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Regular and Chaotic Dynamics, 2003, Volume 8, Issue 2, Pages 163–166
DOI: https://doi.org/10.1070/RD2003v008n02ABEH000235
(Mi rcd774)
 

This article is cited in 32 scientific papers (total in 32 papers)

An integrability of the problem on motion of cylinder and vortex in the ideal fluid

A. V. Borisov, I. S. Mamaev

Institute of Computer Science, Universitetskaya, 1, 426034, Izhevsk, Russia
Citations (32)
Abstract: In this paper we present the nonlinear Poisson structure and two first integrals in the problem on plane motion of circular cylinder and $N$ point vortices in the ideal fluid. A priori this problem is not Hamiltonian. The particular case $N = 1$, i.e. the problem on interaction of cylinder and vortex, is integrable.
Received: 11.11.2002
Bibliographic databases:
Document Type: Article
MSC: 37J35, 70H06, 76B47
Language: English
Citation: A. V. Borisov, I. S. Mamaev, “An integrability of the problem on motion of cylinder and vortex in the ideal fluid”, Regul. Chaotic Dyn., 8:2 (2003), 163–166
Citation in format AMSBIB
\Bibitem{BorMam03}
\by A. V. Borisov, I. S. Mamaev
\paper An integrability of the problem on motion of cylinder and vortex in the ideal fluid
\jour Regul. Chaotic Dyn.
\yr 2003
\vol 8
\issue 2
\pages 163--166
\mathnet{http://mi.mathnet.ru/rcd774}
\crossref{https://doi.org/10.1070/RD2003v008n02ABEH000235}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1988857}
\zmath{https://zbmath.org/?q=an:1112.37315}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003RCD.....8..163B}
Linking options:
  • https://www.mathnet.ru/eng/rcd774
  • https://www.mathnet.ru/eng/rcd/v8/i2/p163
  • This publication is cited in the following 32 articles:
    1. Alexander A. Kilin, Anna M. Gavrilova, Elizaveta M. Artemova, “Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case”, Regul. Chaot. Dyn., 2024  crossref
    2. Leonid Kurakin, Irina Ostrovskaya, “On the influence of circulation on the linear stability of a system of a moving cylinder and two identical parallel vortex filaments”, Bol. Soc. Mat. Mex., 29:3 (2023)  crossref
    3. L. G. Kurakin, I. V. Ostrovskaya, “On the Stability of the System of Thomson’s Vortex $n$-Gon and a Moving Circular Cylinder”, Rus. J. Nonlin. Dyn., 18:5 (2022), 915–926  mathnet  crossref  mathscinet
    4. 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  mathnet  crossref
    5. 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  mathnet  crossref
    6. Banavara N. Shashikanth, Dynamically Coupled Rigid Body-Fluid Flow Systems, 2021, 43  crossref
    7. A. V. Borisov, L. G. Kurakin, “On the Stability of a System of Two Identical Point Vortices and a Cylinder”, Proc. Steklov Inst. Math., 310 (2020), 25–31  mathnet  crossref  crossref  mathscinet  isi  elib
    8. I. A. Bizyaev, I. S. Mamaev, “Dinamika pary tochechnykh vikhrei i profilya s parametricheskim vozbuzhdeniem v idealnoi zhidkosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 618–627  mathnet  crossref
    9. Ivan S. Mamaev, Ivan A. Bizyaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1  crossref
    10. 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  mathnet  mathnet  crossref  crossref  isi  scopus
    11. Evgeny V. Vetchanin, Ivan S. Mamaev, “Dynamics of Two Point Vortices in an External Compressible Shear Flow”, Regul. Chaotic Dyn., 22:8 (2017), 893–908  mathnet  crossref
    12. 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
    13. 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
    14. Valery L. Okulov, “An Acentric Rotation of Two Helical Vortices of the Same Circulations”, Regul. Chaotic Dyn., 21:3 (2016), 267–273  mathnet  crossref  mathscinet
    15. 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  crossref
    16. 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
    17. S. V. Sokolov, I. S. Koltsov, “Scattering of the point vortex by a falling circular cylinder”, Dokl. Phys., 60:11 (2015), 511  crossref
    18. 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
    19. 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
    20. Steffen Weißmann, “Hamiltonian Dynamics of Several Rigid Bodies Interacting with Point Vortices”, J Nonlinear Sci, 24:2 (2014), 359  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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