Direct Hamiltonization - The Generalization of the Two Fold Hamiltonization Procedure Maria Lewtchuk Espindola Universidade Federal da Para´ ıba, DM/CCEN 58051-970, Jo˜aoPessoa, PB, Brazil * 09/11/2009 Abstract A new procedure named direct Hamiltonization gives another founda- tions to Analytical Mechanics, since in this formalism of the Hamiltonian Mechanics the Hamiltonian function can be obtained for all mechanical systems. The principal change proposed in this procedure is that the con- jugate momenta cannot be defined a priori, but instead of this, they are determinate as a consequence of a canonical description of the mechan- ical system. As the direct Hamiltonization contains the alternative one, then the usual Hamiltonization and momenta is recovered while the en- velope solution is selected. Also this procedure assures the existence of a Hamiltonian function without any constraints for any mechanical system therefore the usual quantization is always allowed. Key words: Direct Hamiltonization; Alternative Hamiltonization; Hamiltonian Mechanics; Hamiltonian function; Generalized Momentum. MSC2010: 70A05;70H99. * mariia@mat.ufpb.br 1