Geodesic
Integrability of the Problem of the Motion of a Cylinder and a Vortex in an Ideal Fluid
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 20-23

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In this paper, we obtain a nonlinear Poisson structure and two first integrals in the problem of the plane motion of a circular cylinder and $N$ point vortices in an ideal fluid. This problem is a priori not Hamiltonian; specifically, in the case $N= 1$ (i.e., in the problem of the interaction of a cylinder with a vortex) it is integrable. 
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A. V. Borisov; I. S. Mamaev. Integrability of the Problem of the Motion of a Cylinder and a Vortex in an Ideal Fluid. Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 20-23. http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a2/