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
http://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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Record Number: | CaltechAUTHORS:20100901-112223214 | ||||||

Persistent URL: | http://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: | 01 May 2015 17:32 |

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