Ch. Glocker – författare

This volume contains papers presented at the IUTAM Symposium on unilateral multibody contacts. Multibody systems very often include phenomena like impacts, stick-slip or time-variant kinematical loops which generate an unsteady behaviour of motion. Each of these unilateral phenomena alone leads to more complexity in analyzing the motion, and the situation becomes worse if such processes take place in multiple contacts of a multibody configuration, especially if these contacts are not decoupled by some force laws, for example. For these cases, the complementary properties of contact dynamics and as a consequence the application of complementary algorithms, allows the correct and consistent evaluation of the new constraint situation after each new contact event and avoids extensive combinational searches. The time-variant structure of such mechanical systems and thus the state-dependent change of the constraint combinations and the equations of motion afford special analytical and numerical treatment.Mathematical aspects can be characterized by linear complementarity problems (LCP) for plane contacts and by nonlinear complementarity problems (NLCP), homotopy or projection methods for spatial contacts. Worldwide, there exists an increasing scientific community dealing with these problems where, especially in Europe, the efforts are concentrated on the mathematical foundation, on applications for multibody dynamics and for FE-problems. This volume will be of interest to researchers and engineers in the field of applied mathematics, physical and mechanical sciences, and engineering.

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.