A playground ball finds stability in a saddle when the saddle is rotating at the proper speed.
Mechanical analog of a “Paul Trap” particle confinement—a ball is trapped in a time-varying quadrupole gravitational potential. A large saddle shape (attached to a plywood disk) is mounted on a multi-purpose turntable. The saddle shape is essentially a quadrupole gravitational potential. Rotation of this potential subjects the ball to an alternating repulsive and attractive potential, much like the time-varying electric quadrupole potential of a Paul Trap used in trapping single ions or electrons.
The plastic ball used here is about 25 cm in diameter and was purchased at a toy store. The saddle consists of many layers of fiberglass and was hand-made with help from Justin Georgi. The turntable is driven at about 110 rpm with a DC motor. We have observed this ball at this speed remaining stable for over 2 hours.