I wish to model the motion of a ball that bounces up and down in a vertical line, and whenever it hits the ground, it bounces back with only a fraction of the collision speed.
We expect that the amplitude of the consecutive bounces to diminish and for all practical purposes the ball to come to a standstill. It's not difficult to calculate the motion analytically by hand.
However, when I attempted to solve the equation of motion numerically with Maple's dsolve() and event handling, I ran into a problem. As the amplitude of the bounces approaches zero, numerical noise sets in and the ball tunnels itself underground! See the worksheet below.
I don't know how to prevent the ball from going underground. Any ideas?