Qualitative Analysis Of Nonsmooth Dynamics

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Qualitative Analysis Of Nonsmooth Dynamics

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Author : Alain Léger
language : en
Publisher: Elsevier
Release Date : 2016-04-26

Qualitative Analysis Of Nonsmooth Dynamics written by Alain Léger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Technology & Engineering categories.

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

Poincar Andronov Melnikov Analysis For Non Smooth Systems

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Author : Michal Feckan
language : en
Publisher: Academic Press
Release Date : 2016-06-07

Poincar Andronov Melnikov Analysis For Non Smooth Systems written by Michal Feckan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-07 with Mathematics categories.

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity. - Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity - Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems - Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them - Investigates the relationship between non-smooth systems and their continuous approximations

Advanced Topics In Nonsmooth Dynamics

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Author : Remco Leine
language : en
Publisher: Springer
Release Date : 2018-06-07

Advanced Topics In Nonsmooth Dynamics written by Remco Leine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Technology & Engineering categories.

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.

Non Smooth Dynamical Systems

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Author : Markus Kunze
language : en
Publisher: Springer
Release Date : 2007-05-06

Non Smooth Dynamical Systems written by Markus Kunze and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Dynamics And Bifurcations Of Non Smooth Mechanical Systems

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Author : Remco I. Leine
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19

Dynamics And Bifurcations Of Non Smooth Mechanical Systems written by Remco I. Leine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Mathematics categories.

This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.

Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems

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Author : Bernold Fiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems written by Bernold Fiedler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book summarizes and highlights progress in our understanding of Dy namical Systems during six years of the German Priority Research Program "Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems" . The program was funded by the Deutsche Forschungsgemeinschaft (DFG) and aimed at combining, focussing, and enhancing research efforts of active groups in the field by cooperation on a federal level. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications far into the neighboring disciplines of Science. Three fundamental topics in Dynamical Systems are at the core of our research effort: behavior for large time dimension measure, and chaos Each of these topics is, of course, a highly complex problem area in itself and does not fit naturally into the deplorably traditional confines of any of the disciplines of ergodic theory, analysis, or numerical analysis alone. The necessity of mathematical cooperation between these three disciplines is quite obvious when facing the formidahle task of establishing a bidirectional transfer which bridges the gap between deep, detailed theoretical insight and relevant, specific applications. Both analysis and numerical analysis playa key role when it comes to huilding that bridge. Some steps of our joint bridging efforts are collected in this volume. Neither our approach nor the presentations in this volume are monolithic.

A Smooth And Discontinuous Oscillator

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Author : Qingjie Cao
language : en
Publisher: Springer
Release Date : 2016-09-27

A Smooth And Discontinuous Oscillator written by Qingjie Cao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-27 with Technology & Engineering categories.

This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and the perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.

Mathematics And The 21st Century Proceedings Of The International Conference

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Author : A A Ashour
language : en
Publisher: World Scientific
Release Date : 2001-04-02

Mathematics And The 21st Century Proceedings Of The International Conference written by A A Ashour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-02 with Mathematics categories.

Contents:Millennium Lecture — Cairo, 15 January 2000 (M Atiyah)Trends for Science and Mathematics in the 21st Century (P A Griffiths)Arabic Mathematics and Rewriting the History of Mathematics (R Rashed)The Paradigm Shift in Mathematics Education: A Scenario for Change (W Ebeid)Einstein's Theory of Spacetime and Gravity (J Ehlers)Moduli Problems in Geometry (M S Narasimhan)Enumerative Geometry from the Greeks to Strings (C Procesi)Optical Solitons: Twenty-Seven Years of the Last Millennium and Three More Years of the New? (R K Bullough)Concepts of Non-Smooth Dynamical Systems (T Küpper)Radical Theory: Developments and Trends (R Wiegandt)On Minimal Subgroups of Finite Groups (M Asaad)Totally and Mutually Permutable Products of Finite Groups (A Ballester-Bolinches)Asymptotic Behaviour of Solutions of Evolution Equations (B Basit)On Nonlinear Evolution Equations with Applications (L Debnath)A Robust Layer-Resolving Numerical Method for a Free Convection Problem (J Étienne et al.)Growth Value-Distribution and Zero-Free Regions of Entire Functions and Sections (F F Abi-Khuzam)Three Linear Preserver Problems (A R Sourour)Prediction: Advances and New Research (E K Al-Hussaini)Inference on Parameters of the Laplace Distribution Based on Type-II Censored Samples Using Edgeworth Approximation (N Balakrishnan et al.)Mathematical Models in the Theory of Accelerated Experiments (V Bagdonavicius & M Nikulin)The Vibrations of a Drum with Fractal Boundary (J Fleckinger-Pellé)Intermediate States: Some Nonclassical Properties (M S Abdalla & A-S F Obada)On the Relativistic Two-Body Equation (S R Komy)Singularities in General Relativity and the Origin of Charge (K Buchner)The Inner Geometry of Light Cone in Godel Universe (M Abdel-Megied) Readership: Mathematicians. Keywords:Proceedings;Conference;Mathematics;Cairo (Egypt)

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts

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Author : Pawel Olejnik
language : en
Publisher: #N/A
Release Date : 2017-07-07

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts written by Pawel Olejnik and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-07 with Social Science categories.

This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.

Nonsmooth Mechanics

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Author : Bernard Brogliato
language : en
Publisher: Springer
Release Date : 2016-02-29

Nonsmooth Mechanics written by Bernard Brogliato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-29 with Technology & Engineering categories.

Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange–Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. “The book’s two best features, in my view are its detailed survey of the literature... and its detailed presentation of many examples illustrating both the techniques and their limitations... For readers interested in the field, this book will serve as an excellent introductory survey.” Andrew Lewis in Automatica “It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.” Panagiotis D. Panagiotopoulos in Mathematical Reviews “The presentation is excellent in combining rigorous mathematics with a great number of examples... allowing the reader to understand the basic concepts.” Hans Troger in Mathematical Abstracts “/i>