RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Ufimsk. Mat. Zh., 2018, Volume 10, Issue 4, Pages 64–76 (Mi ufa448)  

Capture and holding of resonance far from equilibrium

L. A. Kalyakin

Institute of Mathematics, Ufa Federal Research Center, RAS, Chernyshevsky str. 112, 450008, Ufa, Russia

Abstract: Capture into resonance occurs in nonlinear oscillating systems. The study of mathematical models of this phenomenon is a part of a modern theory of nonlinear oscillations. The known result in this field were obtained by averaging method in the asymptotic regime with a small parameter. In this way, an initial stage of the capture into resonance was studied in details.
The matter of this approach is an asymptotic passage to a model equation of mathematical pendulum kind. In the present work we consider an asymptotic construction at long time, which describes a slow evolution of a solution captured into resonance. The main aim is to determine a time interval, during which the resonance is held. The problem is reduced to studying a perturbation of a model equation of pendulum type. Our main success is the description of the time interval, in which the resonance is captured, and the description is given in terms of the data in the original problem. Formally we consider a nonlinear oscillating system with a small perturbation. The perturbation is described by an external pumping with a prescribed slowly changing frequency. For the solutions captured into the resonance, we consider asymptotics with respect to the small parameter. We write out an equation, the solution to which allows us to find the time of the capturing into resonance.

Keywords: nonlinear oscillations, perturbation, small parameter, asymptotics, capture in resonance.

Full text: PDF file (403 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2018, 10:4, 64–76 (PDF, 361 kB); https://doi.org/10.13108/2018-10-4-64

Bibliographic databases:

Document Type: Article
UDC: 517.928.7
MSC: 34E13
Received: 05.04.2018

Citation: L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufimsk. Mat. Zh., 10:4 (2018), 64–76; Ufa Math. J., 10:4 (2018), 64–76

Citation in format AMSBIB
\Bibitem{Kal18}
\by L.~A.~Kalyakin
\paper Capture and holding of resonance far from equilibrium
\jour Ufimsk. Mat. Zh.
\yr 2018
\vol 10
\issue 4
\pages 64--76
\mathnet{http://mi.mathnet.ru/ufa448}
\transl
\jour Ufa Math. J.
\yr 2018
\vol 10
\issue 4
\pages 64--76
\crossref{https://doi.org/10.13108/2018-10-4-64}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000457367000006}


Linking options:
  • http://mi.mathnet.ru/eng/ufa448
  • http://mi.mathnet.ru/eng/ufa/v10/i4/p64

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Уфимский математический журнал
    Number of views:
    This page:19
    Full text:6
    References:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019