Routh reduction and Cartan mechanics

Abstract

In the present work a Cartan mechanics version for Routh reduction is considered, as an intermediate step towards Routh reduction in field theory. Motivation for this generalization comes from a scheme for integrable systems (Fehér and Gábor, 2002), used for understanding the occurrence of Toda field theories in so called Hamiltonian reduction of WZNW field theories (Fehér et al., 1992). As a way to accomplish with this intermediate aim, this article also contains a formulation of the Lagrangian Adler–Kostant–Symes systems discussed in Fehér and Gábor (2002) in terms of Routh reduction.