  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.
