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

Dynamics of a Circular Cylinder and Two Point Vortices in a Perfect Fluid We study a mechanical system that consists of a 2D rigid body interacting dynamicallywith 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 bewritten 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} andthus, in addition to the Hamiltonian function, admit three integrals of motion.Under certain restrictions imposed on the system’s parameters these integrals arein involution, thus rendering the system integrable (its order can be reduced bythree degrees of freedom) and allowing for an analytical analysis of the dynamics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/s156035472106006x
Publisher site
See Article on Publisher Site

Abstract

We study a mechanical system that consists of a 2D rigid body interacting dynamicallywith 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 bewritten 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} andthus, in addition to the Hamiltonian function, admit three integrals of motion.Under certain restrictions imposed on the system’s parameters these integrals arein involution, thus rendering the system integrable (its order can be reduced bythree degrees of freedom) and allowing for an analytical analysis of the dynamics.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Nov 1, 2021

Keywords: point vortices; Hamiltonian systems; reduction

References