Analysing the Chaotic Motion of a Driven Pendulum

We analyse the chaotic motion of a periodically driven damped pendulum. Time series of the angular velocity are sampled and investigated numerically. Parameters of the driving force and the damping are reconstructed from the velocity by numerically adapting the equation of motion. The delay time required to embed the attractor in a space of delay coordinates is derived from an extension of the recently suggested wavering product. Dynamical and statical properties of the attractor are determined and predictions of chaotic motions are made by a local method. An estimation of the prediction error is inverted to obtain attractor dimension and-entropy. The results are consistent with those from QR decomposition of the Jacobian of the pendulum equation.