| Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 1031 - 1052 | |
| DOI | https://doi.org/10.1051/m2an/2024018 | |
| Published online | 10 June 2024 | |
Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction
NAVER LABS Europe, 6 chemin de Maupertuis, 38240 Meylan, France
* Corresponding author: chris.dance@naverlabs.com
Received:
2
February
2024
Accepted:
11
March
2024
We prove that there exists a unique solution to the initial value problem describing the motion of a particle subject to a unilateral constraint and Coulomb friction, if the external force acting on the particle is an analytic function of time and of the particle’s position and velocity. Previous work claimed that this problem has a local series solution that corresponds to an analytic function, after any impacts have been resolved. However, a counterexample to that claim was recently discovered, involving a particle starting to slide, in which the series solution is divergent, and thus does not correspond to an analytic function. This paper corrects previous arguments by considering a general formal series solution for a particle that is starting to slide.
Mathematics Subject Classification: 70F40 / 49J52 / 34A60
Key words: Unilateral dynamics with friction / frictional dynamical contact problems
© The authors. Published by EDP Sciences, SMAI 2024
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