Dynamics of a circular cylinder interacting with point vortices

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

doi:10.3934/dcdsb.2005.5.35

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2005, Volume 5, Issue 1: 35-50. Doi: 10.3934/dcdsb.2005.5.35

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Dynamics of a circular cylinder interacting with point vortices

1.
Institute of Computer Science, 1, Universitetskaya str., 426034, Izhevsk
2.
Department of Theoretical Mechanics, Moscow State University, Vorobyevy Gory, 119899, Moscow

Received: August 31, 2003

Revised: November 30, 2003

Published: January 2005

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Abstract

The paper studies the system of a rigid body interacting dynamically with point vortices in a perfect fluid. For arbitrary value of vortex strengths and circulation around the cylinder the system is shown to be Hamiltonian (the corresponding Poisson bracket structure is rather complicated). We also reduced the number of degrees of freedom of the system by two using the reduction by symmetry technique and performed a thorough qualitative analysis of the integrable system of a cylinder interacting with one vortex.

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Mathematics Subject Classification: 37N10, 76B47.

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