By João A. C. Martins, Manuel D. P. Monteiro Marques (auth.)

This quantity comprises forty four papers provided on the 3rd touch Mechanics overseas Symposium (CMIS 2001) held in Praia da Consola9ao, Peniche (portugal), June 17-21,2001. This Symposium was once the direct continuation of the 1st CMIS held in Lausanne (1992) and in Carry-Le-Rouet (1994). different comparable conferences, in what matters clinical subject matters and individuals, came about within the nineties at l. a. Grande Motte (1990), Vadstena (1996), Ferrara (1997), Munich (1998) and Grenoble (1999). The Symposium geared toward accumulating researchers with pursuits in quite a lot of issues in theoretical, computational and experimental touch mechanics. the decision for papers pointed out issues in tribology, mathematical formulations and research, numerical tools in non-smooth mechanics, impression difficulties, instabilities and technological difficulties. the entire variety of individuals used to be 102, from Universities and learn Institutes of nineteen international locations. The clinical Committee reviewed 102 submitted abstracts, and the ultimate software consisted of 6 major lectures, forty three oral communications and 36 poster displays (see Appendix A). The papers during this e-book correspond to just about all of the major lectures and oral communications, and they're assembled in five chapters: • Dynamics and impression • Instabilities, Oscillations and Waves • touch versions, effects and purposes • Mathematical research • Numerical tools. We thank the entire authors for his or her priceless contributions to this quantity. we're indebted to the participants of the medical Committee for his or her assist in refereeing the submitted abstracts and manuscripts. We additionally thank the sequence editor, Prof. Graham Gladwell, for his assistance within the revision process.

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**Example text**

J. (1983) Standard inelastic shocks and the dynamics of unilateral constraints, in Unilateral problems in structural analysis (G. Del Piero and F. Macari Eds), Springer-Verlag, Wien, New-York, 173 - 221. Percivale, D. (1985) Uniqueness in the elastic bounce problem, I, Journal of Differential Equations 56, 206 - 215. Schatzman, M. (1978) A class of nonlinear differential equations of second order in time, Nonlinear Analysis, Theory, Methods (1 Applications 2, No 2, 355-373. Schatzman, M. (1998) Uniqueness and continuous dependence on data for one dimensional impact problems, Mathematical and Oomputational Modelling 28, No.

Collision of a rigid body with a plane. piD~x,t) x(t) Figure 1. Collision of a point with a rigid fixed plan and sliding after the collision. The solid is reduced to a point. Let us consider a point, moving above a rigid fixed plane. Its position at time t is x( t). The system made of the point and the plane is deformable because the distance of the point to the plane changes. The deformation velocity is the velocity ofthe point with respect to the plane, U(t) = dx(t)/dt. In many circumstances the duration of the collisions of the point and the plane is small compared to the duration of the considered evolution: thus we consider that the collisions are instantaneous.

The percussion ~intk is applied at the collision point Ai,j,k' Let the virtual velocities of iiie centers of mass Gi be ~ and the virtual rotation velocity be Wi . Let us define the vector V = (~, Wi) and the function Di,j(V, Ai,j,k) = ~ +Wi X GiAi,j,k - (~+Wj x GjAi,j,k), (19) which gives the velocity of deformation at point Ai,j,k (the relative velocity of the point). 11:t E Dcp .. (Di,j(U+,Ai,j,k)) ~,J,k ~,J,k + Di,j(U-,Ai,j,k)) 2 ' (21) which take into account the impenetrability condition, the principle (20) becomes In order to use law (16), we assume that there exist a normal vector directed from solid j toward solid i with i < j.