An elementary approach based on variational inequalities for modelling a friction-based locomotion problem

TL;DR

This paper introduces a straightforward proof method using penalization to establish the existence and uniqueness of solutions in a variational inequality model for friction-driven locomotion of a two-body system.

Contribution

It presents an elementary approach based on variational inequalities and penalization techniques for modeling friction-based locomotion, ensuring solution existence and uniqueness.

Findings

Proves existence and uniqueness of solutions for the model

Uses a penalization technique for the proof

Models friction-based motion with equal static and dynamic coefficients

Abstract

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.