Falling Motion of a circular cylinder interacting dynamically with $N$ point vortices

The dynamical behavior of a heavy circular cylinder and $N$ point vortices in an unbounded volume of ideal liquid is considered. The liquid is assumed to be irrotational and at rest at infinity. The circulation about the cylinder is different from zero. The governing equations are presented in Hamiltonian form. Integrals of motion are found. Allowable types of trajectories are discussed in the case $N = 1$. The stability of finding equilibrium solutions is investigated and some remarkable types of partial solutions of the system are presented. Poincaré sections of the system demonstrate chaotic behavior of dynamics, which indicates a non-integrability of the system.