On Stability of the Inverted Pendulum Motion with a Vibrating Suspension Point
- Authors: Demidenko G.V.1,2, Dulepova A.V.2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 12, No 4 (2018)
- Pages: 607-618
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213107
- DOI: https://doi.org/10.1134/S1990478918040026
- ID: 213107
Cite item
Abstract
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.
About the authors
G. V. Demidenko
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: demidenk@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
A. V. Dulepova
Novosibirsk State University
Email: demidenk@math.nsc.ru
Russian Federation, ul. Pirogova 2, Novosibirsk, 630090