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INTERNATIONAL JOURNAL OF MODERN PHYSICS A, vol.21, no.3, pp.575-588, 2006 (SCI-Expanded)
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.