Integrability of the problem of motion of a cylinder and a point vortex   in a perfect fluid
  Motion of a cylinder dynamically interacting with n point vortices in a perfect fluid is considered. A nonliniear Poisson structure and two integrals of motion are found. The equations of motion a priori are not Hamiltonian. For n=1, the problem is integrable. 
A.V. Borisov, I.S. Mamaev