In Nambu mechanics, fundamental variables form an $N$-plet, whose time evolution is generated by $N-1$ Hamiltonians according to the Nambu equations. Combining the advantages of the two theories, we conjecture that [*there is a formulation whose master equation has a form of the Nambu equation or its generalization, where the Hamiltonians consist of the original one and the induced constraints.*]{}

Nambu mechanics is a generalization of the Hamiltonian dynamics proposed by Nambu forty years ago [@N]. In his formulation, the dynamics of an $N$-plet is given by the Nambu equation, which is defined by $N-1$ Hamiltonians and the Nambu bracket, a generalization of the Poisson bracket. The structure of Nambu mechanics is so elegant that many authors have investigated its application. However, the applications have been limited to particular systems such as constrained systems, superintegrable systems, and hydrodynamic systems, because Nambu systems (systems of Nambu mechanics) should have multiple Hamiltonians or conserved quantities. For example, researchers have studied how Nambu mechanics can be embedded into constrained Hamiltonian systems [@BF; @CK; @R; @MS; @KT; @KT2] or how constrained systems can be described in terms of Nambu mechanics [@LJ].

In this article, we show that the structure of Nambu mechanics is, in 