Marsden, Jerrold E. and Morrison, Philip J. (1984) Noncanonical Hamiltonian field theory and reduced MHD. In: Fluids and plasmas : geometry and dynamics. Contemporary Mathematics. No.28. American Mathematical Society , Providence, R.I, pp. 133-150. ISBN 0821850288. https://resolver.caltech.edu/CaltechAUTHORS:20100901-112223214
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Abstract
Aspects of noncanonical Hamiltonian field theory are reviewed. Many systems are Hamiltonian in the sense of possessing Poisson bracket structures, yet the equations are not in canonical form. A particular system of this type is considered, namely reduced magnetohydrodynamics (RMHD) which was derived for tokamak modelling. The notion of a lie Poisson bracket is reviewed; these are special Poisson brackets associated to Lie groups. The RMHD equations are shown to be Hamiltonian for brackets closely related to the Poisson bracket of a semi-direct product group. The process by which this bracket may be derived from a canonical Lagrangian description by reduction is described.
Item Type: | Book Section | ||||||
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Additional Information: | © 1984 American Mathematical Society. lResearch partially supported by DOE contract DE-AT03-82ER-12097. 2Research partially supported by DOE contract DE-FGOS-BOETS3088. | ||||||
Funders: |
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Series Name: | Contemporary Mathematics | ||||||
Issue or Number: | 28 | ||||||
Record Number: | CaltechAUTHORS:20100901-112223214 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100901-112223214 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 19756 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Ruth Sustaita | ||||||
Deposited On: | 01 Sep 2010 19:39 | ||||||
Last Modified: | 03 Oct 2019 02:01 |
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