Discrete mechanics and variational integrators

By Jerrold E. Marsden, Matthew West. Acta Numerica, 2001

1,688 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a4a02e104e83a0ae60afedeb732b98522d2774e8

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In Computational Mechanics

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Citations in the corpus

Splitting methods (2002, neutral): “Many Hamiltonian PDEs are also multi-symplectic and geometric integrators exist which preserve this structure (Marsden and West 2001).”
DISCRETE MECHANICS AND OPTIMAL CONTROL: AN ANALYSIS ∗ (2008, methodology): “To this end, we extend the notions in Marsden and West [2001] to Lagrangian control forces.”
Discrete mechanics and optimal control for constrained systems (2010, methodology): “In the context of variational integrators, as in [27], the discretization of the Lagrange-d’Alembert principle leads to the structure-preserving time-stepping equations that serve as equality constraints for the resulting finite-dimensional nonlinear optimization problem.”
Discrete differential forms for computational modeling (2005, background): “In particular, it is striking that the calculus of differential forms has not yet had an impact on the mainstream computational fields, despite excellent initial results in E&M [Bossavit 1998] or Lagrangian mechanics [Marsden and West 2001].”
Geometric numerical integration illustrated by the Störmer–Verlet method (2003, background): “A comprehensive survey of variational integrators can be found in Marsden and West (2001).”
Geometric integrators for ODEs (2006, methodology): “, N − 1, with fixed end points q0 and qN [15, 78].”
Variational integrators for constrained dynamical systems (2008, background): “(4) The proof given in [8] makes use of the Lagrange multiplier theorem (see e.”
Numerical Methods for Evolutionary Differential Equations (2008, methodology): “Interesting results have been developed for these methods in the present context, and favorite symplectic methods have been reproduced in this way; see Marsden and West [126] and references therein.”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, methodology): “A single scale integration of this system could be done by VE with the discrete d’Alembert principle for external forces [82]”
Structure-preserving model reduction for mechanical systems (2003, background): “of discrete mechanics (see [27] for an overview and literature).”
Numerical methods for Hamiltonian PDEs (2006, methodology): “One can also start with the Lagrangian formulation and derive algorithms based on a discrete variational principle leading to variational integrators and this approach is reviewed in Marsden & West [102].”
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems (2011, positive): “The continuous optimal control formulation associated with the maneuver determination is computationally solved through the discrete mechanics methodology [44] which is particularly suitable for systems with nonlinear state spaces and symmetries.”