Abstract:
In this paper, the integrability of the equations of a system of three vortex sources is shown. A reduced system describing, up to similarity, the evolution of the system’s configurations is obtained. Possible phase portraits and various relative equilibria of the system are presented.
The work of I. S. Mamaev and I. A. Bizyaev was supported by the Ministry of Education and
Science of the Russian Federation within the framework of the basic part of the state assignment
to institutions of higher education. The work of A. V. Borisov was supported by the RFBR Grant
14-01-00395-a.
\Bibitem{BizBorMam14}
\by Ivan~A.~Bizyaev, Alexey~V.~Borisov, Ivan~S.~Mamaev
\paper The Dynamics of Three Vortex Sources
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 694--701
\mathnet{http://mi.mathnet.ru/rcd192}
\crossref{https://doi.org/10.1134/S1560354714060070}
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\zmath{https://zbmath.org/?q=an:06507827}
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Linking options:
https://www.mathnet.ru/eng/rcd192
https://www.mathnet.ru/eng/rcd/v19/i6/p694
This publication is cited in the following 16 articles:
Elizaveta Artemova, Evgeny Vetchanin, “The motion of a circular foil in the field of a fixed point singularity: Integrability and asymptotic behavior”, Physics of Fluids, 36:2 (2024)
Elizaveta M. Artemova, Evgeny V. Vetchanin, “The Motion of an Unbalanced Circular Disk
in the Field of a Point Source”, Regul. Chaotic Dyn., 27:1 (2022), 24–42
Kpomahou Yelome Judicael Fernando, Hinvi L.A., Adechinan J.A., Miwadinou C.H., “Chaotic Dynamics of a Mixed Rayleigh-Lienard Oscillator Driven By Parametric Periodic Damping and External Excitations”, Complexity, 2021 (2021), 6631094
E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 604–617
Koiller J., “Getting Into the Vortex: on the Contributions of James Montaldi”, J. Geom. Mech., 12:3 (2020), 507–523
Ivan S. Mamaev, Ivan A. Bizyaev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov, “Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall”, Regul. Chaotic Dyn., 23:3 (2018), 257–272
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636
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
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
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Vortex Sources in a Deformation Flow”, Regul. Chaotic Dyn., 21:3 (2016), 367–376
N. A. Kudryashov, D. I. Sinelshchikov, “On the Integrability Conditions for a Family of Liénard-type Equations”, Regul. Chaotic Dyn., 21:5 (2016), 548–555
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
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions”, Regul. Chaotic Dyn., 20:4 (2015), 486–496
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