In this paper we consider the system of two 2D rigid circular
cylinders immersed in an unbounded volume of inviscid perfect fluid.
The circulations around the cylinders are assumed to be equal in
magnitude and opposite in sign. We also explore some special cases
of this system assuming that the cylinders move along the line
through their centers and the circulation around each cylinder is
zero. A similar system of two interacting spheres was originally
considered in the classical works of Carl and Vilhelm Bjerknes, H.
Lamb and N. E. Joukowski.
By making the radii of the cylinders infinitesimally small, we have
obtained a new mechanical system which consists of two regular point
vortices but with non-zero masses. The study of this system can be
reduced to the study of the motion of a particle subject to
potential and gyroscopic forces. A new integrable case is found. The
Hamiltonian equations of motion for this system have been
generalized to the case of an arbitrary number of mass vortices with
arbitrary intensities. Some first integrals have been obtained.
These equations expand upon the classical Kirchhoff equations of
motion for $n$ point vortices.