Muñoz Masqué, JaimePozo Coronado, Luis Miguel2023-06-202023-06-2019980305-447010.1088/0305-4470/31/29/014https://hdl.handle.net/20.500.14352/57772A projection is defined such that a second-order Lagrangian density factors through this projection module contact forms if and only if it is parameter invariant. In this way, a geometric interpretation of the parameter invariance conditions is obtained. The above projection is then used to prove the strict factorization of the Poincare-Cartan form attached to a parameter-invariant variational problem thus leading us to state the Hamilton-Cartan formalism, the complete description of symmetries and regularity for such problems. The case of the squared curvature Lagrangian in the plane is analysed especially.engjournal articlehttp://iopscience.iop.org/0305-4470/31/29/014/pdf/0305-4470_31_29_014.pdfhttp://iopscience.iop.orgrestricted access514.7Second-order Lagrangian densityParameter invariancePoincare-Cartan formSquared curvature LagrangianGeometría diferencial1204.04 Geometría Diferencial