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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. 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
Full-text PDF (468 kB) Citations (16)
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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
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
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