  Skateboarders perform a reciprocating motion on a curved ramp, called
pumping, by moving their bodies up and down perpendicular to the ramp's
surface. We propose a simple mechanical model for this pumping motion and solve
the equation of motion explicitly in angular coordinates. This allows us to
derive an optimal control strategy to maximize amplitude by dynamically
adjusting the center of mass of the skateboarder. This optimal strategy is
compared to experimental results for the motion of a skilled and an unskilled
skateboarder in a half-pipe, validating that a skilled skateboarder follows the
optimal control strategy more closely.
