COMPUTING II: PROJECT C (00/01)

In lecture 6 a number of simple systems that exhibit chaos were described. Perhaps the simplest of these was the example of two balls dropped from different heights, constrained to move only in the z-direction and suffering perfectly elastic collisions with the floor and with each other. I discussed how, for certain mass ratios, the height to which the upper ball bounced varied chaotically with time. In this project you will graphically model the bouncing ball system and examine the variation of x₂ with time for two different combinations of masses. See pages 73-77 of Giordano for further information on this system.

Use the second order Runge-Kutta method to calculate the positions of the balls as a function of time for m₁=m₂. You will need to consider the velocity changes that occur following a collision of the lower ball (having mass m₁) with the floor and following collisions of the balls with each other. Graphically display the positions of the balls as a function of time. In addition to animating the motion of the balls, save the values of x₂ vs time to a file. Explore the behaviour of the upper ball as a function of the ratio of the masses of the balls.