Nonsmooth impact mechanics. Models, dynamics and control
type: Item
instance of: scholarly article
title: Nonsmooth impact mechanics. Models, dynamics and control
zbMATH Open document ID: 0861.73001
author: B. Brogliato
published in: Lecture Notes in Control and Information Sciences
publication date: 1996-08-22T00:00:00Z
review text: The book deals with very important phenomena in engineering and other fields of applied science, namely dynamic phenomena with impacts. In order to illustrate the importance of such problems in engineering, let us mention clattering oscillations in automobile gear boxes which sometimes occur for wheels which are not shifted to transmit a tourque. These oscillations basically are very high frequency impact oscillations due to the clearances depending on the teeth-meshing of the gear wheels. To understand and to prevent such oscillations, it is essential to have an effective mathematical theory available to treat impact problems in mechanics. To develope such a theory is the main aim of this book which focusses on the mathematical aspects in a very competent and comprehensive way. Basically, the physical impact problem can be transformed into the mathematical problem for a dynamical system with unilateral constraints. The unilateral constraints depending on the position variables are treated in the book. Especially, the control of systems with unilateral constraints is addressed. If the bodies are considered to be rigid as it is in general, then it is well known that certain indetermined problems may arise for which the mathematical question of well-posedness, that is, such properties of solutions as existence, uniqueness and continuous dependence on initial data and parameters, will be very important. However, it should be noted that at several points in the book also the influences of flexibility of the structures are discussed. Further questions of global motions of multibody systems with impacts, the construction of proper Poincaré mappings resulting in time-discrete nonlinear dynamical systems, and stability problems are treated in detail. The presentation is excellent in combining rigorous mathematics with a great number of examples ranging from simple mechanical systems to robotic systems allowing the reader to understand the basic concepts. Abundant literature…
Mathematics Subject Classification ID: 74-02
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 70K99
zbMATH DE Number: 918842
zbMATH Keywords: dynamical system
zbMATH Keywords: unilateral constraints
zbMATH Keywords: well-posedness
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence on initial data
zbMATH Keywords: flexibility
zbMATH Keywords: multibody systems
zbMATH Keywords: Poincaré mappings
zbMATH Keywords: time-discrete nonlinear dynamical systems
zbMATH Keywords: stability
reviewed by: Hans Troger
MaRDI profile type: Publication
DOI: 10.1007/BFB0027733
description: scientific article; zbMATH DE number 918842