Motion of two circular cylinders in a perfect fluid

A planar analog of the Bjeknes problem of interaction of two spheres in a perfect fluid is considered. For the case of equal circulations around the cylinders, the equations of motion in the Poincare–Chetaev form are obtained, the integrals of motion are indicated. The problem is then reduced to a problem with two degrees of freedom. Most probably, this reduced problem is not integrable.