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On Periodic Solutions of One Second-Order Differential Equation. / Demidenko, G. V.; Dulepova, A. V.

In: Journal of Mathematical Sciences (United States), Vol. 278, No. 2, 01.2024, p. 314-327.

Research output: Contribution to journal › Article › peer-review

Harvard

Demidenko, GV & Dulepova, AV 2024, 'On Periodic Solutions of One Second-Order Differential Equation', Journal of Mathematical Sciences (United States), vol. 278, no. 2, pp. 314-327. https://doi.org/10.1007/s10958-024-06922-7

APA

Demidenko, G. V., & Dulepova, A. V. (2024). On Periodic Solutions of One Second-Order Differential Equation. Journal of Mathematical Sciences (United States), 278(2), 314-327. https://doi.org/10.1007/s10958-024-06922-7

Vancouver

Demidenko GV, Dulepova AV. On Periodic Solutions of One Second-Order Differential Equation. Journal of Mathematical Sciences (United States). 2024 Jan;278(2):314-327. doi: 10.1007/s10958-024-06922-7

Author

Demidenko, G. V. ; Dulepova, A. V. / On Periodic Solutions of One Second-Order Differential Equation. In: Journal of Mathematical Sciences (United States). 2024 ; Vol. 278, No. 2. pp. 314-327.

BibTeX

@article{559360a7cb8e418db01552e2908fb5be,
title = "On Periodic Solutions of One Second-Order Differential Equation",
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.",
keywords = "asymptotical stability, inverted pendulum, periodic solution, second-order differential equation",
author = "Demidenko, {G. V.} and Dulepova, {A. V.}",
year = "2024",
month = jan,
doi = "10.1007/s10958-024-06922-7",
language = "English",
volume = "278",
pages = "314--327",
journal = "Journal of Mathematical Sciences (United States)",
issn = "1072-3374",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - On Periodic Solutions of One Second-Order Differential Equation

AU - Demidenko, G. V.

AU - Dulepova, A. V.

PY - 2024/1

Y1 - 2024/1

N2 - 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.

AB - 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.

KW - asymptotical stability

KW - inverted pendulum

KW - periodic solution

KW - second-order differential equation

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85182487980&origin=inward&txGid=fc424bcb85e2aaf3ee8c8e2f545c89f8

UR - https://www.mendeley.com/catalogue/d93fd26f-e9e8-350e-80e8-ae60f6ab7dc6/

U2 - 10.1007/s10958-024-06922-7

DO - 10.1007/s10958-024-06922-7

M3 - Article

VL - 278

SP - 314

EP - 327

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 2

ER -

ID: 60334052