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.