On Stability of the Inverted Pendulum Motion with a Vibrating Suspension Point
- Авторлар: Demidenko G.1,2, Dulepova A.2
-
Мекемелер:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Шығарылым: Том 12, № 4 (2018)
- Беттер: 607-618
- Бөлім: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213107
- DOI: https://doi.org/10.1134/S1990478918040026
- ID: 213107
Дәйексөз келтіру
Аннотация
Under study is the stability of the inverted pendulum motion whose suspension point vibrates according to a sinusoidal law along a straight line having a small angle with the vertical. Formulating and using the contracting mapping principle and the criterion of asymptotic stability in terms of solvability of a special boundary value problem for the Lyapunov differential equation, we prove that the pendulum performs stable periodic movements under sufficiently small amplitude of oscillations of the suspension point and sufficiently high frequency of oscillations.
Авторлар туралы
G. Demidenko
Sobolev Institute of Mathematics; Novosibirsk State University
Хат алмасуға жауапты Автор.
Email: demidenk@math.nsc.ru
Ресей, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
A. Dulepova
Novosibirsk State University
Email: demidenk@math.nsc.ru
Ресей, ul. Pirogova 2, Novosibirsk, 630090