| Summary: | Billiards are simple systems used to investigate Hamiltonian dynamics in physics. When real billiards are examined experimentally, the energy dissipated in each collision must be replaced by an external stimulus to maintain the dynamics. We focus on a specific system of a driven billiard using a wedge shaped boundary to examine nonlinear and chaotic behavior. Mathematical models such as the logistic map are simple low dimensional systems that exhibit nonlinear and chaotic behavior as a single parameter is varied. This logistic map can then be used to identify a very specific mathematical parameter known as the Lyapunov exponent, which helps in identifying chaos more clearly. In the current experiment, the dynamics of a particle free to move near a horizontally shaken vertical boundary will be examined for the presence of chaos. The goal of the research is to extract a Lyapunov exponent between any two trajectories in the system. In addition, the manner in which the dynamics evolve freely through dissipative collisions provides a testbed for measurements of the velocity dependent coefficients of restitution for the billiard. A better description of hard sphere coefficients of restitution would be beneficial to a host of experiments and numerical simulations in granular physics.
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