Asymptotically stable non-falling solutions of the Kapitza-Whitney pendulum (Q6172059)

The article discusses a generalization of the famous Kapitza-Whitney pendulum. In the absence of additional horizontal force, the system under consideration is equivalent to the Kapitza pendulum. Some results are obtained on the existence of asymptotically stable periodically non-falling solutions. In particular, the numerical results obtained allow the author to analyze the classical conditions for asymptotic stabilization upper Kapitza equilibrium position pendulum. The author draws attention to some unsolved problems for the system under consideration.