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Qualitative Analysis Of Nonsmooth Dynamics

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Qualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics Book
Author : Alain Léger,Elaine Pratt
Publisher : Elsevier
Release : 2016-04-26
ISBN : 0081012012
Language : En, Es, Fr & De

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Book Description :

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

Qualitative Analysis of Nonsmooth Dynamics

Qualitative Analysis of Nonsmooth Dynamics Book
Author : Alain Léger,Elaine Pratt
Publisher : Unknown
Release : 2016-04-04
ISBN : 9781785480942
Language : En, Es, Fr & De

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Book Description :

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

Poincar   Andronov Melnikov Analysis for Non Smooth Systems Book
Author : Michal Fečkan,Michal Pospíšil
Publisher : Academic Press
Release : 2016-06-07
ISBN : 0128043644
Language : En, Es, Fr & De

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Book Description :

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

Stability and Convergence of Mechanical Systems with Unilateral Constraints

Stability and Convergence of Mechanical Systems with Unilateral Constraints Book
Author : Remco I. Leine,Nathan van de Wouw
Publisher : Springer Science & Business Media
Release : 2007-12-29
ISBN : 9783540769750
Language : En, Es, Fr & De

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Book Description :

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

Advanced Topics in Nonsmooth Dynamics Book
Author : Remco Leine,Vincent Acary,Olivier Brüls
Publisher : Springer
Release : 2018-06-07
ISBN : 3319759728
Language : En, Es, Fr & De

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Book Description :

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

Ergodic Theory  Analysis  and Efficient Simulation of Dynamical Systems Book
Author : Bernold Fiedler
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642565891
Language : En, Es, Fr & De

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Book Description :

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.

A Smooth and Discontinuous Oscillator

A Smooth and Discontinuous Oscillator Book
Author : Qingjie Cao,Alain Léger
Publisher : Springer
Release : 2016-09-27
ISBN : 3662530945
Language : En, Es, Fr & De

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Book Description :

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.

Modeling with Nonsmooth Dynamics

Modeling with Nonsmooth Dynamics Book
Author : Mike R. Jeffrey
Publisher : Springer Nature
Release : 2020-02-22
ISBN : 3030359875
Language : En, Es, Fr & De

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Book Description :

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.

Dynamics and Bifurcations of Non Smooth Mechanical Systems

Dynamics and Bifurcations of Non Smooth Mechanical Systems Book
Author : Remco I. Leine,Henk Nijmeijer
Publisher : Springer Science & Business Media
Release : 2013-03-19
ISBN : 3540443983
Language : En, Es, Fr & De

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Book Description :

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.

Mathematics and the 21st Century

Mathematics and the 21st Century Book
Author : A. A. Ashour,A.-S. F. Obada
Publisher : World Scientific
Release : 2001
ISBN : 9812810242
Language : En, Es, Fr & De

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Book Description :

The Conference on "Mathematics and the 21st Century" was held in Cairo, Egypt during the period 15-20 January 2000. The conference's sessions consisted of plenary lectures and topical sessions. Some of the plenary lectures covered general fields such as: rewriting the history of mathematics; education of mathematics; relation between mathematics and sciences; and mathematical aspects of transportation.

Multibody Dynamics with Unilateral Contacts

Multibody Dynamics with Unilateral Contacts Book
Author : Friedrich Pfeiffer,Christoph Glocker
Publisher : Springer Science & Business Media
Release : 2000-11-10
ISBN : 9783211833308
Language : En, Es, Fr & De

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Book Description :

The volume introduces basic concepts necessary for a modern treatment of inequality problems in finite degree of freedom dynamics. Tools from convex analysis, by now well established in non-smooth mechanics, are used to formulate the constitutive equations and impact laws. The lectures cover a broad area of non-smooth dynamics from primal and dual energy functions in variational and differential form to application problems as chimney dampers or vibration conveyors. This includes frictional oscillations with bifurcation scenarios as well as analogies to small displacement quasi-static problems. The course is on an advanced level, designed primarily for postgraduate students, but should also be of value for scientists working on dynamic complementarity problems.

