Routh's procedure for non-Abelian symmetry groups

Abstract

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 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 Phys

References in corpus (1)

• Reduction and reconstruction aspects of second-order dynamical systems with symmetry

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