On the motion of a heavy rigid body in an ideal fluid with circulation
  Chaplygin's equations describing the planar motion of a rigid body in an unbounded volume of an ideal fluid involved in a circular flow around the body are considered. Hamiltonian structures, new integrable cases, and partial solutions are revealed, and their stability is examined. The problems of non-integrability of the equations of motion because of a chaotic behavior of the system are discussed. 
A. V. Borisov, I. S. Mamaev