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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 23:44:17 +0000The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices
https://resolver.caltech.edu/CaltechAUTHORS:SHApof02
Authors: {'items': [{'id': 'Shashikanth-B-N', 'name': {'family': 'Shashikanth', 'given': 'Banavara N.'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Burdick-J-W', 'name': {'family': 'Burdick', 'given': 'Joel W.'}}, {'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott D.'}}]}
Year: 2002
DOI: 10.1063/1.1445183
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.https://authors.library.caltech.edu/records/nr58s-atj40Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape
https://resolver.caltech.edu/CaltechAUTHORS:20101005-085628821
Authors: {'items': [{'id': 'Shashikanth-B-N', 'name': {'family': 'Shashikanth', 'given': 'Banavara N.'}}, {'id': 'Sheshmani-A', 'name': {'family': 'Sheshmani', 'given': 'Artan'}}, {'id': 'Kelly-S-D', 'name': {'family': 'Kelly', 'given': 'Scott David'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}]}
Year: 2008
DOI: 10.1007/s00162-007-0065-y
We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.https://authors.library.caltech.edu/records/tgxfy-9t725