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.


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.


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



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

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