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February  2005, 5(1): 35-50. doi: 10.3934/dcdsb.2005.5.35

Dynamics of a circular cylinder interacting with point vortices

A. V. Borisov 1, , I. S. Mamaev 1, and  S. M. Ramodanov 2,

1. 

Institute of Computer Science, 1, Universitetskaya str., 426034, Izhevsk, Russian Federation, Russian Federation
2. 

Department of Theoretical Mechanics, Moscow State University, Vorobyevy Gory, 119899, Moscow, Russian Federation

Received  September 2003 Revised  December 2003 Published  November 2004

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.
Keywords: Point vortex, integrable system, Hamiltonian system, qualitative and topological analysis., Poisson bracket structure, first integral, advection.
Mathematics Subject Classification: 37N10, 76B4.
Citation: A. V. Borisov, I. S. Mamaev, S. M. Ramodanov. Dynamics of a circular cylinder interacting with point vortices. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : 35-50. doi: 10.3934/dcdsb.2005.5.35
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