Andrew Miller discusses his presentation, “Nonlinear Dynamics in the Periodically Forced Bouncing Car,” at SDSU’s fifth annual Student Research Symposium. Andrew, who is working with Dr. Carretero, converted a 5th floor office into an experimental lab (the first one in the history of our Dept) where he created his research project. Andrew is currently studying for his degree in Applied Mathematics with an emphasis in Computational Science.
“We consider, experimentally and theoretically, a mechanical system consisting of a sliding car on an inclined plane that bounces on an oscillating piston. The main aim of our study is to reproduce the different types of orbits displayed by nonlinear dynamical systems. In particular, we are looking to identify the parameters and initial conditions for which periodic and chaotic (irregular) behavior are exhibited. The data in our experimental model is collected by using infrared lights that are monitored by a Nintendo Wii remote which is linked to a laptop computer via Bluetooth.
By varying the piston’s frequency and amplitude, it is possible to produce, for relatively small amplitudes, periodic orbits. As the amplitude of the piston is increased (for a fixed piston frequency) we observe bifurcations where the original, stable, periodic orbit is destabilized and replaced by a higher order periodic orbit. For larger amplitudes, periodic orbits are destabilized and replaced by chaotic trajectories. After carefully measuring all experimental parameters, we are able to successfully produce periodic orbits (up to period 3), sticking solutions (the car does not bounce, but gets stuck to the piston), and seemingly chaotic (irregular/unpredictable) behavior that are in very good agreement with the model for the same parameter values.”