Foucault pendulum sharing the rotation of the earth about its own axis, the suspension point of the pendulum traces out a circular path during one sidereal day. At the latitude of Paris, 48 degrees 51 minutes north, a full precession cycle takes just under 32 hours, so after one sidereal day, when the Earth is back in the same orientation as one sidereal day before, the oscillation plane has turned by just over 270 degrees. If the plane of swing was north-south at the outset, it is east-west one sidereal day later. This also implies that there has been exchange of momentum;
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