Motion of a circular cylinder and n point vortices in a perfect fluid

TL;DR

This paper explores the Hamiltonian dynamics of a circular cylinder interacting with point vortices in a perfect fluid, including symmetry reduction and analysis of integrable cases.

Contribution

It demonstrates the Hamiltonian structure for arbitrary vortex strengths and simplifies the system by symmetry reduction, providing a detailed qualitative analysis of the integrable case.

Findings

System is Hamiltonian for arbitrary vortex strengths.

Reduced degrees of freedom using symmetry techniques.

Analyzed the integrable system with one vortex.

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.