No abstract

The behavior of a chaotic physical pendulum is significantly modified through the addition of a magnetic interaction. The extended behavior is studied through identifying distinct characteristics in the Poincar e sections and turning point maps of the systems. The validity of our model is shown through simulated bifurcations generated from coefficients estimated at a number of different frequencies. These simulated bifurcations also demonstrate that coefficients estimated at one frequency can be used to predict the behavior of the system at a different drive frequency. A quantitative measure of the correlation dimension shows that the simulated Poincar e diagrams are in good agreement with experiment and theory. Possible sources of bias in modeled systems are identified. Although it has been the subject of many papers, books, and commercial experimental systems, the ubiquitous physical pendulum still has untapped physics. By taking advantage of magnetic dipoles, we developed a chaotic pendulum that tests our ability to model a system over a broad range of driving conditions with different interaction potentials. Notably, we find the presence of two very different attractors in our system depending on how the system is driven. This differentiates its behavior from other pendulums where the attractor is either wrapped or unwrapped depending on the drive mechanism. We introduce turning point maps that track regions of net torque, as well as Poincar e sections to help visualize the attractors due to the different interaction potentials. Comparisons between bifurcation diagrams and correlation dimension measurements indicate that large scale system behavior encompassing different attractors can be predicted using a single region of chaotic response. In particular, we show that determining correlation dimension values from a single phase slice could introduce bias and that using fitting parameters from a single frequency in simulations may underestimate the uncertainty in the model.