Euler-Poincaré reduction for discrete field theories

DOI10.1063/1.2712419zbMath1137.70367arXivmath-ph/0606033OpenAlexW3100541481MaRDI QIDQ3442243

Joris Vankerschaver

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0606033

Mathematics Subject Classification ID

Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05)

Related Items (15)

Remarks on multisymplectic reduction ⋮ Geometry of discrete-time spin systems ⋮ Lagrangian dynamics on matched pairs ⋮ Constraints in Euler-Poincaré reduction of field theories ⋮ Symmetry reduction, integrability and reconstruction in \(k\)-symplectic field theory ⋮ Field theories: reduction, constraints and variational integrators ⋮ First variation formula for discrete variational problems in two independent variables ⋮ Hamel's formalism for classical field theories ⋮ A variational integrator for the Chaplygin-Timoshenko sleigh ⋮ Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups ⋮ Discrete Lagrange problems with constraints valued in a Lie group ⋮ First variation formula and conservation laws in several independent discrete variables ⋮ Hamel's formalism for infinite-dimensional mechanical systems ⋮ Discrete formulation for the dynamics of rods deforming in space ⋮ The problem of Lagrange in discrete field theory

Cites Work

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• Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products
• Multi-symplectic structures and wave propagation
• SYMMETRIES IN CLASSICAL FIELD THEORY
• Discrete Euler-Poincaré and Lie-Poisson equations
• Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids
• p -form electromagnetism on discrete spacetimes
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
• Euler-Poincaré reduction on principal bundles

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