Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems

By C. Kane, Jerrold E. Marsden, Magdalena Ortiz, Matthew West. 2000

475 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/dacb3998633e374858757445c4b39d296d643b5e

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In Computational Mechanics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Variational time integrators (2004, methodology): “Nonetheless it was shown in Reference [28] that the Newmark method with = 1 2 and any can be generated from a discrete Lagrangian,”
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns (2013, unknown): “[43] for variational integrators of dynamic problems.”
Variational integrators for constrained dynamical systems (2008, background): “It eliminates the constraint forces (including the Lagrange multipliers) from the timestepping scheme and subsequently reduces its dimension to the minimal possible number.”
DISCRETE MECHANICS AND OPTIMAL CONTROL: AN ANALYSIS ∗ (2008, methodology): “The variational view of discrete mechanics and its numerical implementation is further developed in Wendlandt and Marsden [1997a,b] and then extended in Bobenko and Suris [1999a,b]; Kane, Marsden, and Ortiz [1999]; Kane, Marsden, Ortiz, and West [2000]; Marsden, Pekarsky, and Shkoller [1999a,b].”
Optimal and Cooperative Control of Vehicle Formations (2002, background): “This approach to integration, developed by Marsden and coworkers [54, 55, 101], is attractive in that it preserves both conserved quantities and the underlying geometric (in this case symplectic) structure of the equations.”
Structure-preserving model reduction for mechanical systems (2003, background): “[13]; see also[20] for an asynchronous generalization to the PDE context and with applications to nonlinear elastodynamic simulations.”
Asynchronous Variational Integrators (2003, background): “, Knuth [1998]) containing the elements of the triangulation.”
Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, result): “This is in line with the works of Radovitzky and Ortiz (1999) and Kane et al. (2000) for variational integrators of dynamic problems.”