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Moreau’s Rule and The Penalty Method

  • L. Paoli
  • M. Schatzman
Part of the Solid Mechanics and its Applications book series (SMIA, volume 72)

Abstract

Moreau’s rule for anelastic impact in non smooth domains does not give a full description of the pathologies of multiconstraint impact. In particular, it does not lead to continuous dependence on the domain or on the data. However, the set of pathological initial data is negligible in phase space, at least in a simple case. Outside of this set, Moreau’s rule can be completely justified by a penalty approximation. The proof uses very precise asymptotics for a two-dimensional autonomous dynamical system with almost singular initial data.

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References

  1. 1.
    Bernard Brogliato. Nonsrnooth impact mechanics, volume 220 of Lecture Notes in Control and Information Sciences. Springer-Verlag London Ltd., London, 1996.Google Scholar
  2. 2.
    Jean-Jacques Moreau. Liaisons unilatérales sans frottement et chocs inélastiques. C. R. Acad. Sci. Paris Sér. II Méc. Phys. Chim. Sci. Univers Sci. Terre, 296(19): 1473–1476, 1983.zbMATHGoogle Scholar
  3. 3.
    Laetitia Paoli and Michelle Schatzman. Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales: cas avec perte d’énergie, Modél. Math. Anal. Num.(M2AN), 27:673–717, 1993.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • L. Paoli
    • 1
  • M. Schatzman
    • 2
  1. 1.CNRS UMR 5585 “Equipe d’Analyse Numérique Lyon—Saint-Etienne”Université Jean MonnetSaint-Etienne CedexFrance
  2. 2.CNRS UMR 5585 “Equipe d’Analyse Numérique Lyon”Saint-Etienne”Université Claude Bernard — Lyon 1Villeurbanne CedexFrance

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