Singular Lagrangians and the Faddeev-Jackiw Formalism in Classical Mechanics

Classical mechanical systems with internal constraints will be examined using the extended symplectic formalism of Faddeev-Jackiw. We will derive the generalized brackets of the theory and the corresponding equations of motion. The investigation will include the analysis of a gauge system, leading to the identification of associated gauge transformations. The obtained results will be compared with those obtained through the Dirac-Bergmann algorithm, as previously documented in the literature. The symplectic approach turns out to be simpler and efficient compared to the Dirac methods in its mathematical operations, and easy for computer implementation.