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Author : J.J. Moreau
Release : 2014-05-04
Genre : Science
Kind : eBook
Book Rating : 24X/5 ( reviews)
Book Synopsis Nonsmooth Mechanics and Applications by : J.J. Moreau
Download or read book Nonsmooth Mechanics and Applications written by J.J. Moreau. This book was released on 2014-05-04. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernard Brogliato
Release : 2012-12-06
Genre : Technology & Engineering
Kind : eBook
Book Rating : 575/5 ( reviews)
Book Synopsis Nonsmooth Mechanics by : Bernard Brogliato
Download or read book Nonsmooth Mechanics written by Bernard Brogliato. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.
Author : Samir Adly
Release : 2018-02-19
Genre : Mathematics
Kind : eBook
Book Rating : 585/5 ( reviews)
Book Synopsis A Variational Approach to Nonsmooth Dynamics by : Samir Adly
Download or read book A Variational Approach to Nonsmooth Dynamics written by Samir Adly. This book was released on 2018-02-19. Available in PDF, EPUB and Kindle. Book excerpt: This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process. The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality and provides a multidisciplinary view as it outlines fundamental results in nonsmooth dynamics and explains how to use them to study various problems in engineering. In particular, the author explores the question of how to redefine the notion of dynamical systems in light of modern variational and nonsmooth analysis. With the aim of bridging between the communities of applied mathematicians, engineers and researchers in control theory and nonlinear systems, this brief outlines both relevant mathematical proofs and models in unilateral mechanics and electronics.
Author : Jaroslav Haslinger
Release : 2007-08-03
Genre : Technology & Engineering
Kind : eBook
Book Rating : 431/5 ( reviews)
Book Synopsis Nonsmooth Mechanics of Solids by : Jaroslav Haslinger
Download or read book Nonsmooth Mechanics of Solids written by Jaroslav Haslinger. This book was released on 2007-08-03. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth mechanics is a relatively complex field and requires a good knowledge of mechanics as well as a good background in some parts of modern mathematics. The present volume of lecture notes follows a very successful advanced school, with the aim to cover as much as possible all these aspects. It includes contributions that cover mechanical aspects as well as the mathematical and numerical treatment.
Author : Vincent Acary
Release : 2008-01-30
Genre : Technology & Engineering
Kind : eBook
Book Rating : 923/5 ( reviews)
Book Synopsis Numerical Methods for Nonsmooth Dynamical Systems by : Vincent Acary
Download or read book Numerical Methods for Nonsmooth Dynamical Systems written by Vincent Acary. This book was released on 2008-01-30. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.
