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


IssuesArchive of Issues2010-4pp.389-400

Archive of Issues

Total articles in the database: 10482
In Russian (ΟΜΜ): 9683
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 74, Issue 4 / 2010 | Next article >>
D.A. Kulikov, "Self-similar cycles and their local bifurcations in the problem of two weakly coupled oscillators," J. Appl. Math. Mech. 74 (4), 389-400 (2010)
Year 2010 Volume 74 Issue 4 Pages 389-400
Title Self-similar cycles and their local bifurcations in the problem of two weakly coupled oscillators
Author(s) D.A. Kulikov (Yaroslavl, Russia, kulikov_d_a@mail.ru)
Abstract A system of two non-linear differential equations is considered that simulates the dynamics of two completely identical weakly coupled oscillators both in the case of dissipative and active coupling. The system of normal modes is investigated. All the self-similar periodic solutions, including the asymmetric solutions describing the natural ascillations of oscillators with dissimilar amplitude's, are found analytically. The stability is investigated as well as the local bifurcations of the self-similar cycles when there is a change in stability. In particular, the possibility of the creation of two-dimensional invariant tori is pointed out. In the case of active coupling, it is shown that the basic version of the natural oscillations is a stable antiphase cycle that was observed in Huygens experiments.
Received 06 November 2008
Link to Fulltext
<< Previous article | Volume 74, Issue 4 / 2010 | 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 https://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Journal of Applied Mathematics and Mechanics
webmaster
Rambler's Top100