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).
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 are:
open source code,
documentation and a
simple-compiled version
which is more customizable.
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.