Advanced Topics In Nonsmooth Dynamics

Author : Remco Leine,Vincent Acary,Olivier Brüls
Publisher : Springer
Page : 457 pages
File Size : 49,7 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 9783319759722

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Advanced Topics in Nonsmooth Dynamics by Remco Leine,Vincent Acary,Olivier Brüls Pdf

This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European locations. The network brings together 40 specialists from 9 different countries in and outside Europe and a wealth of scientific knowledge has been gathered and developed by this group of experts in recent years. The book is of interest to both new and experienced researchers in the field of nonsmooth dynamics. Each chapter is written in such a way as to provide an introduction to the topic for researchers from other fields.

Author : David Yang Gao,Raymond W. Ogden
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 50,6 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781475744354

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Advances in Mechanics and Mathematics by David Yang Gao,Raymond W. Ogden Pdf

Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.

Author : Paul Glendinning,Mike R. Jeffrey
Publisher : Springer Nature
Page : 129 pages
File Size : 53,9 Mb
Release : 2019-10-21
Category : Mathematics
ISBN : 9783030236892

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An Introduction to Piecewise Smooth Dynamics by Paul Glendinning,Mike R. Jeffrey Pdf

This book is aimed at mathematicians, scientists, and engineers, studying models that involve a discontinuity, or studying the theory of nonsmooth systems for its own sake. It is divided in two complementary courses: piecewise smooth flows and maps, respectively. Starting from well known theoretical results, the authors bring the reader into the latest challenges in the field, going through stability analysis, bifurcation, singularities, decomposition theorems and an introduction to kneading theory. Both courses contain many examples which illustrate the theoretical concepts that are introduced.

Author : Gaetan Kerschen,M. R. W. Brake,Ludovic Renson
Publisher : Springer
Page : 271 pages
File Size : 52,5 Mb
Release : 2019-06-28
Category : Science
ISBN : 9783030123918

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Nonlinear Structures and Systems, Volume 1 by Gaetan Kerschen,M. R. W. Brake,Ludovic Renson Pdf

Nonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification

Author : Michael Günther,Wil Schilders
Publisher : Springer Nature
Page : 348 pages
File Size : 45,9 Mb
Release : 2022-03-30
Category : Mathematics
ISBN : 9783030961732

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Novel Mathematics Inspired by Industrial Challenges by Michael Günther,Wil Schilders Pdf

This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.

Author : Bilen Emek Abali,Ivan Giorgio
Publisher : Springer Nature
Page : 491 pages
File Size : 50,7 Mb
Release : 2020-07-18
Category : Science
ISBN : 9783030504601

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Developments and Novel Approaches in Nonlinear Solid Body Mechanics by Bilen Emek Abali,Ivan Giorgio Pdf

This book features selected manuscripts presented at ICoNSoM 2019, exploring cutting-edge methods for developing novel models in nonlinear solid mechanics. Innovative methods like additive manufacturing—for example, 3D printing— and miniaturization mean that engineers need more accurate techniques for modeling solid body mechanics. The book focuses on the formulation of continuum and discrete models for complex materials and systems, particularly the design of metamaterials.

Author : Riccardo Caponetto
Publisher : World Scientific
Page : 208 pages
File Size : 41,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812814050

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Advanced Topics on Cellular Self-organizing Nets and Chaotic Nonlinear Dynamics to Model and Control Complex Systems by Riccardo Caponetto Pdf

This book focuses on the research topics investigated during the three-year research project funded by the Italian Ministero dell'Istruzione, dell'Universite e della Ricerca (MIUR: Ministry of Education, University and Research) under the FIRB project RBNE01CW3M. With the aim of introducing newer perspectives of the research on complexity, the final results of the project are presented after a general introduction to the subject. The book is intended to provide researchers, PhD students, and people involved in research projects in companies with the basic fundamentals of complex systems and the advanced project results recently obtained.

Author : Vincent Acary,Bernard Brogliato
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 52,9 Mb
Release : 2008-01-30
Category : Technology & Engineering
ISBN : 9783540753926

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Numerical Methods for Nonsmooth Dynamical Systems by Vincent Acary,Bernard Brogliato Pdf

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.

Author : Giacomo Albi,Sara Merino-Aceituno,Alessia Nota,Mattia Zanella
Publisher : Springer Nature
Page : 251 pages
File Size : 50,6 Mb
Release : 2021-07-15
Category : Science
ISBN : 9783030671044

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Trails in Kinetic Theory by Giacomo Albi,Sara Merino-Aceituno,Alessia Nota,Mattia Zanella Pdf

In recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School “Trails in Kinetic Theory: Foundational Aspects and Numerical Methods”, hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program “Kinetic Theory”. Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.

