Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Download PDF
17 pages

Loading next page...
 
/lp/springer-journals/dynamics-of-a-circular-cylinder-and-two-point-vortices-in-a-perfect-Rwcc40YGMT
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 Dynamics – Springer Journals

Published: Nov 1, 2021

Keywords: point vortices; Hamiltonian systems; reduction

References

  • Dynamics of a Pair of Point Vortices and a Foil with Parametric Excitation in an Ideal Fluid
    Bizyaev, I. A.; Mamaev, I. S.
  • Lie Algebras in Vortex Dynamics and Celestial Mechanics: 4
    Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S.
  • On the Stability of a System of Two Identical Point Vortices and a Cylinder
    Borisov, A. V.; Kurakin, L. G.
  • An Integrability of the Problem on Motion of Cylinder and Vortex in the Ideal Fluid
    Borisov, A. V.; Mamaev, I. S.
  • On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation
    Borisov, A. V.; Mamaev, I. S.
  • Dynamics of a Circular Cylinder Interacting with Point Vortices
    Borisov, A. V.; Mamaev, I. S.; Ramodanov, S. M.
  • Self-Propulsion of a Smooth Body in a Viscous Fluid under Periodic Oscillations of a Rotor and Circulation
    Borisov, A. V.; Mamaev, I. S.; Vetchanin, E. V.
  • Bifurcation Analysis of a Problem on the Motion of a Cylinder and a Point Vortex in an Ideal Fluid
    Borisov, A. V.; Ryabov, P. E.; Sokolov, S. V
  • Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces: 1
    Borisov, A. V.; Vetchanin, E. V.; Mamaev, I. S.
  • On the Action of a Plane-Parallel Air Flow upon a Cylindrical Wing Moving within It
    Chaplygin, S. A.
  • Generalised Hamiltonian Dynamics
    Dirac, P. A. M.
  • Chaotic Capture of Vortices by a Moving Body: 1. The Single Point Vortex Case
    Kadtke, J. B.; Novikov, E. A.
  • Mechanics, Dynamics, and Control of a Single-Input Aquatic Vehicle With Variable Coefficient of Lift
    Kelly, S. D.; Hukkeri, R. B.
  • Stability of a Coupled Body-Vortex System
    Kanso, E.; Oskouei, B. Gh.
  • The Dynamics of Point Vortices Inside and Outside a Circular Domain
    Kilin, A. A.; Borisov, A. V.; Mamaev, I. S.; Borisov, A. V.; Mamaev, I. S.; Sokolovskiy, M. A.
  • On a Heavy Cylindrical Body Falling in a Fluid
    Kozlov, V. V.
  • Dynamics of an Unbalanced Circular Foil and Point Vortices in an Ideal Fluid
    Mamaev, I. S.; Bizyaev, I. A.
  • Falling Cards and Flapping Flags: Understanding Fluid–Solid Interactions Using an Unsteady Point Vortex Model
    Michelin, S.; Llewellyn Smith, S. G.
  • Motion of a Circular Cylinder and a Vortex in an Ideal Fluid
    Ramodanov, S. M.
  • On the Influence of Circulation on the Behavior of a Rigid Body Falling in a Fluid
    Ramodanov, S. M.
  • Motion of a Circular Cylinder and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} Point Vortices in a Perfect Fluid
    Ramodanov, S. M.
  • Phase Topology of Two Vortices of Identical Intensities in a Bose—Einstein Condensate
    Ryabov, P. E.; Sokolov, S. V.
  • Poisson Brackets for the Dynamically Interacting System of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}D Rigid Cylinder and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} Point Vortices: The Case of Arbitrary Smooth Cylinder Shapes
    Shashikanth, B. N.
  • Symmetric Pairs of Point Vortices Interacting with a Neutrally Buoyant Two-Dimensional Circular Cylinder
    Shashikanth, B. N.
  • The Hamiltonian Structure of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}D Rigid Circular Cylinder Interacting Dynamically with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} Point Vortices
    Shashikanth, B. N.; Marsden, J. E.; Burdick, J. W.; Kelly, S. D.
  • Falling Motion of a Circular Cylinder Interacting Dynamically with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} Point Vortices
    Sokolov, S. V.
  • Falling Motion of a Circular Cylinder Interacting Dynamically with a Vortex Pair in a Perfect Fluid
    Sokolov, S. V.
  • Scattering of the Point Vortex by a Falling Circular Cylinder
    Sokolov, S. V.; Koltsov, I. S.
  • Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex
    Sokolov, S. V.; Ramodanov, S. M.
  • Bifurcation Analysis of the Dynamics of Two Vortices in a Bose–Einstein Condensate. The Case of Intensities of Opposite Signs
    Sokolov, S. V.; Ryabov, P. E.
  • Bifurcation Diagram of the Two Vortices in a Bose – Einstein Condensate with Intensities of the Same Signs
    Sokolov, S. V.; Ryabov, P. E.