Routh reduction and Cartan mechanics

In the present work a Cartan mechanics version for Routh reduction is considered, as an intermediate step toward Routh reduction in field theory. Motivation for this generalization comes from an scheme for integrable systems [12], used for understanding the occurrence of Toda field theories in so called Hamiltonian reduction of WZNW field theories [11]. As a way to accomplish with this intermediate aim, this article also contains a formulation of the Lagrangian Adler-Kostant-Symes systems discussed in [12] in terms of Routh reduction.