A. V. Borisov, I. S. Mamaev, “On the problem of motion of vortex sources on a plane”, Regul. Chaotic Dyn., 11:4 (2006), 455

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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 4, Pages 455–466
DOI: https://doi.org/10.1070/RD2006v011n04ABEH000363 (Mi rcd686)

This article is cited in 19 scientific papers (total in 19 papers)

On the problem of motion of vortex sources on a plane

A. V. Borisov, I. S. Mamaev

Institute of Computer Science, Udmurt State University, 1, Universitetskaya Str., Izhevsk 426034, Russia

Citations (19)

DOI: https://doi.org/10.1070/RD2006v011n04ABEH000363

Abstract: Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Particular solutions analogous to the homothetic configurations in celestial mechanics are given.

Keywords: vortex sources, integrability, Hamiltonian, point vortex.

Received: 05.09.2005
Revised: 07.03.2006

Bibliographic databases:

Document Type: Article

MSC: 37N05, 76M23

Language: English

Citation: A. V. Borisov, I. S. Mamaev, “On the problem of motion of vortex sources on a plane”, Regul. Chaotic Dyn., 11:4 (2006), 455–466

Citation in format AMSBIB

\Bibitem{BorMam06}

\by A. V. Borisov, I. S. Mamaev

\paper On the problem of motion of vortex sources on a plane

\jour Regul. Chaotic Dyn.

\yr 2006

\vol 11

\issue 4

\pages 455--466

\mathnet{http://mi.mathnet.ru/rcd686}

\crossref{https://doi.org/10.1070/RD2006v011n04ABEH000363}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2292204}

\zmath{https://zbmath.org/?q=an:1164.37353}

Linking options:

https://www.mathnet.ru/eng/rcd686

https://www.mathnet.ru/eng/rcd/v11/i4/p455

This publication is cited in the following 19 articles:

Björn Gustafsson, “Vortex Pairs and Dipoles on Closed Surfaces”, J Nonlinear Sci, 32:5 (2022)
Armand Vic, Xavier Carton, Jonathan Gula, “The Interaction of Two Unsteady Point Vortex Sources in a Deformation Field in 2D Incompressible Flows”, Regul. Chaotic Dyn., 26:6 (2021), 618–646
Jaime Andrade, Stefanella Boatto, Thierry Combot, Gladston Duarte, Teresinha J. Stuchi, “ $N$ -body Dynamics on an Infinite Cylinder: the Topological Signature in the Dynamics”, Regul. Chaotic Dyn., 25:1 (2020), 78–110
E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 604–617
Koiller J., “Getting Into the Vortex: on the Contributions of James Montaldi”, J. Geom. Mech., 12:3 (2020), 507–523
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Vortex Sources in a Deformation Flow”, Regul. Chaotic Dyn., 21:3 (2016), 367–376
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Three Vortex Sources”, Regul. Chaotic Dyn., 19:6 (2014), 694–701
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika trekh vikhreistochnikov”, Nelineinaya dinam., 10:3 (2014), 319–327
Valery V. Kozlov, “Remarks on Integrable Systems”, Regul. Chaotic Dyn., 19:2 (2014), 145–161
Darren Crowdy, “Analytical formulae for source and sink flows in multiply connected domains”, Theor. Comput. Fluid Dyn., 27:1-2 (2013), 1
Alexey V. Bolsinov, Alexey V. Borisov, Ivan S. Mamaev, “The Bifurcation Analysis and the Conley Index in Mechanics”, Regul. Chaotic Dyn., 17:5 (2012), 451–478
A. V. Borisov, I. S. Mamaev, A. V. Vaskina, “Novye otnositelnye ravnovesiya v sisteme trekh tochechnykh vikhrei v krugovoi oblasti i ikh ustoichivost”, Nelineinaya dinam., 7:1 (2011), 119–138
A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Bifurkatsionnyi analiz i indeks Konli v mekhanike”, Nelineinaya dinam., 7:3 (2011), 649–681
James Montaldi, Tadashi Tokieda, “Dynamics of poles with position-dependent strengths and its optical analogues”, Physica D: Nonlinear Phenomena, 240:20 (2011), 1636
Stefan G. Llewellyn Smith, “How do singularities move in potential flow?”, Physica D: Nonlinear Phenomena, 240:20 (2011), 1644
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface”, Regul. Chaotic Dyn., 15:4 (2010), 440–461

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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