Mathematical Notes

, Volume 75, Issue 1–2, pp 19–22 | Cite as

Integrability of the Problem of the Motion of a Cylinder and a Vortex in an Ideal Fluid

  • A. V. Borisov
  • I. S. Mamaev
Article

Abstract

In this paper, we obtain a nonlinear Poisson structure and two first integrals in the problem of the plane motion of a circular cylinder and n point vortices in an ideal fluid. This problem is a priori not Hamiltonian; specifically, in the case n= 1 (i.e., in the problem of the interaction of a cylinder with a vortex) it is integrable.

ideal fluid motion of a circular cylinder in an ideal fluid point vortices Poisson structure Poisson bracket Casimir function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    S. M. Ramodanov, “Motion of a Circular Cylinder and a Vortex in an Ideal Fluid,” Reg. & Chaot. Dyn., 6 (2001), no. 1, 33–38.Google Scholar
  2. 2.
    B. N. Shashikanth, J. E. Marsden, and J. W. Burdick, and S. D. Kelly, “The Hamiltonian structure of a 2D rigid circular cylinder interacting dynamically with N point vortices,” Phys. of Fluids, 14 (2002), 1214–1227.Google Scholar
  3. 3.
    A. V. Borisov and I. S. Mamaev, Poisson Structures and Lie Algebras in Hamiltonian Mechanics [in Russian], RKhD, Izhevsk, 1999.Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • A. V. Borisov
    • 1
  • I. S. Mamaev
    • 2
  1. 1.Institute of Computer StudiesIzhevsk
  2. 2.Udmurt State UniversityRusssia

Personalised recommendations