Gauge transformations for higher-order Lagrangians

Noether's symmetry transformations for higher-order Lagrangians are studied. A characterization of these transformations is presented, which is useful for finding gauge transformations for higher-order singular Lagrangians. The case of second-order Lagrangians is studied in detail. Some examples that illustrate our results are given; in particular, for the Lagrangian of a relativistic particle with curvature, Lagrangian gauge transformations are obtained, though there are not Hamiltonian gauge generators for them.