Motion of Point Vortices and a Smooth Foil with Variable Mass Distribution in an Ideal Fluid

This paper considers the motion of an elliptic foil in the presence of point vortices. For the case of a vortex pair, a bifurcation analysis of the relative equilibria (a generalization of Föppl solutions) is carried out. These solutions correspond to the motion of the system on an invariant manifold on which the dynamics is governed by a system with $\frac{3}{2}$ degrees of freedom. Using a period advance Poincaré map, a numerical analysis of the dynamics on the invariant manifold is performed for the case where the center of mass of the system moves periodically in an impulse-like manner. The occurrence of new periodic, quasiperiodic and chaotic modes of motion is demonstrated.