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 -