Open AccessOn Periodic Solutions of One Second-Order Differential Equation
Author(s) -
Г. В. Демиденко,
Г. В. Демиденко,
A. V. Dulepova,
A. V. Dulepova
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-3-535-548
Subject(s) - kapitza's pendulum , double pendulum , inverted pendulum , pendulum , suspension (topology) , periodic function , mathematical analysis , differential equation , motion (physics) , mathematics , point (geometry) , function (biology) , physics , double inverted pendulum , line (geometry) , classical mechanics , control theory (sociology) , geometry , computer science , nonlinear system , pure mathematics , control (management) , quantum mechanics , evolutionary biology , homotopy , artificial intelligence , biology
In this paper, we investigate the movement of an inverted pendulum, the suspension point of which performs high-frequency oscillations along a line making a small angle with the vertical. We prove that under certain conditions on the function describing the oscillations of the suspension point of the pendulum, a periodic motion of the pendulum arises, and it is asymptotically stable.