IUTAM Symposium on Unilateral Multibody Contacts, 1999 Proceedings of the IUTAM Symposium held in Munich, Germany, August 3–7, 1998 Solid Mechanics and Its Applications Series, Vol. 72

Multibody dynamics started with the ideas of Jacob and Daniel Bernoul­ li and later on with d'Alembert's principle. In establishing a solution for the problem of the center of oscillation for a two-mass-pendulum Jacob Ber­ noulli spoke about balancing the profit-and-Ioss account with respect to the motion of the two masses. Daniel Bernoulli extended these ideas to a chain pendulum and called forces not contributing to the motion "lost forces", thus being already very close to d'Alembert's principle. D'Alembert considered a "system of bodies, which are interconnected in some arbitrary way. " He suggested separating the motion into two parts, one moving, the other being at rest. In modern terms, or at least in terms being applied in engineering mechanics, this means that the forces acting on a system of bodies are split into active and passive forces. Active forces generate motion, passive forces do not; they are a result of constraints. This interpretation of d'Alembert's principle is due to Lagrange and up to now has been the basis of multi body dynamics (D' Alembert, Traite de Dynamique, 1743; Lagrange, Mecanique Analytique, 1811). Thus, multibody dynamics started in France. During the nineteenth century there were few activities in the multi body field even though industry offered plenty of possible applications and famous re­ presentatives of mechanics were aware of the problems related to multibody dynamics. Poisson in his "Traite de Mecanique" (Paris 1833) gave an im­ pressive description of these problems, including impacts and friction.

I. Fundamentals.- Some Basics of Unilateral Dynamics.- Decomposition of Scalar Force Interactions.- On the Well-Posedness of Painleve’s Example.- Moreau’s Rule and the Penalty Method.- Formulations and Solution Methods of the Dynamical Spatial Contact Problem.- II. Impacts.- Dynamic Grasping Problem with Impact.- Experimental Investigation of Impacts with Friction.- Dynamics of the Generator of the Impact Force.- Control of Impacting System via Inverse Model.- Simultaneous Parametric and Internal Resonances in Systems Simulating Liquid Sloshing Impact.- On the Problem of Constrained Collision.- Response of Secondary Structures in Stochastic Systems with Impacts.- Influence of the Stop Stiffness on the Impact Oscillator Dynamics.- Mechanics of Impact for Compliant Multi-Body Systems.- A Multi-Degree of Freedom Approach to Coefficient of Restitution Models for Impact Oscillators.- III. Friction.- On (Non-)Existence and (Non-)Uniqueness of Solutions in Frictional Contact Problems.- An Efficient, Hybrid Frequency-Time Domain Method for the Dynamics of Large-Scale Dry-Friction damped Structural Systems.- Bifurcations and Instabilities in Some Finite Dimensional Frictional Contact Problems.- IV. Multibody Aspects.- Collision Detection and Contact Approaches for Hybrid Multibody System / Finite Element Simulation.- CAD-Based Contact Modelling for Multibody Systems.- An Algorithm for Rigid Body Contact with Coulomb Friction.- Dynamics of Piecewise Linear Oscillators with Viscous and Constant Damping.- Examples of Non-Smooth Mechanical Systems -An Overview-.- Conservative Discretization Algorithms for Dynamic Contact Between Nonlinear Elastic Bodies.- V. Local Contact Behavior.- A Temperature Field in Rolling Contact Problem.- Finite Element Treatment of Thermoelastic WearProblems.- VI. Applications.- Dynamics of Belt/Pulley Frictional Contact.- Unilateral Contacts in Machine Dynamics.- Chimney Dampers.- The Parts Transportation in a Vibratory Feeder.- Vibrations of Turbine Blade Assemblies with Stick and Slip Conditions.