Multisymplectic variational integrators and space/time symplecticity

DOI10.1142/S0219530515500025zbMath1338.65271arXiv1310.4772MaRDI QIDQ2805228

François Gay-Balmaz, François Demoures, Tudor S. Ratiu

Publication date: 10 May 2016

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.4772

zbMATH Keywords

numerical examplepartial differential equationvariational integratordiscrete mechanicsstructure-preservingmultisymplectic structurebeam modelLie group symmetrydiscrete global Noether theoremdiscrete momentum map

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Hamilton's principle (70H25) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Symmetries and conservation laws in mechanics of particles and systems (70S10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (9)

MULTISYMPLECTIC VARIATIONAL INTEGRATORS FOR NONSMOOTH LAGRANGIAN CONTINUUM MECHANICS ⋮ Variational Methods for Fluid-Structure Interactions ⋮ Multisymplectic Galerkin Lie group variational integrators for geometrically exact beam dynamics based on unit dual quaternion interpolation -- no shear locking ⋮ Variational integrators for forced Lagrangian systems based on the local path fitting technique ⋮ A multisymplectic integrator for elastodynamic frictionless impact problems ⋮ Discrete formulation for the dynamics of rods deforming in space ⋮ Unified discrete multisymplectic Lagrangian formulation for hyperelastic solids and barotropic fluids ⋮ The problem of Lagrange in discrete field theory ⋮ Multisymplectic variational integrators for fluid models with constraints

Cites Work

• Symmetry reduced dynamics of charged molecular strands
• Lagrange-Poincaré field equations
• A new Lagrangian dynamic reduction in field theory
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Discrete variational Lie group formulation of geometrically exact beam dynamics
• Discrete mechanics and variational integrators
• Reduction in principal fiber bundles: Covariant Euler-Poincaré equations
• Geometric Numerical Integration
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Multisymplectic variational integrators and space/time symplecticity