Recipient of the 2006 AMS Award for Exemplary Department or Program
HMC

Inverted Pendulum

The inverted pendulum is a surprising demo. Imagine first a pendulum. The equilibrium state is generically with the pendulum at rest, hanging straight down. However, there is another possible equilibrium state with the pendulum inverted 180 degrees ("straight up"). This equilibrium point is unstable, the slightest perturbation and the pendulum will oscillate until it is eventually at rest, hanging straight down.

Now, here is the surprising part -- if we periodically force the pendulum at its pivot, then the inverted unstable equilibrium state actually becomes stable! The video below demonstrates this point. The pendulum starts near the inverted equilibrium, starts to fall down (swinging to the left) then stands back up approaching the inverted equilibrium state!

To create this demo we modified a standard jigsaw to allow us to attach a pendulum to vibrating blade. Working in the demo lab we also discovered a new physical phenomenon...

We are still modeling this strange bevavior :-)