Pendulum plane of oscillation of a pendulum, like a gyroscope, tends to stay constant regardless of the motion of the pivot, and that this could be used to demonstrate the rotation of the Earth. He suspended a pendulum free to swing in two dimensions (later named the Foucault pendulum) from the dome of the Panthéon in Paris. The length of the cord was . Once the pendulum was set in motion, the plane of swing was observed to precess or rotate 360° clockwise in about 32 hours. This was the first demonstration of the Earth's rotation that didn't depend on celestial
Kapitza's pendulum become stable in Kapitza's pendulum. The rotating solutions of the Kapitza's pendulum occur when the pendulum rotates around the pivot point at the same frequency that the pivot point is driven. There are two rotating solutions, one for a rotation in each direction. We shift to the rotating reference frame using formula_59 and the equation for formula_39 becomes: Again considering the limit in which formula_5 is much higher than the proper frequency formula_38, we find that the rapid-formula_5 slow-formula_65 limit leads to the equation: The effective potential is just that of a simple pendulum equation. There is a stable equilibrium