  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.
