Vector hamiltonians in Nambu mechanics

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 invariant. 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. We give an example the fifth integral invariant of Euler top.