The Motion of Solid Bodies in Potential Flow With Circulation: A Geometric Outlook

The motion of a circular body in 2D potential flow is studied using symplectic reduction. The equations of motion are obtained starting from a kinetic-energy type system on a space of embeddings and reducing by the particle relabelling symmetry group and the special Euclidian group. In the process, we give a geometric interpretation for the Kutta-Joukowski lift force in terms of the curvature of a connection on the original phase space.