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Regul. Chaotic Dyn., 2013, Volume 18, Issue 1-2, Pages 184–193 (Mi rcd104)  

This article is cited in 11 scientific papers (total in 11 papers)

Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex

Sergei V. Sokolov, Sergei M. Ramodanov

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

Abstract: The dynamical behavior of a heavy circular cylinder and a point vortex in an unbounded volume of ideal liquid is considered. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The governing equations are Hamiltonian and admit an evident autonomous integral of motion the horizontal component of the linear momentum. Using the integral we reduce the order and thereby obtain a system with two degrees of freedom. The stability of equilibrium solutions is investigated and some remarkable types of partial solutions of the system are presented.

Keywords: point vortices, Hamiltonian systems, reduction, stability of equilibrium solutions

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation NSh-2519.2012.1.
The work of the second author was supported by the Support grant of leading scientific schools NSh-2519.2012.1.


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Document Type: Article
MSC: 70Hxx, 70G65
Received: 11.08.2012
Language: English

Citation: Sergei V. Sokolov, Sergei M. Ramodanov, “Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex”, Regul. Chaotic Dyn., 18:1-2 (2013), 184–193

Citation in format AMSBIB
\by Sergei V. Sokolov, Sergei M. Ramodanov
\paper Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 184--193

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    This publication is cited in the following articles:
    1. S. V. Sokolov, “Dvizhenie krugovogo tsilindra, vzaimodeistvuyuschego s vikhrevoi paroi, v pole sily tyazhesti v idealnoi zhidkosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 86–99  mathnet
    2. S. V. Sokolov, “Dvizhenie krugovogo tsilindricheskogo tverdogo tela, vzaimodeistvuyuschego s $N$ tochechnymi vikhryami, v pole sily tyazhesti”, Nelineinaya dinam., 10:1 (2014), 59–72  mathnet
    3. Sergey P. Kuznetsov, “Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models”, Regul. Chaotic Dyn., 20:3 (2015), 345–382  mathnet  crossref  mathscinet  zmath  adsnasa
    4. S. V. Sokolov, I. S. Koltsov, “Khaoticheskoe rasseyanie tochechnogo vikhrya krugovym tsilindricheskim tverdym telom, dvizhuschimsya v pole tyazhesti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 184–196  mathnet  elib
    5. S. V. Sokolov, I. S. Koltsov, “Scattering of the point vortex by a falling circular cylinder”, Dokl. Phys., 60:11 (2015), 511–514  crossref  isi  scopus
    6. A. V. Borisov, P. E. Ryabov, S. V. Sokolov, “Bifurcation Analysis of the Motion of a Cylinder and a Point Vortex in an Ideal Fluid”, Math. Notes, 99:6 (2016), 834–839  mathnet  crossref  crossref  mathscinet  isi  elib
    7. S. V. Sokolov, “On the problem of falling motion of a circular cylinder and a vortex pair in a perfect fluid”, Dokl. Math., 94:2 (2016), 594–597  crossref  mathscinet  zmath  isi  scopus
    8. Sergei V. Sokolov, Pavel E. Ryabov, “Bifurcation Analysis of the Dynamics of Two Vortices in a Bose Einstein Condensate. The Case of Intensities of Opposite Signs”, Regul. Chaotic Dyn., 22:8 (2017), 976–995  mathnet  crossref
    9. A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525  crossref  mathscinet  zmath  isi  scopus
    10. S. V. Sokolov, “Motion of a cylinder rigid body interacting with point vortices”, Coupled Problems in Science and Engineering VII (Coupled Problems 2017), eds. M. Papadrakakis, E. Onate, B. Schrefler, Int. Center Numerical Methods Engineering, 2017, 204–215  isi
    11. S. V. Sokolov, P. E. Ryabov, “Bifurcation diagram of the two vortices in a Bose–Einstein condensate with intensities of the same signs”, Dokl. Math., 97:3 (2018), 286–290  crossref  zmath  isi  scopus
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