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WOLFRAM|DEMONSTRATIONS PROJECT

Bouncing Ball in a Closed Room

​
initial position at locator
{0,0}
initial speed
absolute value
25
direction to horizontal
30°
air drag coefficient
0.05
time
actual position:
final position:
A perfectly elastic ball bounces between the rigid walls and floor of a closed rectangular room.
You can drag the locator to determine the initial position, initial speed, and direction of the ball. You can also vary the air drag coefficient. The resulting motion displays a variety of periodic and chaotic trajectories.
With only gravity and air drag acting on the ball, the equations of motion are:
′′
x
(t)-
c
d
2
′
x
(t)
,
′′
y
(t)-g-
c
d
2
′
y
(t)
,
where
(x(t),y(t))
is the position of the ball at time
t
.
Here
c
d
is the air drag coefficient and
g
is the acceleration due to gravity.
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