Lagrange-Poincare field equations

TL;DR

This paper extends Lagrange-Poincare equations to a field theory setting, establishing a variational principle, integrability conditions, and applications across physics and image processing.

Contribution

It introduces a field theoretic formulation of Lagrange-Poincare equations with a new integrability condition and demonstrates diverse applications.

Findings

Formulated Lagrange-Poincare equations in a field context

Established an integrability/reconstruction condition

Applied theory to physics and image analysis problems

Abstract

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.