Geodesic
Vector hamiltonians in Nambu mechanics
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 32-38

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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.
Keywords: first integrals, integral invariants, splitting cohomology. 
@article{IVM_2018_2_a3,
     author = {V. N. Dumachev},
     title = {Vector hamiltonians in {Nambu} mechanics},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {32--38},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_2_a3/}
}
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V. N. Dumachev. Vector hamiltonians in Nambu mechanics. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 32-38. http://geodesic.mathdoc.fr/item/IVM_2018_2_a3/