Shashikanth, Banavara N. and Marsden, Jerrold E. and Burdick, Joel W. and Kelly, Scott D. (2002) The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices. Physics of Fluids, 14 (3). pp. 1214-1227. ISSN 1070-6631. https://resolver.caltech.edu/CaltechAUTHORS:SHApof02
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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.
Item Type: | Article | |||||||||||||||||||||
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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. | |||||||||||||||||||||
Subject Keywords: | UNDERWATER VEHICLE; DEFORMABLE BODY; FLOW-FIELD; STABILITY; MOTION; EQUATIONS; VORTEX | |||||||||||||||||||||
Issue or Number: | 3 | |||||||||||||||||||||
Record Number: | CaltechAUTHORS:SHApof02 | |||||||||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:SHApof02 | |||||||||||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||||||||
ID Code: | 10489 | |||||||||||||||||||||
Collection: | CaltechAUTHORS | |||||||||||||||||||||
Deposited By: | Tony Diaz | |||||||||||||||||||||
Deposited On: | 12 May 2008 | |||||||||||||||||||||
Last Modified: | 03 Oct 2019 00:10 |
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