Chaotic Dynamics On Rippled Surfaces

W. J. Antel Jr.

The chaotic dynamics of a point mass bouncing between a rippled surface and a flat surface is numerically investigated using an Intel 66 MHz workstation running NEXTSTEP. The system is in the near integrable case where the amplitude of the ripples is small relative to the height of the flat wall. Using a two-dimensional sinusoid for the rippled surface, a plot of the four-dimensional space of initial conditions is attempted. Low resolution plots are obtained, but high resolution plots prove too numerically intensive. Next, a point mass bouncing between a flat line and a rippled line (represented by a quartic) is investigated. Intermingled basins of attraction in the space of initial conditions are observed. The metamorphosis of the basins of attractions is investigated as the amplitude of the ripples and height of the flat wall are varied. It is found that the basins of attraction become increasingly intermingled as the amplitude of the ripples is increased. Additionally, the phase space of the bounded orbits in relation to the space of initial conditions is plotted.