Stability of equilibrium states in a simple system with unilateral contact and Coulomb friction

Stéphanie Basseville (1, 2) , Alain Leger (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 École des Mines de Paris

The aim of this paper is to study the stability of equilibrium states in a mechanical system involving unilateral contact with Coulomb friction. Since the assumptions made in classical stability theorems are not satisfied with this class of systems, we return to the basic definitions of stability by studying the time evolution of the distance between a given equilibrium and the solution of a Cauchy problem where the initial conditions are in a neighborhood of the equilibrium. It was recently established that the dynamics is well posed in the case of analytical data. In the present study, we focus in particular on the stability of the equilibrium states under a constant force and deal only with a simple mass-spring system in $\mathbb{R}^2$.

Mots clés: Stability; Coulomb friction; Klarbring’s system; Discrete dynamics; Unilateral contact

Domaines: Mécanique [physics]; Mécanique [physics.med-ph]

Stéphanie Basseville, Alain Leger. Stability of equilibrium states in a simple system with unilateral contact and Coulomb friction. Archive of Applied Mechanics, 2006, 76 (7), pp.403-428. ⟨10.1007/s00419-006-0040-x⟩. ⟨hal-01310671⟩