2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173344We present a picture of Lagrangean mechanics, free of some unnatural features (such as complete divergences). As a byproduct, a completely natural U(1)-bundle over the phase space appears. The correspondence between classical and quantum mechanics is very clear, e.g. no topological ambiguities remain. Contact geometry is the basic tool.LaTeX, 7 pages, 3 figures, mssymb.sty includedMathematical Physicstext