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

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Matematicheskie Zametki, 2016, Volume 99, Issue 6, Pages 848–854
DOI: https://doi.org/10.4213/mzm11051 (Mi mzm11051)

This article is cited in 15 scientific papers (total in 16 papers)

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

A. V. Borisov^ab, P. E. Ryabov^cd, S. V. Sokolov^cd

^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

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

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.

Received: 25.12.2015

English version:
Mathematical Notes, 2016, Volume 99, Issue 6, Pages 834–839
DOI: https://doi.org/10.1134/S0001434616050217

Bibliographic databases:

Document Type: Article

UDC: 517.938.5+512.77

PACS: 02.30.Ik

Language: Russian

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

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This publication is cited in the following 16 articles:

Sergei V. Sokolov, Pavel E. Ryabov, Sergei M. Ramodanov, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2022, 3030, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2022, 2024, 080001
Sergei V. Sokolov, Sergei M. Ramodanov, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021, 2611, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021, 2022, 100007
S. V. Sokolov, “Pamyati Alekseya Vladimirovicha Borisova”, Kompyuternye issledovaniya i modelirovanie, 13:1 (2021), 9–14
Ivan A. Bizyaev, Ivan S. Mamaev, “Qualitative Analysis of the Dynamics of a Balanced Circular Foil and a Vortex”, Regul. Chaotic Dyn., 26:6 (2021), 658–674
Sergey M. Ramodanov, Sergey V. Sokolov, “Dynamics of a Circular Cylinder and Two Point Vortices in a Perfect Fluid”, Regul. Chaotic Dyn., 26:6 (2021), 675–691
I. S. Mamaev, I. A. Bizyaev, “Dynamics of an unbalanced circular foil and point vortices in an ideal fluid”, Phys. Fluids, 33:8 (2021), 087119
Ivan S. Mamaev, Ivan A. Bizyaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
P. E. Ryabov, “Bifurcations of Liouville tori in a system of two vortices of positive intensity in a Bose–Einstein condensate”, Dokl. Math., 99:2 (2019), 225–229
P. E. Ryabov, S. V. Sokolov, “Phase Topology of Two Vortices of Identical Intensities in a Bose – Einstein Condensate”, Rus. J. Nonlin. Dyn., 15:1 (2019), 59–66
Pavel E. Ryabov, Artemiy A. Shadrin, “Bifurcation Diagram of One Generalized Integrable Model of Vortex Dynamics”, Regul. Chaotic Dyn., 24:4 (2019), 418–431
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
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
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
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
P. E. Ryabov, “YaVNOE INTEGRIROVANIE SISTEMY INVARIANTNYKh SOOTNOShENII DLYa SLUChAYa M. ADLERA I P. VAN MERBEKE, “Doklady Akademii nauk””, Doklady Akademii nauk, 2017, no. 2, 130
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

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

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