CaltechAUTHORS
  A Caltech Library Service

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

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. http://resolver.caltech.edu/CaltechAUTHORS:SHApof02

[img]
Preview
PDF
See Usage Policy.

215Kb
[img]
Preview
PDF - Erratum
See Usage Policy.

18Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:SHApof02

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.1445183 DOIUNSPECIFIED
http://pof.aip.org/resource/1/phfle6/v14/i3/p1214_s1PublisherUNSPECIFIED
http://dx.doi.org/10.1063/1.1511733 DOIUNSPECIFIED
http://pof.aip.org/resource/1/phfle6/v14/i11/p4099_s1PublisherUNSPECIFIED
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
Record Number:CaltechAUTHORS:SHApof02
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:SHApof02
Alternative URL:http://dx.doi.org/10.1063/1.1445183
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:26 Dec 2012 10:01

Repository Staff Only: item control page