 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 80, Issue 6 / 2016 | Next article >> |
| Yu.N. Bibikov, V.R. Bukaty, and N.V. Trushina, "On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent," J. Appl. Math. Mech. 80 (6), 443-448 (2016) |
| Year |
2016 |
Volume |
80 |
Issue |
6 |
Pages |
443-448 |
| DOI |
10.1016/j.jappmathmech.2017.06.002 |
| Title |
On the stability of the equilibrium under periodic perturbations of an oscillator with a power-law restoring force with a rational exponent |
| Author(s) |
Yu.N. Bibikov (Saint Petersburg State University, Saint Petersburg, Russia, bibicoff@yandex.ru)
V.R. Bukaty (Saint Petersburg State University, Saint Petersburg, Russia)
N.V. Trushina (Saint Petersburg State University, Saint Petersburg, Russia) |
| Abstract |
Small time-periodic perturbations of the oscillator
dx2/dt2+xp/q=0
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. |
| Received |
19 February 2015 |
| Link to Fulltext |
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