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. Two different models were created, the first using midpoint discretization and the second using trapezoidal discretization:

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).