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


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 


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  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

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