Rimless Wheel

Limit cycle for a non-uniform rimless wheel with 5 spokes.

Limit cycle for a non-uniform rimless wheel with 10 spokes.

Bouncing

A bouncing coin on a parabolic table where the nonholonomic constraint of rolling without slipping is enforced at each impact.

The classical bouncing ball on an oscillating table.

Mechanical systems on a Möbius Strip

Trajectory of a particle restricted to the Möbius strip subject to a conservative force pushing the particle towards the “equator.”

Trajectory of a free particle restricted to the Möbius strip with impacts occurring at the boundary.

Pendulum on a cart

Trajectory of the pendulum on a cart.

Optimally controlled trajectory for inverting the pendulum.

Trajectory of the pendulum on a cart subject to collisions of the cart.

Optimally controlled trajectory for inverting the pendulum by utilizing the presence of the walls.