Author : J.J. Moreau,P.D. Panagiotopoulos
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 51,8 Mb
Release : 1988-09-21
Category : Science
ISBN : 3211820663

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Nonsmooth Mechanics and Applications by J.J. Moreau,P.D. Panagiotopoulos Pdf

Author : Jaroslav Haslinger,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 48,5 Mb
Release : 2007-08-03
Category : Technology & Engineering
ISBN : 9783211482438

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Nonsmooth Mechanics of Solids by Jaroslav Haslinger,Georgios E. Stavroulakis Pdf

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 : T P Leung,Hua Shu Qin
Publisher : World Scientific
Page : 257 pages
File Size : 51,6 Mb
Release : 2001-06-08
Category : Technology & Engineering
ISBN : 9789814492256

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Advanced Topics In Nonlinear Control Systems by T P Leung,Hua Shu Qin Pdf

Over the last 50 years or so, a number of textbooks, monographs and even popular books have been published on nonlinear control theory and design methods. In the area of classical control, for example, there exist books concerned with phase-plane analysis, describing function approach, absolute stability and so on. In the area of modern control there are those related to optimal control, using differential geometry and the differential algebra method, variable structural control, H-infinite control and so on. These books have been useful in promoting the development of automatic control science and technology. Since 1990 there have been many new results and contributions in the area of nonlinear control. This book introduces those topics to interested readers. It will also benefit automation engineers, researchers and scholars in related fields.

Author : Alain Léger,Elaine Pratt
Publisher : Elsevier
Page : 222 pages
File Size : 42,9 Mb
Release : 2016-04-26
Category : Technology & Engineering
ISBN : 9780081012017

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Qualitative Analysis of Nonsmooth Dynamics by Alain Léger,Elaine Pratt Pdf

Qualitative Analysis of Nonsmooth Dynamics: A Simple Discrete System with Unilateral Contact and Coulomb Friction explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems. By analyzing these non-regularities successively this work explores the set of equilibria and properties of periodic solutions of elementary mechanical systems, where no classical results issued from the theory of ordinary differential equations are readily available, such as stability, continuation or approximation of solutions. The authors focus on unilateral contact in presence of Coulomb friction and show, in particular, how any regularization would greatly simplify the mathematics but lead to unacceptable physical responses. Explores the effects of small and large deformations to understand how shocks, sliding, and stick phases affect the trajectories of mechanical systems Includes theoretical results concerning the full investigation of the behavior under constant or oscillating loadings, even in the case of the simplest mechanical systems Provides a focus on unilateral contact in presence of Coulomb friction Helps you gain an accurate understanding of how the transition occurs to ensure the safe use of any machine involving rotating or sliding mechanisms

Author : Mike R. Jeffrey
Publisher : Springer Nature
Page : 104 pages
File Size : 44,5 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9783030359874

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Modeling with Nonsmooth Dynamics by Mike R. Jeffrey Pdf

This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.

Author : Yury V. Orlov,Luis T. Aguilar
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 40,8 Mb
Release : 2014-02-20
Category : Science
ISBN : 9781493902927

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Advanced H∞ Control by Yury V. Orlov,Luis T. Aguilar Pdf

This compact monograph is focused on disturbance attenuation in nonsmooth dynamic systems, developing an H∞ approach in the nonsmooth setting. Similar to the standard nonlinear H∞ approach, the proposed nonsmooth design guarantees both the internal asymptotic stability of a nominal closed-loop system and the dissipativity inequality, which states that the size of an error signal is uniformly bounded with respect to the worst-case size of an external disturbance signal. This guarantee is achieved by constructing an energy or storage function that satisfies the dissipativity inequality and is then utilized as a Lyapunov function to ensure the internal stability requirements. Advanced H∞ Control is unique in the literature for its treatment of disturbance attenuation in nonsmooth systems. It synthesizes various tools, including Hamilton–Jacobi–Isaacs partial differential inequalities as well as Linear Matrix Inequalities. Along with the finite-dimensional treatment, the synthesis is extended to infinite-dimensional setting, involving time-delay and distributed parameter systems. To help illustrate this synthesis, the book focuses on electromechanical applications with nonsmooth phenomena caused by dry friction, backlash, and sampled-data measurements. Special attention is devoted to implementation issues. Requiring familiarity with nonlinear systems theory, this book will be accessible to g raduate students interested in systems analysis and design, and is a welcome addition to the literature for researchers and practitioners in these areas.