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Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency. / Bibikov, Yu. N.; Bukaty, V. R.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 3, 01.07.2019, p. 259-262.

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

Harvard

Bibikov, YN & Bukaty, VR 2019, 'Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency', Vestnik St. Petersburg University: Mathematics, vol. 52, no. 3, pp. 259-262. https://doi.org/10.1134/S1063454119030051

APA

Bibikov, Y. N., & Bukaty, V. R. (2019). Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency. Vestnik St. Petersburg University: Mathematics, 52(3), 259-262. https://doi.org/10.1134/S1063454119030051

Vancouver

Bibikov YN, Bukaty VR. Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency. Vestnik St. Petersburg University: Mathematics. 2019 Jul 1;52(3):259-262. https://doi.org/10.1134/S1063454119030051

Author

Bibikov, Yu. N. ; Bukaty, V. R. / Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency. In: Vestnik St. Petersburg University: Mathematics. 2019 ; Vol. 52, No. 3. pp. 259-262.

BibTeX

@article{1bde1d5f175645a0a4383de8fe8e34df,
title = "Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency",
abstract = "Abstract: We consider the stability of the equilibrium state of an oscillator with an infinitely high natural oscillation frequency under time-periodic perturbations of the oscillator. It is shown that the problem of stability in the case of general equilibrium can be solved by considering only a linear approximation of the perturbation. In the singular case, a procedure is proposed to construct a nonzero constant, if it exists, whose sign specifies whether the state of equilibrium is asymptotically stable or unstable.",
keywords = "infinite frequency, oscillator, periodic perturbations, second-order differential equation, stability",
author = "Bibikov, {Yu. N.} and Bukaty, {V. R.}",
year = "2019",
month = jul,
day = "1",
doi = "10.1134/S1063454119030051",
language = "English",
volume = "52",
pages = "259--262",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Stability of the Equilibrium of an Oscillator with an Infinitely High Natural Oscillation Frequency

AU - Bibikov, Yu. N.

AU - Bukaty, V. R.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Abstract: We consider the stability of the equilibrium state of an oscillator with an infinitely high natural oscillation frequency under time-periodic perturbations of the oscillator. It is shown that the problem of stability in the case of general equilibrium can be solved by considering only a linear approximation of the perturbation. In the singular case, a procedure is proposed to construct a nonzero constant, if it exists, whose sign specifies whether the state of equilibrium is asymptotically stable or unstable.

AB - Abstract: We consider the stability of the equilibrium state of an oscillator with an infinitely high natural oscillation frequency under time-periodic perturbations of the oscillator. It is shown that the problem of stability in the case of general equilibrium can be solved by considering only a linear approximation of the perturbation. In the singular case, a procedure is proposed to construct a nonzero constant, if it exists, whose sign specifies whether the state of equilibrium is asymptotically stable or unstable.

KW - infinite frequency

KW - oscillator

KW - periodic perturbations

KW - second-order differential equation

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85071987679&partnerID=8YFLogxK

UR - https://link.springer.com/article/10.1134/S1063454119030051

U2 - 10.1134/S1063454119030051

DO - 10.1134/S1063454119030051

M3 - Article

AN - SCOPUS:85071987679

VL - 52

SP - 259

EP - 262

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 49226386