Structure-preserving model reduction for mechanical systems

DOI10.1016/S0167-2789(03)00227-6zbMath1041.70011OpenAlexW2168386575MaRDI QIDQ1407936

Sanjay Lall, Jerrold E. Marsden, Petr Krysl

Publication date: 21 September 2003

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(03)00227-6

zbMATH Keywords

balancingKarhunen-Loève expansionLagrangian structurespatial decompositiondocking devicefinite element elasticity modelsNewmark implicit integrator

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Lagrange's equations (70H03)

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Cites Work

• Unnamed Item
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• Estimation, principal components and Hamiltonian systems
• Hamiltonian structure for the modulation equations of a sine-Gordon wavetrain
• Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
• Nonlinear dynamics by mode superposition
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Asynchronous variational integrators
• The anisotropic Lagrangian averaged Euler and Navier-Stokes equations
• Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry
• The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
• Error estimation and adaptive meshing in strongly nonlinear dynamic problems
• Dimensional model reduction in non‐linear finite element dynamics of solids and structures
• Lagrangian reduction by stages
• All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
• Discrete mechanics and variational integrators
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry
• Natural hierarchical refinement for finite element methods
• On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities
• A subspace approach to balanced truncation for model reduction of nonlinear control systems
• H∞ balancing for nonlinear systems