Dynamics with Inequalities: Impacts and Hard Constraints

This monograph introduces the current state of the theory for systems with inequality constraints. The applications of the theory include dynamics of mechanical systems that incorporate impacts and friction, diode and transistor circuits, economic and transport systems, biological systems with resource constraints, etc. The author introduces the notion of an index of a system, which is a key notion for the determination of the mathematical apparatus for its investigation. The apparatus includes variational inequalities, complementarity, convex optimization, Hilbert spaces, numerical procedures. It should be noted that many of said methods have been developed during the last twenty years and the publications with their descriptions in Russian are insufficient.

All the necessary auxiliary information is given in the applications, which makes the book more accessible. The study is heavily illustrated and contains a lot of practical examples.

The book is intended for specialists in the fields of mechanics, nonsmooth dynamics and theory of optimization. It will be of interest to senior students and undergraduates.