We propose an elementary proof based on a penalization technique to show the existence and uniqueness of the solution to a system of variational inequalities modelling the friction-based motion of a two-body crawling system. Here for each body, the static and dynamic friction coefficients are equal.
Cite
@article{arxiv.2407.03707,
title = {An elementary approach based on variational inequalities for modelling a friction-based locomotion problem},
author = {Panyu Chen and Alvaro Mateos Gonzalez and Laurent Mertz},
journal= {arXiv preprint arXiv:2407.03707},
year = {2024}
}