Abstract:
The paper is concerned with a class of problems which involves the dynamical interaction of a rigid body with point vortices on the surface of a two-dimensional sphere. The general approach to the 2D hydrodynamics is further developed. The problem of motion of a dynamically symmetric circular body interacting with a single vortex is shown to be integrable. Mass vortices on S2 are introduced and the related issues (such as equations of motion, integrability, partial solutions, etc.) are discussed. This paper is a natural progression of the author’s previous research on interaction of rigid bodies and point vortices in a plane.
Keywords:
hydrodynamics on a sphere, coupled body-vortex system, mass vortex, equations of motion, integrability.
Citation:
A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface”, Regul. Chaotic Dyn., 15:4-5 (2010), 440–461
\Bibitem{BorMamRam10}
\by A. V. Borisov, I. S. Mamaev, S. M. Ramodanov
\paper Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 4-5
\pages 440--461
\mathnet{http://mi.mathnet.ru/rcd509}
\crossref{https://doi.org/10.1134/S1560354710040040}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2679758}
\zmath{https://zbmath.org/?q=an:1258.76050}
Linking options:
https://www.mathnet.ru/eng/rcd509
https://www.mathnet.ru/eng/rcd/v15/i4/p440
This publication is cited in the following 8 articles:
Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair Koiller, “On the Interplay Between Vortices and Harmonic Flows: Hodge Decomposition of Euler’s Equations in 2d”, Regul. Chaotic Dyn., 29:2 (2024), 241–303
Clodoaldo Grotta-Ragazzo, “Vortex on Surfaces and Brownian Motion in Higher Dimensions: Special Metrics”, J Nonlinear Sci, 34:2 (2024)
Mamaev I.S., Bizyaev I.A., “Dynamics of An Unbalanced Circular Foil and Point Vortices in An Ideal Fluid”, Phys. Fluids, 33:8 (2021), 087119
Krishnamurthy V.S., “The Vorticity Equation on a Rotating Sphere and the Shallow Fluid Approximation”, Discret. Contin. Dyn. Syst., 39:11 (2019), 6261–6276
Clodoaldo Grotta Ragazzo, Humberto Henrique de Barros Viglioni, “Hydrodynamic Vortex on Surfaces”, J Nonlinear Sci, 27:5 (2017), 1609
C. Grotta Ragazzo, “The motion of a vortex on a closed surface of constant negative curvature”, Proc. R. Soc. A., 473:2206 (2017), 20170447
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
A San Miguel, “Numerical description of the motion of a point vortex pair on ovaloids”, J. Phys. A: Math. Theor., 46:11 (2013), 115502
Citation in format AMSBIB
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