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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.Comment: 46 pages, comments are welcome. Version 2 contains an additional
section concerning reduced equations of motion in quasicoordinate
The Theory of Caustics and Wavefront Singularities with Physical Applications
This is intended as an introduction to and review of the work of V, Arnold
and his collaborators on the theory of Lagrangian and Legendrian submanifolds
and their associated maps. The theory is illustrated by applications to
Hamilton-Jacobi theory and the eikonal equation, with an emphasis on null
surfaces and wavefronts and their associated caustics and singularities.Comment: Figs. not include
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