Inverted pendulum with oscillated base

aka Kapitsa's pendulum

http://simulations.narod.ru/

The base of the pendulum oscillated vertically. This makes up equilibrium point stable.

video:
http://www.youtube.com/watch?v=UccK5i-OHAU

Note: frequency is oscillation is big, on the video it is small because of aliasing.

run test1.m

see formulas.jpg for derivative the motion equation using lagrangian mechanics