In the end of the seventies, Schatzman and Moreau undertook to revisit the venerable dynamics of rigid bodies with contact and dry friction in the light of more recent mathematics. One claimed objective was to reach, for the first time, a mathematically consistent formulation of an initial value problem associated with the dynamics. The purpose of this article is to make a review of the today state-of-art concerning not only the formulation, but also the issues of existence and uniqueness of solution.
À la fin des années 70, Schatzman et Moreau entreprirent de reformuler l'antique dynamique des solides rigides en présence de contact et frottement sec à la lumière de mathématiques plus récentes. Un des objectifs revendiqués était de parvenir, pour la première fois, à la formulation d'un problème d'évolution à partir d'une condition initiale, qui soit mathématiquement cohérent. Le but de cet article est de brosser un état de l'art actuel, concernant non seulement les questions de formulation, mais également d'existence et d'unicité de solution.
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Mot clés : Dynamique, Solide rigide, Système discret, Impact, Frottement, Contact, Existence, Unicité
Patrick Ballard 1; Alexandre Charles 2
@article{CRMECA_2018__346_3_222_0,
author = {Patrick Ballard and Alexandre Charles},
title = {An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction},
journal = {Comptes Rendus. M\'ecanique},
pages = {222--236},
publisher = {Elsevier},
volume = {346},
number = {3},
year = {2018},
doi = {10.1016/j.crme.2017.12.010},
language = {en},
}
TY - JOUR AU - Patrick Ballard AU - Alexandre Charles TI - An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction JO - Comptes Rendus. Mécanique PY - 2018 SP - 222 EP - 236 VL - 346 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2017.12.010 LA - en ID - CRMECA_2018__346_3_222_0 ER -
%0 Journal Article %A Patrick Ballard %A Alexandre Charles %T An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction %J Comptes Rendus. Mécanique %D 2018 %P 222-236 %V 346 %N 3 %I Elsevier %R 10.1016/j.crme.2017.12.010 %G en %F CRMECA_2018__346_3_222_0
Patrick Ballard; Alexandre Charles. An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction. Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 222-236. doi : 10.1016/j.crme.2017.12.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.010/
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