Applications of Nambu Mechanics to Systems of Hydrodynamical Type II

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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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  -