Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

In the 1970s of the last century, the progress in powerful simulation software for mechanical multibody systems and for electrical circuits led to a new class of models that is characterized by differential equations and algebraic constraints. These Differential-Algebraic Equations (DAEs) became soon a hot topic, and the methodology that has emerged since then represents now a general field in applied and computational mathematics, with various new applications in science and engineering. Taking a historical approach, the present article introduces a summarizing view at DAEs, with emphasis on numerical aspects and without aiming for completeness. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.