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Mat. Zametki, 2016, Volume 99, Issue 6, Pages 848–854 (Mi mz11051)  

This article is cited in 5 scientific papers (total in 5 papers)

Bifurcation Analysis of the Motion of a Cylinder and a Point Vortex in an Ideal Fluid

A. V. Borisovab, P. E. Ryabovcd, S. V. Sokolovcd

a Udmurt State University, Izhevsk
b Izhevsk State Technical University
c A. A. Blagonravov Mechanical Engineering Institute RAS, Moscow
d Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: We consider an integrable Hamiltonian system describing the motion of a circular cylinder and a vortex filament in an ideal fluid. We construct bifurcation diagrams and bifurcation complexes for the case in which the integral manifold is compact and for various topological structures of the symplectic leaf. The types of motions corresponding to the bifurcation curves and their stability are discussed.

Keywords: Hamiltonian system, integrability, bifurcation complex.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00395-а
15-08-09093-а
14-01-00119
16-01-00170
15-41-02049
16-01-00809
The first author was supported by the Russian Foundation for Basic Research under grants 14-01-00395-a and 15-08-09093-a. The second author was supported by the Russian Foundation for Basic Research under grants 14-01-00119 and 16-01-00170 and by the Russian Foundation for Basic Research together with the Government of the Volgograd oblast under joint grant 15-41-02049. The third author was supported by the Russian Foundation for Basic Research under grants 16-01-00170 and 16-01-00809.


DOI: https://doi.org/10.4213/mzm11051

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English version:
Mathematical Notes, 2016, 99:6, 834–839

Bibliographic databases:

Document Type: Article
UDC: 517.938.5+512.77
PACS: 02.30.Ik
Received: 25.12.2015

Citation: 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”, Mat. Zametki, 99:6 (2016), 848–854; Math. Notes, 99:6 (2016), 834–839

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Vetchanin, A. A. Kilin, I. S. Mamaev, “Control of the motion of a helical body in a fluid using rotors”, Regul. Chaotic Dyn., 21:7-8 (2016), 874–884  mathnet  crossref  mathscinet  zmath  isi  scopus
    2. P. E. Ryabov, “Explicit integration of the system of invariant relations for the case of M. Adler and P. Van Moerbeke”, Dokl. Math., 95:1 (2017), 17–20  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. 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
    5. 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  crossref  isi  elib  scopus
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