DIRECT HAMILTONIZATION — GENERALIZATION OF AN ALTERNATIVE HAMILTONIZATION

Abstract

A new procedure named direct Hamiltonization presents an alternative foundation to Analytical Mechanics, since in this formalism the Hamiltonian function can be obtained for all mechanical systems. The principal change proposed in this procedure is that the conjugate momenta cannot be defined a priori, but are established as a consequence of a canonical description of the mechanical system. The direct Hamiltonization is a generalization of the alternative one, where the usual Hamiltonization and momenta are recovered whenever they exist. Also this procedure assures the existence of a Hamiltonian function without any constraints for any mechanical system, therefore the usual quantization is always allowed. This procedure can be applied to non-Lagrangian, Nambu, nonholonomic and dynamical systems since there are no restrictions in this formalism as, for example, the number of equations of motion.