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities

Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities Book
Author : Marian Wiercigroch,Bram de Kraker
Publisher : World Scientific
Release : 2000-04-28
ISBN : 9814497908
Language : En, Es, Fr & De

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Book Description :

Rapid developments in nonlinear dynamics and chaos theory have led to publication of many valuable monographs and books. However, most of these texts are devoted to the classical nonlinear dynamics systems, for example the Duffing or van der Pol oscillators, and either neglect or refer only briefly to systems with motion-dependent discontinuities. In engineering practice a good part of problems is discontinuous in nature, due to either deliberate reasons such as the introduction of working clearance, and/or the finite accuracy of the manufacturing processes. The main objective of this volume is to provide a general methodology for describing, solving and analysing discontinuous systems. It is compiled from the dedicated contributions written by experts in the field of applied nonlinear dynamics and chaos. The main focus is on mechanical engineering problems where clearances, piecewise stiffness, intermittent contact, variable friction or other forms of discontinuity occur. Practical applications include vibration absorbers, percussive drilling of hard materials and dynamics of metal cutting. Contents:PreliminariesMathematical Models of Mechanical Systems with DiscontinuitiesTemporal and Spatial Discontinuity TransformationsExtensions of Cell Mapping for Discontinuous SystemsImpact OscillatorDynamics of Piecewise Linear OscillatorsQuenching of Self-Excited Vibrations by Impact DamperDynamic Phenomena in Gear BoxesRigorous Methods and Numerical Results for Dry Friction ProblemsForced Self-Excited Vibration with Dry FrictionStick–Slip and the Phase-Space ReconstructionMultidegree of Freedom Systems with Dry FrictionDynamic Instabilities in Spinning DisksImpacts and Dry FrictionNonlinear Dynamics of Orthogonal Metal CuttingDynamics of Ultrasonic Drilling of Hard Materials Readership: Mechanical engineers. keywords:Nonlinear Dynamics;Discontinuity;Mechanical System;Impacts;Dry Friction;Applications;Chaos “… this volume provides readers with an excellent treatment of such discontinuous systems and can be a good source of ideas to attack those systems effectively … one is immediately obliged to recognize that it is in fact a series of fifteen jewels, which one would hardly find in the relevant more mathematically oriented literature.” Mathematical Reviews

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts

Modeling  Analysis And Control Of Dynamical Systems With Friction And Impacts Book
Author : Olejnik Pawel,Feckan Michal,Awrejcewicz Jan
Publisher : #N/A
Release : 2017-07-07
ISBN : 9813225300
Language : En, Es, Fr & De

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Book Description :

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.

Singularity and Dynamics on Discontinuous Vector Fields

Singularity and Dynamics on Discontinuous Vector Fields Book
Author : Albert C.J. Luo
Publisher : Elsevier
Release : 2006-07-07
ISBN : 9780080480930
Language : En, Es, Fr & De

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Book Description :

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 Mechanics

Nonsmooth Mechanics Book
Author : Bernard Brogliato
Publisher : Springer
Release : 2016-02-29
ISBN : 3319286641
Language : En, Es, Fr & De

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Book Description :

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>

Complexity in Biological and Physical Systems

Complexity in Biological and Physical Systems Book
Author : Ricardo Lopez-Ruiz
Publisher : BoD – Books on Demand
Release : 2018-05-02
ISBN : 1789230500
Language : En, Es, Fr & De

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Book Description :

Modeling and simulating biological and physical systems are nowadays active branches of science. The diversity and complexity of behaviors and patterns present in the natural world have their reciprocity in life systems. Bifurcations, solitons and fractals are some of these ubiquitous structures that can be indistinctively identified in many models with the most diverse applications, from microtubules with an essential role in the maintenance and the shaping of cells, to the nano/microscale structure in disordered systems determined with small-angle scattering techniques. This book collects several works in this direction, giving an overview of some models and theories, which are useful for the study and analysis of complex biological and physical systems. It can provide a good guidance for physicists with interest in biology, applied research scientists and postgraduate students.

