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arXiv · 1802.01037

Vector Hamiltonians in Nambu mechanics

V. N. Dumachev
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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.

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V. N. Dumachev. 2018-02-03. Vector Hamiltonians in Nambu mechanics. https://arxiv.org/abs/1802.01037

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