The motion of solid bodies in potential flow with circulation: A geometric outlook

Vankerschaver, J., E. Kanso and J. E. Marsden

Proc. of 2008 Dynamic Systems and Control Conference, (2008), 1-8

Abstract:

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.