Nonsmooth Dynamics of Contacting Thermoelastic Bodies

Nonsmooth Dynamics of Contacting Thermoelastic Bodies Book
Author : Jan Awrejcewicz,Yuriy Pyr'yev
Publisher : Springer Science & Business Media
Release : 2008-12-10
ISBN : 0387096531
Language : En, Es, Fr & De

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Book Description :

This work is devoted to an intensive study in contact mechanics, treating the nonsmooth dynamics of contacting bodies. Mathematical modeling is illustrated and discussed in numerous examples of engineering objects working in different kinematic and dynamic environments. Topics covered in five self-contained chapters examine non-steady dynamic phenomena which are determined by key factors: i.e., heat conduction, thermal stresses, and the amount of wearing. New to this monograph is the importance of the inertia factor, which is considered on par with thermal stresses. Nonsmooth Dynamics of Contacting Thermoelastic Bodies is an engaging accessible practical reference for engineers (civil, mechanical, industrial) and researchers in theoretical and applied mechanics, applied mathematics, physicists, and graduate students.

IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics

IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics Book
Author : Giuseppe Rega,F. Vestroni
Publisher : Springer Science & Business Media
Release : 2006-06-22
ISBN : 1402032684
Language : En, Es, Fr & De

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Book Description :

The interest of the applied mechanics community in chaotic dynamics of engineering systems has exploded in the last fifteen years, although research activity on nonlinear dynamical problems in mechanics started well before the end of the Eighties. It developed first within the general context of the classical theory of nonlinear oscillations, or nonlinear vibrations, and of the relevant engineering applications. This was an extremely fertile field in terms of formulation of mechanical and mathematical models, of development of powerful analytical techniques, and of understanding of a number of basic nonlinear phenomena. At about the same time, meaningful theoretical results highlighting new solution methods and new or complex phenomena in the dynamics of deterministic systems were obtained within dynamical systems theory by means of sophisticated geometrical and computational techniques. In recent years, careful experimental studies have been made to establish the actual occurrence and observability of the predicted dynamic phenomena, as it is vitally needed in all engineering fields. Complex dynamics have been shown to characterize the behaviour of a great number of nonlinear mechanical systems, ranging from aerospace engineering applications to naval applications, mechanical engineering, structural engineering, robotics and biomechanics, and other areas. The International Union of Theoretical and Applied Mechanics grasped the importance of such complex phenomena in the Eighties, when the first IUTAM Symposium devoted to the general topic of nonlinear and chaotic dynamics in applied mechanics and engineering was held in Stuttgart (1989).

Applied Non Linear Dynamical Systems

Applied Non Linear Dynamical Systems Book
Author : Jan Awrejcewicz
Publisher : Springer
Release : 2014-10-21
ISBN : 3319082663
Language : En, Es, Fr & De

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Book Description :

The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the International Conference on Dynamical Systems: Theory and Applications, held in Łódź, Poland on December 2-5, 2013. The studies give deep insight into both the theory and applications of non-linear dynamical systems, emphasizing directions for future research. Topics covered include: constrained motion of mechanical systems and tracking control; diversities in the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic solutions to the problem of vortex structure around a cylinder; investigation of the regular and chaotic dynamics; rare phenomena and chaos in power converters; non-holonomic constraints in wheeled robots; exotic bifurcations in non-smooth systems; micro-chaos; energy exchange of coupled oscillators; HIV dynamics; homogenous transformations with applications to off-shore slender structures; novel approaches to a qualitative study of a dissipative system; chaos of postural sway in humans; oscillators with fractional derivatives; controlling chaos via bifurcation diagrams; theories relating to optical choppers with rotating wheels; dynamics in expert systems; shooting methods for non-standard boundary value problems; automatic sleep scoring governed by delay differential equations; isochronous oscillations; the aerodynamics pendulum and its limit cycles; constrained N-body problems; nano-fractal oscillators and dynamically-coupled dry friction.

Bifurcation and Chaos in Nonsmooth Mechanical Systems

Bifurcation and Chaos in Nonsmooth Mechanical Systems Book
Author : Anonim
Publisher : Unknown
Release : 2021-07-30
ISBN : 9814485403
Language : En, Es, Fr & De

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Book Description :

Download Bifurcation and Chaos in Nonsmooth Mechanical Systems book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.