Application: Bouncing Ball - Maple Help
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Ball Bouncing on Hilly Terrain

The following application demonstrates how event modeling in the dsolve command can be used to model a ball bouncing on a hilly terrain.

Define the Surface

We define the surface, surf, in the line below.  It is possible to modify this equation to show different "terrains".

Derive the Hilly Surface

The velocity vector of a ball:

 

The surface normal:

 

The velocity vector after reflection across the surface normal:

 

Restitution coefficient:

Using  represents an inelastic collision between the ball and the surface, whereas using  represents an elastic collision.

Differential Equations and Initial Conditions

Gravity acts in the -y direction:

Solve and Animate the Differential Equations

Animate the Ball Bouncing on the Terrain


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