Direct Hamiltonization - the Generalization of the Alternative Hamiltonization

A new procedure named direct Hamiltonization gives another foundations to Hamiltonian Analytical Mechanics, since in this formalism the Hamiltonian function can be obtained for any mechanical system. The main change proposed in this procedure is that the conjugate momenta cannot be defined a priori, but instead of this, they are determinate as a consequence of a canonical description of the mechanical system. As the direct Hamiltonization contains the alternative one, then the usual Hamiltonization and momenta is recovered while the envelope solution is selected. Also this procedure assures the existence of a Hamiltonian function without any constraints whatsoever mechanical system is considered, therefore the usual quantization is always allowed.