Dynamics of two interacting circular cylinders in perfect fluid
Institute of Computer Science, Udmurt State University, Universitetskaya ul. 1, 426034 Izhevsk, Russian Federation, Russian Federation
Institute of Computer Science, Udmurt State University, 426034 Izhevsk
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.
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