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 Institut für Theoretische Physik |
Basic Physics Course with MATLAB's Symbolic Toolbox and Live Editor
Animation 8: Billiard Chaos
Here we consider the 'free' motion of one (or two) balls in a stadium-shaped area. The reflection on the boundary is simulated by a harmonic potential. The distance between two adjacent paths, initially very close to each other, increases exponentially with time. There is a positive Liyapunov exponent. The reflections on the boundary prevent the separation of the degrees of freedom. The system is chaotic. |
The equations of motion are solved numerically. We see a green and a red ball moving in the station. The starting positions and velocities are almost identical. After about 10 reflections, any information about the initial conditions of the trajectories has disappeared. Further details can be found in Chap07_4 .
