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Russia Izhevsk
Section  Mathematics 
Title  Falling motion of a circular cylinder interacting dynamically with a vortex pair in a perfect fluid 
Author(s)  Sokolov S.V.^{a} 
Affiliations  Udmurt State University^{a} 
Abstract  We consider a system which consists of a circular cylinder subject to gravity interacting with $N$ vortices in a perfect fluid. Generically, the circulation about the cylinder is different from zero. The governing equations are Hamiltonian and admit evident integrals of motion: the horizontal and vertical components of the momentum; the latter is obviously nonautonomous. We then focus on the study of a configuration of the Foppl type: a falling cylinder is accompanied with a vortex pair ($N=2$). Now the circulation about the cylinder is assumed to be zero and the governing equations are considered on a certain invariant manifold. It is shown that, unlike the Foppl configuration, the vortices cannot be in a relative equilibrium. A restricted problem is considered: the cylinder is assumed to be sufficiently massive and thus its falling motion is not affected by the vortices. Both restricted and general problems are studied numerically and remarkable qualitative similarity between the problems is outlined: in most cases, the vortex pair and the cylinder are shown to exhibit scattering. 
Keywords  point vortices, vortex pair, Hamiltonian systems, reduction 
UDC  512.77, 517.912 
MSC  70Hxx, 70G65 
DOI  10.20537/vm140206 
Received  19 May 2014 
Language  Russian 
Citation  Sokolov S.V. Falling motion of a circular cylinder interacting dynamically with a vortex pair in a perfect fluid, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 2, pp. 8699. 
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