Journal of Nonlinear Mathematical Physics

Volume 11, Issue 2, May 2004, Pages 223 - 232

Applications of Nambu Mechanics to Systems of Hydrodynamical Type II

Authors
Partha Guha
Corresponding Author
Partha Guha
Received 12 September 2003, Accepted 15 January 2004, Available Online 1 May 2004.
DOI
10.2991/jnmp.2004.11.2.7How to use a DOI?
Abstract

In this paper we further investigate some applications of Nambu mechanics in hydrdynamical systems. Using the Euler equations for a rotating rigid body Névir and Blender [J. Phys. A 26 (1993), L1189­L1193] had demonstrated the connection btween Nambu mechanics and noncanonical Hamiltonian mechanics. Nambu mechanics is extended to incompressible ideal hydrodynamical fields using energy and helicity in three dimensional (enstrophy in two dimensional). In this paper we discuss the Lax representation of systems of Névir-Blender type. We also formulate the three dimesional Euler equations of incompressible fluid in terms of Nambu-Poisson geometry. We discuss their Lax representation. We also briefly discuss the Lax representation of ideal incompressible magnetohydrodynamics equations.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - 2
Pages
223 - 232
Publication Date
2004/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2004.11.2.7How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Partha Guha
PY  - 2004
DA  - 2004/05/01
TI  - Applications of Nambu Mechanics to Systems of Hydrodynamical Type II
JO  - Journal of Nonlinear Mathematical Physics
SP  - 223
EP  - 232
VL  - 11
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.2.7
DO  - 10.2991/jnmp.2004.11.2.7
ID  - Guha2004
ER  -