On Periodic Solutions of One Second-Order Differential Equation

In this paper, we investigate the motion 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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.278 (2), p.314-327
Main Authors: Demidenko, G. V., Dulepova, A. V.
Format: Article
Language:English
Subjects:
Differential equations
Laws, regulations and rules
Mathematics
Mathematics and Statistics
Oscillations
Pendulums
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Summary:In this paper, we investigate the motion 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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-06922-7