Vector Hamiltonians in Nambu Mechanics

Abstract

We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in ℝ n can be represented as a generalized Nambu mechanics with n − 1 integral invariants. For the case when the phase flow in ℝ n has n − 3 or less first integrals, we introduce the Cartan concept of mechanics. As an example we give the fifth integral invariant of Euler top.