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
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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.|
|Subject Keywords:||UNDERWATER VEHICLE; DEFORMABLE BODY; FLOW-FIELD; STABILITY; MOTION; EQUATIONS; VORTEX|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||12 May 2008|
|Last Modified:||26 Dec 2012 10:01|
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