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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






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


Nelin. Dinam., 2007, Volume 3, Number 4, Pages 379–391 (Mi nd145)  

This article is cited in 2 scientific papers (total in 2 papers)

Dynamics of perturbed equilateral and collinear configurations of three point vortices

A. I. Gudimenko

V. I. Il'ichev Pacific Oceanological Institute of the Far Eastern Branch of RAS

Abstract: Dynamics of perturbed stable equilateral and collinear configurations of three point vortices in an incompressible ideal fluid is studied. The asymptotics of the perturbed motion to the unperturbed one is obtained. It is shown that in the first approximation in a appropriate coordinate system the vortices rotate about their undisturbed positions in elliptical orbits. The velocity of the rotation is calculated. It is shown that the eccentricities of the orbits are coincide. The ratio of major axes of any two orbits is calculated. In case of equilateral configuration this ratio is equal to the ratio of inverse intensities of the corresponding vortices. The angle between major axes of any two orbits of the vortices is calculated. In case of equilateral configuration this angle is $\pm 120$ degrees.

Keywords: point vortices, integrable dynamics, perturbation theory.

Full text: PDF file (185 kB)
UDC: 551.465.7
MSC: 37D45, 76U05, 76B47, 76E20

Citation: A. I. Gudimenko, “Dynamics of perturbed equilateral and collinear configurations of three point vortices”, Nelin. Dinam., 3:4 (2007), 379–391

Citation in format AMSBIB
\Bibitem{Gud07}
\by A.~I.~Gudimenko
\paper Dynamics of perturbed equilateral and collinear configurations of three point vortices
\jour Nelin. Dinam.
\yr 2007
\vol 3
\issue 4
\pages 379--391
\mathnet{http://mi.mathnet.ru/nd145}


Linking options:
  • http://mi.mathnet.ru/eng/nd145
  • http://mi.mathnet.ru/eng/nd/v3/i4/p379

    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

    This publication is cited in the following articles:
    1. M. A. Guzev, Yu. G. Izrailskii, K. V. Koshel, “Effekt globalnoi khaotizatsii v tsepochke chastits”, Nelineinaya dinam., 6:2 (2010), 291–305  mathnet
    2. Sokolovskiy M.A., Verron J., “Dynamics of Vortex Structures in a Stratified Rotating Fluid”: Sokolovskiy, MA Verron, J, Dynamics of Vortex Structures in a Stratified Rotating Fluid, Atmospheric and Oceanographic Sciences Library, 47, Springer Int Publishing Ag, 2014  crossref  isi
  • Нелинейная динамика
    Number of views:
    This page:70
    Full text:29
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020