This article is cited in 2 papers

Falling motion of a circular cylinder interacting dynamically with a point vortex

Sergey V. Sokolov, Sergey M. Ramodanov

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

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.

UDC: 512.77, 517.912

MSC: 70Hxx, 70G65

Received: 11.08.2012
Revised: 14.09.2012