## Trajectory Optimization on the Putting Green

Viewing the 3-D model on this page requires a VRML plugin such as
Cosmoplayer/2.1.
Click on the flag to start the animation. The golf ball will get whacked by
an invisible putter with just the right amount of force and direction to put
the ball in the cup. The ball will arrive at the cup with the smallest
possible final speed.
LOQO was used to compute this optimal trajectory.
To see the AMPL file that was used to generate
the surface shown above, click here.

To read a description of the physical derivation of the model,
click here.

Here's another optimal trajectory to the same problem.

Here are some more optimal trajectories arising from different greens
(and perhaps different coefficients of friction).