Travelable Period-1 Motions to Chaos in a Periodically Excited Pendulum

In this chapter, the analytical bifurcation trees of travelable period-1 motions to chaos in a periodically excited pendulum will be presented with varying excitation amplitude. The analytical prediction is based on the implicit discrete maps obtained from the midpoint scheme of the corresponding differential equation. Using the discrete maps, mapping structures will be developed for various periodic motions, and analytical bifurcation trees of periodic motions to chaos can be obtained.