  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.
