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

Yu N. Bibikov, V. R. Bukaty, N. V. Trushina

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

2 Цитирования (Scopus)

Аннотация

Small time-periodic perturbations of the oscillator 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.
Язык оригиналаанглийский
Страницы (с-по)443-448
Число страниц6
ЖурналJournal of Applied Mathematics and Mechanics
Том80
Номер выпуска6
DOI
СостояниеОпубликовано - 1 янв 2016

Предметные области Scopus

  • Прикладная математика

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