Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics

By Vincent Acary, B. Brogliato. 2008

314 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/94565a7335726366cf9d7fc9c85820ddee903c1b

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Citations in the corpus

A direct method for trajectory optimization of rigid bodies through contact (2014, methodology): “One straightforward approach to extending to 3D would be to treat both λx and ψ(q, q̇) as two-vectors, and write down a set of nonlinear constraints for Coulomb friction in the tangent plane, such as in [1].”
Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts (2012, unknown): “For more details on the modeling of multibody systems with unilateral constraints, we refer to [3,35,30] and for the mathematical analysis, we refer to [37,26,39,9].”
Well-posedness, stability and invariance results for a class of multivalued Lur'e dynamical systems (2011, methodology): “It is noteworthy that for such types of nonsmooth dynamical systems, event-drivenmethods [26]may fail to integrate the systemeven on arbitrarily small intervals of time, and time-stepping methods are the only available methods.”
A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids (2015, background): “Many researchers have considered the complementarity formulation associated with Moreau’s time-stepping algorithm for contact modeling in multibody systems over the last years [55-57].”
A nonsmooth generalized‐ α scheme for flexible multibody systems with unilateral constraints (2013, methodology): “Reduction to a sequential linear complementarity problems In this section, we propose to reformulate the iteration in (36) as a LCP, see [9, 40, 41], which replaces the linearized system that we have to solve at each Newton’s step.”
On solving contact problems with Coulomb friction: formulations and numerical comparisons (2018, methodology): “For a description of the derivation of such problems in various practical situations we refer to (Laursen, 2003; Wriggers, 2006; Acary and Brogliato, 2008; Acary and Cadoux, 2013).”