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On Periodic Solutions of One Second-Order Differential Equation

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Abstract

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    G. V. Demidenko

  2. Novosibirsk State University, Novosibirsk, Russia

    A. V. Dulepova

Authors
  1. G. V. Demidenko
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  2. A. V. Dulepova
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Correspondence to G. V. Demidenko.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 3, In honor of the 70th anniversary of Professor V. M. Filippov, 2021.

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Demidenko, G.V., Dulepova, A.V. On Periodic Solutions of One Second-Order Differential Equation. J Math Sci 278, 314–327 (2024). https://doi.org/10.1007/s10958-024-06922-7

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  • DOI: https://doi.org/10.1007/s10958-024-06922-7

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