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 ${\mathbb{R}}^n$ can be represented as a generalized Nambu mechanics with $n-1$ integral invariants. For the case when the phase flow in ${\mathbb{R}}^n$ 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.

6 pages