Abstract
This review article focuses on the problems related to numerical simulation of finite dimensional nonsmooth multibody mechanical systems. The rigid body dynamical case is examined here. This class of systems involves complementarity conditions and impact phenomena, which make its study and numerical analysis a difficult problem that cannot be solved by relying on known Ordinary Differential Equation (ODE) or Differential Algebraic Equation (DAE) integrators only. The main techniques, mathematical tools, and existing algorithms are reviewed. The article utilizes 233 references.
Highlights
This article focuses on the problem of numerical simulation of systems composed of interacting rigid bodies
What is called the rigid body approach does not preclude the incorporation of deformation effects, though the way they appear in the dynamics may differ from the usual spring-dashpot formulations
Since the rigid body model has to be seen as a limit modelin a sense it is the model that contains the least physical information on the processthese peculiarities are not surprising: the less information, the worse prediction
Summary
This article focuses on the problem of numerical simulation of systems composed of interacting rigid bodies It aims at showing the state of the art in this field and, at the same time, introduces the main features, difficulties, and proposed solutions to simulation of nonsmooth multibody dynamics. It is noteworthy that the tools and models described in this paper concern essentially mechanical systems subject to unilateral constraints with or without dry friction They may be suitable to the simulation of other nonsmooth physical systems, like electrical networks27,42͔. Infinite-dimensional as well as quasi-static or static problems with unilateral contacts are not examined in this paper, see, eg, ͓60͔ for a survey
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