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Published March 2002 | Erratum
Journal Article Open

The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices

Abstract

This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the equations of motion for this system and show that, in particular, if the vortex strengths sum to zero and the rigid-body has a circular shape, the equations are Hamiltonian with respect to a Poisson bracket structure that is the sum of the rigid body Lie–Poisson bracket on Se(2)*, the dual of the Lie algebra of the Euclidean group on the plane, and the canonical Poisson bracket for the dynamics of N point vortices in an unbounded plane. We then use this Hamiltonian structure to study the linear and nonlinear stability of the moving Föppl equilibrium solutions using the energy-Casimir method.

Additional Information

© 2002 American Institute of Physics. Received 8 May 2001; accepted 27 November 2001. B.N.S. would like to thank Richard Murray for the support of a postdoctoral fellowship and for the encouragement to work on this problem while at CDS, Caltech.

Errata

1.Erratum: "The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices" [Phys. Fluids 14, 1214 (2002)] Banavara N. Shashikanth et al.

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Erratum - PhysFluids_14_4099.pdf

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August 21, 2023
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