  Journal of Applied Mathematics and Mechanics Russian Academy of Sciences   Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 00218928 (print version) 
Archive of Issues
Total articles in the database:   1813 
In Russian (ÏÌÌ):   1014

In English (J. Appl. Math. Mech.):   799 

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Yu.N. Bibikov, V.R. Bukaty and N.V. Trushina, "On the stability of the equilibrium under periodic perturbations of an oscillator with a powerlaw restoring force with a rational exponent," J. Appl. Math. Mech. 80 (6), 443448 (2016) 
Year 
2016 
Volume 
80 
Issue 
6 
Pages 
443448 
DOI 
10.1016/j.jappmathmech.2017.06.002 
Title 
On the stability of the equilibrium under periodic perturbations of an oscillator with a powerlaw 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 timeperiodic perturbations of the oscillator
dx^{2}/dt^{2}+x^{p/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 
http://www.sciencedirect.com/science/article/pii/S0021892817300278 
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