Generalization of Nambu's mechanics

We look for a generalization of the mechanics of Hamilton and Nambu. We have found the equations of motion of a classical physical system ofS basic dynamic variables characterized byS – 1 constants of motion and by a function of the dynamical variables and the time whose value also remains constant during the evolution of the system. The numberS may be even or odd. We find that any locally invertible transformations are canonical transformations. We show that the equations of motion obtained can be put in a form similar to Nambu's equations by means of a time transformation. We study the relationship of the present formalism to Hamiltonian mechanics and consider an extension of the formalism to field theory.