Issue |
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
|
|
---|---|---|
Page(s) | 1437 - 1449 | |
DOI | https://doi.org/10.1051/m2an/2022033 | |
Published online | 27 June 2022 |
A counterexample to analyticity in frictional dynamics⋆
NAVER LABS Europe, 6 chemin de Maupertuis, 38240 Meylan, France
* Corresponding author: chris2707@gmail.com
Received:
28
January
2022
Accepted:
4
April
2022
We consider the motion of a particle acted on by dry friction and a force that is an analytic function of time. We give a counterexample to the claim that such motions are given by analytic functions of time. Several published arguments concerning existence and uniqueness in unilateral dynamics with friction rely on the analyticity of such motions. The counterexample invalidates those arguments for motions in three or more dimensions.
Mathematics Subject Classification: 70F40 / 49J52 / 34A60
Key words: Unilateral dynamics with friction / frictional dynamical contact problems / uniqueness
Supplementary Online Material is only available in electronic form at https://doi.org/10.1051/m2an/2022033/olm.
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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