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On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent. / Bibikov, Yu N.; Bukaty, V. R.; Trushina, N. V.

In: Journal of Applied Mathematics and Mechanics, Vol. 80, No. 6, 01.01.2016, p. 443-448.

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

Harvard

Bibikov, YN, Bukaty, VR & Trushina, NV 2016, 'On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent', Journal of Applied Mathematics and Mechanics, vol. 80, no. 6, pp. 443-448. https://doi.org/10.1016/j.jappmathmech.2017.06.002

APA

Bibikov, Y. N., Bukaty, V. R., & Trushina, N. V. (2016). On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent. Journal of Applied Mathematics and Mechanics, 80(6), 443-448. https://doi.org/10.1016/j.jappmathmech.2017.06.002

Vancouver

Bibikov YN, Bukaty VR, Trushina NV. On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent. Journal of Applied Mathematics and Mechanics. 2016 Jan 1;80(6):443-448. https://doi.org/10.1016/j.jappmathmech.2017.06.002

Author

Bibikov, Yu N. ; Bukaty, V. R. ; Trushina, N. V. / On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent. In: Journal of Applied Mathematics and Mechanics. 2016 ; Vol. 80, No. 6. pp. 443-448.

BibTeX

@article{a5468e67a02142c58653797b8c96ff9d,
title = "On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent",
abstract = "Small time-periodic perturbations of the oscillator [Figure presented] where p and q are odd numbers, p > q, are considered. The stability of the equilibrium x = 0 is investigated. The problem is distinguished by the fact that the frequency of unperturbed oscillations is an infinitesimal function of the amplitude. It is shown that in the case of a general equilibrium, for fixed value of q, the Lyapunov constant for values of p that are equal modulo 4q is calculated by the same algorithms, i.e., the problem reduces to a consideration of a finite number (equal to 2q − 2 if q > 1, and equal to 2 if q = 1) of values of p. An estimate, depending on q, of the number of terms of the transformation required for the calculation of the Lyapunov constant for values of p that are equal modulo 4q is given. Particular cases are considered.",
author = "Bibikov, {Yu N.} and Bukaty, {V. R.} and Trushina, {N. V.}",
year = "2016",
month = jan,
day = "1",
doi = "10.1016/j.jappmathmech.2017.06.002",
language = "English",
volume = "80",
pages = "443--448",
journal = "Journal of Applied Mathematics and Mechanics",
issn = "0021-8928",
publisher = "Elsevier",
number = "6",

}

RIS

TY - JOUR

T1 - On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent

AU - Bibikov, Yu N.

AU - Bukaty, V. R.

AU - Trushina, N. V.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Small time-periodic perturbations of the oscillator [Figure presented] where p and q are odd numbers, p > q, are considered. The stability of the equilibrium x = 0 is investigated. The problem is distinguished by the fact that the frequency of unperturbed oscillations is an infinitesimal function of the amplitude. It is shown that in the case of a general equilibrium, for fixed value of q, the Lyapunov constant for values of p that are equal modulo 4q is calculated by the same algorithms, i.e., the problem reduces to a consideration of a finite number (equal to 2q − 2 if q > 1, and equal to 2 if q = 1) of values of p. An estimate, depending on q, of the number of terms of the transformation required for the calculation of the Lyapunov constant for values of p that are equal modulo 4q is given. Particular cases are considered.

AB - Small time-periodic perturbations of the oscillator [Figure presented] where p and q are odd numbers, p > q, are considered. The stability of the equilibrium x = 0 is investigated. The problem is distinguished by the fact that the frequency of unperturbed oscillations is an infinitesimal function of the amplitude. It is shown that in the case of a general equilibrium, for fixed value of q, the Lyapunov constant for values of p that are equal modulo 4q is calculated by the same algorithms, i.e., the problem reduces to a consideration of a finite number (equal to 2q − 2 if q > 1, and equal to 2 if q = 1) of values of p. An estimate, depending on q, of the number of terms of the transformation required for the calculation of the Lyapunov constant for values of p that are equal modulo 4q is given. Particular cases are considered.

UR - http://www.scopus.com/inward/record.url?scp=85021721126&partnerID=8YFLogxK

U2 - 10.1016/j.jappmathmech.2017.06.002

DO - 10.1016/j.jappmathmech.2017.06.002

M3 - Article

AN - SCOPUS:85021721126

VL - 80

SP - 443

EP - 448

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 6

ER -

ID: 49226771