Journal of Applied Mathematics and Mechanics (about journal) 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)

Russian  English English About Journal | Issues | Editorial Board | Contact Us
 


 Web hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2016-6pp.443-448

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

<< 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 http://www.sciencedirect.com/science/article/pii/S0021892817300278
<< Previous article | Volume 80, Issue 6 / 2016 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 245, 119526 Moscow, Russia (+7 495) 434-2149 pmm@ipmnet.ru pmmedit@ipmnet.ru http://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Journals on Mechanics Ltd.
© Journals on Mechanics Ltd.
Webmaster: Alexander Levitin
Rambler's Top100