Nambu brackets with constraint functionals

Abstract

If a Hamiltonian dynamical system with $n$ degrees of freedom admits $m$ constants of motion more than $2n-1$, then there exist some functional relations between the constants of motion. Among these relations the number of functionally independent ones are $s=m-(2n-1)$. It is shown that for such a system in which the constants of motion constitute a polynomial algebra closing in Poisson bracket, the Nambu brackets can be written in terms of these $s$ constraint functionals. The exemplification is very rich and several of them are analyzed in the text.

arXiv comment15 pages

References in corpus (6)

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Cited by in corpus (1)

• Algebraic derivation of the Energy Eigenvalues for the quantum oscillator defined on the Sphere and the Hyperbolic plane