Routh’s procedure for non-Abelian symmetry groups.

We 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 analyze 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 quasivelocities. We discuss the reconstruction of solutions of the full Euler–Lagrange equations from those of the reduced equations. [ABSTRACT FROM AUTHOR]