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

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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.

Original languageEnglish
Pages (from-to)259-262
JournalVestnik St. Petersburg University: Mathematics
Volume52
Issue number3
DOIs
StatePublished - 1 Jul 2019

Scopus subject areas

  • Mathematics(all)

Keywords

  • infinite frequency
  • oscillator
  • periodic perturbations
  • second-order differential equation
  • stability

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