Bouncing Ball in a Closed Room

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A perfectly elastic ball bounces between the rigid walls and floor of a closed rectangular room.

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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:

,

,

where is the position of the ball at time .

Here is the air drag coefficient and is the acceleration due to gravity.

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Contributed by: Erik Mahieu (February 2015)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshots 1, 2, and 3 are examples of periodic orbits.



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