Whirling Planar Pendulum Bifurcations of the Whirling Planar Pendulum C. A. Woolsey Abstract Existence and stability of equilibria for the planar whirling pendulum are explored where the angular rate and the pivot eccentricity are treated as parameters. Bifurcations of equilibria are discussed in the context of the cusp catastrophe.
Global bifurcations are also explored.
In particular, it is shown numerically that the system demonstrates chaos of two different types when subjected to a sinusoidal angular velocity perturbation of sufficient amplitude. One of these types of chaos was demonstrated experimentally.