On Generalized Nambu Mechanics

Details On Generalized Nambu Mechanics On Generalized Nambu Mechanics

1996-09-21

arxiv.org/abs/chao-dyn/9609015v1

Nonlinear Sciences

Chaotic Dynamics

13 Pages, ReVTeX

Scientific paper

A geometric formulation of a generalization of Nambu mechanics is proposed. This formulation is carried out, wherever possible, in analogy with that of Hamiltonian systems. In this formulation, a strictly nondegenerate constant 3-form is attached to a 3n-dimensional phase space. Time evolution is governed by two Nambu functions. A Poisson bracket of 2-forms is introduced, which provides a Lie-algebra structure on the space of 2-forms. This formalism is shown to provide a suitable framework for the descrip tion of non-integrable fluid flow such as the Arter flow, the Chandrashekhar flow and of the coupled rigid bodies.

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