Castrillón López, MarcoNielsen, F.Barbaresco, F.2023-09-112023-09-112023-08-0110.1007/978-3-031-38299-4_26https://hdl.handle.net/20.500.14352/87663This note collects a series of results into a single formulation. Namely, it is proved that, when reduction is performed to a symmetric Lagrangian, the reduced variational equations can be split into two parts, one of them is exactly the Noether theorem. Conservation laws enter into reduction as part of the new variational equations. We give a short description of this situation in the case of evolution of circles in the plane.engbook partembargoed access512Conservation lawReductionSymmetryÁlgebra1201 Álgebra