Routh reduction for first-order field theories

Abstract

We present a reduction theory for first order Lagrangian field theories which takes into account the conservation of momenta. The relation between the solutions of the original problem with a prescribed value of the momentum and the solutions of the reduced problem is established. An illustrative example is discussed in detail.

arXiv commentv2: a few references added, some typos corrected

References in corpus (8)

• Geometry of Lagrangian First-order Classical Field Theories
• Lagrange-Poincare field equations
• Routhian reduction for quasi-invariant Lagrangians
• Reduction of polysymplectic manifolds
• Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations
• Remarks on multisymplectic reduction
• Routh reduction and Cartan mechanics
• Implicit Lagrange-Routh Equations and Dirac Reduction

Cited by in corpus (2)

• A Hamiltonian formalism for general variational problems, with applications to first order gravity with basis
• Cotangent bundle reduction and Routh reduction for polysymplectic manifolds