2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59554Section 1 refines the theory of harmonic and potential maps. Section 2 defines a generalized Lorentz world-force law and shows that any PDEs system of order one generates such a law in suitable geometrical structure. In other words, the solutions of any PDEs system of order one are harmonic or potential maps, if we use semi-Riemann-Lagrange structures. Section 3 formulates open problems regarding the geometry of semi-Riemann manifolds $(J^1(T,M), S_1)$, $(J^2(T,M), S_2)$, and shows that the Lorentz-Udriste world-force law is equivalent to covariant Hamilton PDEs on $(J^1(T,M), S_1)$.14 pagesDynamical Systems31C12, 53C43, 58E20, 58J60text