Hamiltonian dynamics of N vortices in concentric annular region

Abstract

The problem of N vortex dynamics in annular domain is considered. The region is canonical one and allows by conformal mapping apply results to an arbitrary position of two cylinders in the plane. Using previous solution, obtained by the authors in terms of the q-elementary functions [1] we now concentrate on the Hamiltonian formulation of the problem. The integrability of the problem of two vortices in the annular domain according to Liouville has been proved by using canonical transformations. Different motion characteristics depending on initial conditions are studied.