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 
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/
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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.

[1] Ramodanov S. M., “Motion of a Circular Cylinder and a Vortex in an Ideal Fluid”, Reg. Chaot. Dyn., 6:1 (2001), 33–38 | DOI | MR | Zbl

[2] Shashikanth B. N., Marsden J. E., Burdick J. W., Kelly S. D., “The Hamiltonian structure of a 2D rigid circular cylinder interacting dynamically with $N$ point vortices”, Phys. of Fluids, 14 (2002), 1214–1227 | DOI | MR | Zbl

[3] Borisov A. V., Mamaev I. S., Puassonovy struktury i algebry Li v gamiltonovoi mekhanike, RKhD, Izhevsk, 1999 | MR