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Nelin. Dinam., 2009, Volume 5, Number 3, Pages 319–343 (Mi nd96)  

Coupled motion of a rigid body and point vortices on a sphere

A. V. Borisov, I. S. Mamaev, S. M. Ramodanov

Institute of Computer Science

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 $S^2$ 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.

Full text: PDF file (429 kB)

Document Type: Article
UDC: 512.77 517.912
MSC: 76B47, 70Exx, 70Hxx
Received: 06.06.2009

Citation: A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Coupled motion of a rigid body and point vortices on a sphere”, Nelin. Dinam., 5:3 (2009), 319–343

Citation in format AMSBIB
\Bibitem{BorMamRam09}
\by A.~V.~Borisov, I.~S.~Mamaev, S.~M.~Ramodanov
\paper Coupled motion of a rigid body and point vortices on a sphere
\jour Nelin. Dinam.
\yr 2009
\vol 5
\issue 3
\pages 319--343
\mathnet{http://mi.mathnet.ru/nd96}


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