2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184578The properties of Lagrangians affine in velocities are analyzed in a geometric way. These systems are necessarily singular and exhibit, in general, gauge invariance. The analysis of constraint functions and gauge symmetry leads us to a complete classification of such Lagrangians.AMSTeX, 22 pagesMathematical PhysicsHigh Energy Physics - Theory70H45, 37J15, 70G45text