A system of rigid bodies with dry friction
Résumé
The mechanical system we propose to deal with is a finite set of perfectly rigid bodies submitted to: (a) usual constraints, meaning holonomous, bilateral, frictionless constraints, depending or not on time; (b) forces, they are functions of time, velocity, and the generalized variables of the system; (c) punctual contacts with dry friction between some bodies of the system or between bodies of the system and some extraneous rigid bodies, the motion of which is explicitly given as a function of time. In the first part, the general equations of the problem are introduced, existence theorems are given, and comments are made about the mechanical significance of both the assumptions and the foregoing results. The equations are set in the second part, which is thus essentially concerned with mechanics and may be read independently. The proofs of the theorems are to be found in the third part.