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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:29:59 +0000The Hamiltonian structure of the BBGKY hierarchy equations
https://resolver.caltech.edu/CaltechAUTHORS:20100902-100636174
Authors: {'items': [{'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Morrison-P-J', 'name': {'family': 'Morrison', 'given': 'Philip J.'}}, {'id': 'Weinstein-Alan-J-Math', 'name': {'family': 'Weinstein', 'given': 'Alan J.'}}]}
Year: 1984
The BBGKY hierarchy equations for the evolution of the i-point functions of a plasma with electrostatic interactions are shown to be Hamiltonian. The Poisson brackets are Lie-Poisson brackets on the dual of a Lie algebra. This algrebra is constructed from the algebra of n-point functions under Poisson bracket and the filtration obtained by considering subspaces of i-point functions, 1 ≤ i ≤ n.https://authors.library.caltech.edu/records/5wgjf-ra209Reduction and Hamiltonian structures on duals of semidirect product Lie algebras
https://resolver.caltech.edu/CaltechAUTHORS:20100908-070424350
Authors: {'items': [{'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Ratiu-T-S', 'name': {'family': 'Ratiu', 'given': 'Tudor'}, 'orcid': '0000-0003-1972-5768'}, {'id': 'Weinstein-Alan-J-Math', 'name': {'family': 'Weinstein', 'given': 'Alan J.'}}]}
Year: 1984
With the heavy top and compressible flow as guiding examples, this paper discusses the Hamiltonian structure of systems on duals of semidirect product Lie algebras by reduction from Lagrangian to Eulerian coordinates. Special emphasis is placed on the left-right duality which brings out the dual role of the spatial and body (i.e. Eulerian and convective) descriptions. For example, the heavy top in spatial coordinates has a Lie-Poisson structure on the dual of a semidirect product Lie algebra in which the moment of inertia is a dynamic variable. For compressible fluids in the convective picture, the metric tensor similarly becomes a dynamic variable. Relationships to the existing literature are given.https://authors.library.caltech.edu/records/vq5zx-0e540Stability of rigid body motion using the Energy-Casimir method
https://resolver.caltech.edu/CaltechAUTHORS:20100812-150925524
Authors: {'items': [{'id': 'Holm-D-D', 'name': {'family': 'Holm', 'given': 'Darryl'}}, {'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold'}}, {'id': 'Ratiu-T-S', 'name': {'family': 'Ratiu', 'given': 'T.'}, 'orcid': '0000-0003-1972-5768'}, {'id': 'Weinstein-Alan-J-Math', 'name': {'family': 'Weinstein', 'given': 'Alan J.'}}]}
Year: 1984
The Energy-Casimir method, due to Newcomb, Arnold and others is illustrated by application to the motion of a free rigid body and the heavy top.https://authors.library.caltech.edu/records/rh3q2-ps618Some Comments on the History, Theory, and Applications of Symplectic Reduction
https://resolver.caltech.edu/CaltechAUTHORS:20100913-083049249
Authors: {'items': [{'id': 'Marsden-J-E', 'name': {'family': 'Marsden', 'given': 'Jerrold E.'}}, {'id': 'Weinstein-Alan-J-Math', 'name': {'family': 'Weinstein', 'given': 'Alan J.'}}]}
Year: 2001
DOI: 10.1007/978-3-0348-8364-1_1
In this Preface, we make some brief remarks about the history, theory and applications of symplectic reduction. We concentrate on developments surrounding our paper Marsden
and Weinstein [1974] and the closely related work of Meyer [1973], so the reader may find some important references omitted. This is inevitable in a subject that has grown so large and has penetrated so deeply both pure and applied mathematics, as well as into engineering and theoretical physics.https://authors.library.caltech.edu/records/j756t-ghn45