Stability of the Inverted Pendulum—A Topological Explanation

摘要: An explanation and a proof of stability the inverted pendulum whose suspension point undergoes vertical periodic oscillations is given. The main idea argument topological; as it turns out, existence stable regimes can be proven with little effort using only very crude qualitative information about system. More precisely, let n number times becomes during one forcing period. If changes by more than 4 change parameter $\mu $, then for an open interval intermediate values $ will stable.