Routh's procedure for non-Abelian symmetry groups

Details Routh's procedure for non-Abelian symmetry groups Routh's procedure for non-Abelian symmetry groups

2008-02-05

arxiv.org/abs/0802.0528v1

J Math Phys (2008) 49, 032901.

Mathematics

Differential Geometry

30 pages, to appear in J Math Phys

Scientific paper

10.1063/1.2885077

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.

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