| A steam engine with Watt's centrifugal governor was formerly analyzed by Vyshnegradskii ([Vys76], 1876). A simplified version of Vyshnegradskii's analysis was then presented by Pontryagin ([Pon62], 1962) in his book on ordinary differential equations. A more complete analysis of the classical (non-degenerate) Hopf bifurcations of the centrifugal governor was given by Hassard ([Has79], 1979), and by Hassard, Kazarinoff and Wan ([HKW81], 1981) in their book on Theory and Applications of Hopf bifurcation. In this thesis we analyze the degenerate Hopf bifurcations of the centrifugal governor by studying the recognition problems for (topological) normal forms, as well as the recognition problems for (singularity theoretic) normal forms and universal unfoldings along a certain curve in the parameter space of the centrifugal governor. We also show that the centrifugal governor, in fact, undergoes a doubly degenerate (or codimension three) Hopf bifurcation and we locate this doubly degenerate Hopf bifurcation point. |
