The Dynamics of Discrete Mechanical Systems with Perfect Unilateral Constraints

By P. Ballard. 2000

197 citations recorded by the source corpus.

Abstract: The dynamics of discrete mechanical systems with perfect unilateral constraints is formulated in a very general setting. The well-posedness of the resulting evolution problem is studied. It is proved that existence and uniqueness of a maximal solution is ensured provided strong assumptions are made on the regularity of the data: they are supposed to be analytic. Simple examples show that this regularity assumption may not be relaxed. Sufficient conditions to ensure that the maximal solution is defined for all time are supplied. The continuous dependence of the solution on initial conditions is also studied and the numerical computation of the solution is discussed.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/167d13ede9a496d83539beaa95dffb45a8d5d059

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts (2012, unknown): “…continuous and admits a right velocity v + ( ) at every instant t of [ 0 , T ] and such that the function Assumption 1 is ensured in the framework introduced by Ballard [9] who proves the existence and uniqueness of a solution in a general framework mainly based on the analyticity of data.”
A second-order differential system with hessian-driven damping; application to non-elastic shock laws (2012, background): “One can consult [1, 14, 19, 29] for an extended presentation of the theory of impact dynamics.”
Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem (2005, methodology): “References [1] P. Ballard, The dynamics of discrete mechanical systems with perfect unilateral constraints.”