2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156517We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum in velocity phase space. We present a new method of analysis based on the use of quasi-velocities. We discuss the reconstruction of solutions of the full Euler-Lagrange equations from those of the reduced equations.30 pages, to appear in J Math PhysDifferential GeometryMathematical Physics34A26; 37J15; 53C05; 70H03text