This article is cited in 12 papers

Special Issue: 200th birthday of Hermann von Helmholtz

Dynamics of a Circular Cylinder and Two Point Vortices in a Perfect Fluid

Sergey M. Ramodanov^a, Sergey V. Sokolov<sup>b

a</sup> Financial University under the Government of the Russian Federation, Department of Data Analysis and Machine Learning, 4th Veshnyakowski pr. 4, 125993 Moscow, Russia
^b Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudny, 141701 Moscow, Russia

Abstract: We study a mechanical system that consists of a 2D rigid body interacting dynamically with two point vortices in an unbounded volume of an incompressible, otherwise vortex-free, perfect fluid. The system has four degrees of freedom. The governing equations can be written in Hamiltonian form, are invariant under the action of the group $E(2)$ and thus, in addition to the Hamiltonian function, admit three integrals of motion. Under certain restrictions imposed on the system’s parameters these integrals are in involution, thus rendering the system integrable (its order can be reduced by three degrees of freedom) and allowing for an analytical analysis of the dynamics.

Keywords: point vortices, Hamiltonian systems, reduction.

MSC: 76M23, 34A05

Received: 05.08.2021
Accepted: 03.11.2021

Language: English

DOI: 10.1134/S156035472106006X

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