KEYNOTE: Remco Leine - Nonsmooth Dynamics: a journey from convex analysis to computer code

Over the past three decades, there has been a growing interest in dynamical systems characterized by non-differentiability, switches, and discontinuities. This surge has given rise to a novel research domain known as Nonsmooth Dynamics, finding diverse applications such as sliding mode control theory, switched electronic circuits, plasticity theory and multibody systems with friction and impact. Mechanics, as one of the oldest natural sciences, has played a forerunner role in formalizing a theory to describe evolution problems involving varying degrees of nonsmoothness. Traditionally, engineering sciences and physics have mostly adhered to a classical modeling approach, expressing all relationships within a system through explicit equalities; a dogma reinforced with the advent of computers. A crucial point in dealing with nonsmoothness is to leave the equality dogma and allow ourselves to think and work with (variational) inequalities and inclusions. The key merit of modern Nonsmooth Dynamics is the development of a mathematical framework based on convex analysis that effectively describes nonsmooth or set-valued relations within a system. This mathematical framework facilitates a comprehensive understanding of unilateral and nonsmooth behavior, unraveling the intrinsic structure of nonsmooth systems, and allows to devise numerical integration methods for simulating them – prerequisites for the analysis of the nonlinear dynamics of nonsmooth systems. in this talk, we will embark on a journey through Nonsmooth Dynamics, commencing with fundamental concepts from convex analysis and showing how, in the end, this leads to very effective algorithms for the simulation of nonsmooth systems.