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},
year = {2018},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2018_2_a3/}
}
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/
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