understand the important properties of the system such as conservation laws and form of interactions, and can also calculate physical quantities in a systematic way [@W1; @W2].

Therefore, it is interesting to explore the general features of formulations including redundant degrees of freedom. Here we base this on a principle (or brief) that [*physics should be independent of the choice of variables to describe it*]{}, and make an attempt to formulate Hamiltonian systems (systems of Hamiltonian dynamics) in terms of new sets of variables including redundant ones. What kind of dynamics describes the time evolution of the new variables?

Our strategy and conjecture are as follows. Consider a Hamiltonian system described by a canonical doublet $(q, p)$. Take $N(\ge 3)$ variables $(x_1, \cdots, x_{N})$ that are functions of the canonical doublet, and deal with them as fundamental variables to describe the system. If they contain redundant variables, constraints between some variables must be induced. To handle the constraints, Dirac formalism [@D1; @D2] provides a helpful perspective, where constraints with Lagrange multipliers are added to the original Hamiltonian. The induced constraints play a similar role to the Hamiltonian. As for the dynamics of $N$ variables, Nambu mechanics [@N] is quite suggestive. 