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2013
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# Sergei Sokolov

Universitetskaya 1, Izhevsk, 426034 Russia
Institute of Computer Science, Udmurt State University

## Publications:

 Sokolov S. V. Falling motion of a circular cylinder interacting dynamically with $N$ point vortices 2014, Vol. 10, No. 1, pp.  59-72 Abstract 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. Poincar´e sections of the system demonstrate chaotic behavior of dynamics, which indicates a non-integrability of the system. Keywords: point vortices, Hamiltonian systems, reduction, stability of equilibrium solutions Citation: Sokolov S. V.,  Falling motion of a circular cylinder interacting dynamically with $N$ point vortices, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 1, pp.  59-72 DOI:10.20537/nd1401005
 Sokolov S. V., Ramodanov S. M. Falling motion of a circular cylinder interacting dynamically with a point vortex 2012, Vol. 8, No. 3, pp.  617-628 Abstract We consider a system which consists of a heavy circular cylinder and a point vortex in an unbounded volume of ideal liquid. 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 Hamiltonian and admit an evident integral of motion — the horizontal component of the momentum. Using the integral we reduce the order and thereby obtain a system with two degrees of freedom. Most remarkable types of partial solutions of the system are presented and stability of equilibrium solutions is investigated. Keywords: point vortices, Hamiltonian systems, reduction, stability of equilibrium solutions Citation: Sokolov S. V., Ramodanov S. M.,  Falling motion of a circular cylinder interacting dynamically with a point vortex, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  617-628 DOI:10.20537/nd1203014