WOLFRAM|DEMONSTRATIONS PROJECT

Chaotic Dynamics for Ball Bouncing between Two Constant Slopes

​
x
0
0.5
y
0
1.042
m
0.589
x
f
227.
Perhaps the simplest situation of elastic collisions that exhibit chaotic motion is a ball bouncing between two constant slopes of opposite sign. Here the ball starts at position
(
x
0
,
y
0
)
(green point), the slope is
m
, and the bounces are traced ending at a blue point at time
t
f
but with a maximum of 200 bounces (the count appears at the top of the graphic). The Poincaré map is shown in the above the graphic.