APPROACHING NONLINEAR DYNAMICS BY STUDYING THE MOTION OF A PENDULUM II: ANALYZING CHAOTIC MOTION

Using a driven damped pendulum as a demonstration model we illustrate some fundamental concepts of nonlinear dynamics. We find deterministic chaos in the motion of the pendulum by observing its sensitive dependence on the initial state. We calculate the corresponding Lyapunov exponents from the equation of motion. The largest exponent gives the average predictability time scale. We estimate fractal dimensions of the attractor by determining the Kaplan Yorke dimension. Further we investigate the organization of unstable periodic orbits embedded in the attractor of the pendulum.