Physics-based simulation of a vibrating double pendulum whose support point is oscillating rapidly up and down. Surprisingly, the inverted position where the pendulum stands straight up is stable.
Click near the pendulum to reposition it. The anchor point is also dragable. You can set gravity, frequency of oscillation, magnitude of oscillation, and damping (friction).
Experiments to try:
The math for this simulation is similar to the Moveable Double Pendulum except that there is a periodic force for oscillating the anchor point. We assume the anchor/support point is so massive compared to the pendulum that it is not affected by the motion of the pendulums.
Also available: source code, documentation and how to customize.
Most of the references on the internet for a double inverted pendulum are for a different set up, where the double pendulum is attached to a moveable cart, similar to the cart + pendulum simulation. Also most of the these references are concerned with control theory for making an autonomous "brain" that can balance the inverted pendulum. In contrast, the experiment shown here uses only vertical vibration of the support point to make the inverted position stable.
