Annular Billiards

A point ball travels in the region between two circles suffering specular reflections at the boundaries, that is no loss of energy and angle of incidence is equal to that of reflection. If the circles are concentric, there is rotational symmtery and apart from energy the angular momentum is conserved. The system in this case is integrable. If the distance between the two circles (of radii R and r) is not zero, the angular momentum is no longer conserved and the system shows a mixture of regular and chaotic orbits. To operate enter values of R,r, (default 200, 100), distance, (default 0), angle of launch (in degrees, wrt horizontal, the speed is immaterial as this is a constant throughout), number of initial bounces with the walls and how many times you would like to further go with the "next" button. Click on any colour and then click at a point between the two circles to fix the point of launch and then click "draw". Use the "clear" button for refreshing.