general, hidden in systems of Hamiltonian dynamics. That is, Hamiltonian systems can be described by Nambu mechanics or its generalization by means of a change of variables from canonical doublets to multiplets. Our formulation can be generalized to many degrees of freedom systems, and the associated partition functions are given. We also apply our formulation to systems with first class constraints. Our approach can be regarded as a complementary one to the previous works [@BF; @CK; @R; @MS; @KT; @KT2; @LJ].

The outline of this article is as follows. In the next section, we give a formulation of Hamiltonian systems using Nambu mechanics and its generalizations. As an application, Hamiltonian systems with first class constraints are also formulated as Nambu systems in Sect. 3. In the last section, we give conclusions and discussions on the direction of future work. In Appendix A, we derive the Nambu equation from the least action principle. In Appendix B, we show that a Nambu system of an $N$-plet can be described by Nambu mechanics with an $N+r$-plet ($r\ge1$).

Nambu systems hidden in Hamiltonian systems {#Nambu systems hidden in Hamiltonian systems}
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Review {#Review}
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We begin with a brief review of Hamiltonian systems and 