Numerical Methods for Nonsmooth Dynamical Systems

Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts.- Nonsmooth Dynamical Systems: Motivating Examples and Basic Concepts.- Formulations of Nonsmooth Dynamical Systems.- Nonsmooth Dynamical Systems: A Short Zoology.- Mechanical Systems with Unilateral Constraints and Friction.- Complementarity Systems.- Higher Order Constrained Dynamical Systems.- Specific Features of Nonsmooth Dynamical Systems.- Time Integration of Nonsmooth Dynamical Systems.- Event-Driven Schemes for Inclusions with AC Solutions.- Event-Driven Schemes for Lagrangian Systems.- Time-Stepping Schemes for Systems with AC Solutions.- Time-Stepping Schemes for Mechanical Systems.- Time-Stepping Scheme for the HOSP.- Numerical Methods for the One-Step Nonsmooth Problems.- Basics on Mathematical Programming Theory.- Numerical Methods for the Frictional Contact Problem.- The SICONOS Software: Implementation and Examples.- The SICONOS Platform.

From the reviews:

"This monograph is a valuable and concise contribution to the numerics of nonsmooth ODEs ... . It is clearly designed for engineering applications in computational mechanics, and the main concern is the discussion of the construction of algorithms and their properties ... . written in a formal mathematical style with precise definitions, followed by results stated as Lemma, Proposition, or Theorem (and references to the literature for the proofs). This makes the overall work accessible for both, researchers in mechanics and in mathematics." (Christian Wieners, Zentralblatt für Angewandte Mathemtik und Mechanik, Vol. 88 (7), 2008)

"The present book is a research monograph with numerous information and references to original publications which gives to the book an encyclopaedic nature. ... parallel presentation of nonsmooth models in mechanics and electronics indicates that the mentioned effects will also be of interest for people working in mechatronics, microelectromechanics and multiphysics. The book is intended for graduate students and scientists doing research and development in mechanics and electrical engineering, designers of modern electromechanical devices, as well as to researchers from other scientific communities ... ." (Georgios E. Stavroulakis, Zentralblatt MATH, Vol. 1173, 2009)

From the reviews:"This monograph is a valuable and concise contribution to the numerics of nonsmooth ODEs … . It is clearly designed for engineering applications in computational mechanics, and the main concern is the discussion of the construction of algorithms and their properties … . written in a formal mathematical style with precise definitions, followed by results stated as Lemma, Proposition, or Theorem (and references to the literature for the proofs). This makes the overall work accessible for both, researchers in mechanics and in mathematics." (Christian Wieners, Zentralblatt für Angewandte Mathemtik und Mechanik, Vol. 88 (7), 2008)“The present book is a research monograph with numerous information and references to original publications which gives to the book an encyclopaedic nature. … parallel presentation of nonsmooth models in mechanics and electronics indicates that the mentioned effects will also be of interest for people working in mechatronics, microelectromechanics and multiphysics. The book is intended for graduate students and scientists doing research and development in mechanics and electrical engineering, designers of modern electromechanical devices, as well as to researchers from other scientific communities … .” (Georgios E. Stavroulakis, Zentralblatt MATH, Vol. 1173, 2009)