qualitative analysis of nonsmooth dynamics

Qualitative Analysis Of Nonsmooth Dynamics
Author: Alain Léger
Publisher: Elsevier
Release Date: 2016-04-26
Pages: 222
ISBN:
Available Language: English, Spanish, And French
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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

Stability And Convergence Of Mechanical Systems With Unilateral Constraints
Author: Remco I. Leine
Publisher: Springer Science & Business Media
Release Date: 2007-12-29
Pages: 236
ISBN:
Available Language: English, Spanish, And French
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While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.

Advanced Topics In Nonsmooth Dynamics
Author: Remco Leine
Publisher: Springer
Release Date: 2018-06-07
Pages: 457
ISBN:
Available Language: English, Spanish, And French
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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.

Ergodic Theory  Analysis  And Efficient Simulation Of Dynamical Systems
Author: Bernold Fiedler
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Pages: 820
ISBN:
Available Language: English, Spanish, And French
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Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Nonsmooth Mechanics
Author: Bernard Brogliato
Publisher: Springer
Release Date: 2016-02-29
Pages: 628
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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>

Singularity And Dynamics On Discontinuous Vector Fields
Author: Albert C.J. Luo
Publisher: Elsevier
Release Date: 2006-07-07
Pages: 310
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones’ thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics. Challenging continuous Newton's dynamics Original theory and seeds of new researches in the field Wide spectrum of applications in science and engineering Systematic presentation and clear illustrations

Nonsmooth Modeling And Simulation For Switched Circuits
Author: Vincent Acary
Publisher: Springer Science & Business Media
Release Date: 2010-10-19
Pages: 284
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Nonsmooth Modeling and Simulation for Switched Circuits concerns the modeling and the numerical simulation of switched circuits with the nonsmooth dynamical systems (NSDS) approach, using piecewise-linear and multivalued models of electronic devices like diodes, transistors, switches. Numerous examples (ranging from introductory academic circuits to various types of power converters) are analyzed and many simulation results obtained with the INRIA open-source SICONOS software package are presented. Comparisons with SPICE and hybrid methods demonstrate the power of the NSDS approach. Nonsmooth Modeling and Simulation for Switched Circuits is intended to researchers and engineers in the field of circuits simulation and design, but may also attract applied mathematicians interested by the numerical analysis for nonsmooth dynamical systems, as well as researchers from Systems and Control.

Piecewise Smooth Dynamical Systems
Author: Mario Bernardo
Publisher: Springer Science & Business Media
Release Date: 2008-01-01
Pages: 482
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Reviews In Global Analysis  1980 86 As Printed In Mathematical Reviews
Author:
Publisher:
Release Date: 1988
Pages: 808
ISBN:
Available Language: English, Spanish, And French
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Modeling With Nonsmooth Dynamics
Author: Mike R. Jeffrey
Publisher: Springer Nature
Release Date: 2020-02-22
Pages: 104
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

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.

Mathematical Reviews
Author:
Publisher:
Release Date: 2007
Pages:
ISBN:
Available Language: English, Spanish, And French
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Proceedings
Author:
Publisher:
Release Date: 2009
Pages:
ISBN:
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Methods Of Qualitative Theory In Nonlinear Dynamics
Author: Leonid P. Shilnikov
Publisher: World Scientific
Release Date: 1998
Pages: 392
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need. Following the footsteps of Poincare, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form. In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced studentsof nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.

Qualitative Analysis Of Nonlinear Elliptic Partial Differential Equations
Author: Vicentiu D. Radulescu
Publisher: Hindawi Publishing Corporation
Release Date: 2008
Pages: 208
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

Practical Bifurcation And Stability Analysis
Author: Rüdiger Seydel
Publisher: Springer Science & Business Media
Release Date: 2009-12-14
Pages: 477
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Probably the first book to describe computational methods for numerically computing steady state and Hopf bifurcations. Requiring only a basic knowledge of calculus, and using detailed examples, problems, and figures, this is an ideal textbook for graduate students.

Neural Networks And Qualitative Physics
Author: Jean-Pierre Aubin
Publisher: Cambridge University Press
Release Date: 1996-03-29
Pages: 283
ISBN:
Available Language: English, Spanish, And French
EBOOK SYNOPSIS:

Artificial intelligence covering neural networks, cognitive systems, qualitative physics.

Journal Of Economic Literature
Author:
Publisher:
Release Date:
Pages:
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Dissertation Abstracts International
Author:
Publisher:
Release Date: 2008
Pages:
ISBN:
Available Language: English, Spanish, And French
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IEEE Intelligent Vehicles Symposium
Author:
Publisher:
Release Date: 2005
Pages:
ISBN:
Available Language: English, Spanish, And French
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Bibliography For Dynamical Systems
Author: Kenichi Shiraiwa
Publisher:
Release Date: 1985
Pages: 390
ISBN:
Available Language: English, Spanish, And French
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