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

Authors
  • Ramodanov, Sergey M.1
  • Sokolov, Sergey V.2
  • 1 Financial University under the Government of the Russian Federation, Department of Data Analysis and Machine Learning, 4th Veshnyakowski pr. 4, Moscow, 125993, Russia , Moscow (Russia)
  • 2 Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudny, Moscow, 141701, Russia , Moscow (Russia)
Type
Published Article
Journal
Regular and Chaotic Dynamics
Publisher
Pleiades Publishing
Publication Date
Nov 01, 2021
Volume
26
Issue
6
Pages
675–691
Identifiers
DOI: 10.1134/S156035472106006X
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E(2)$$\end{document} 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.

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