Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs 6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations."

model. They conclude that the models using three fitting parameters provide the best fit over a wide range of suctions. Models for soil-water characteristic curves are only useful if we have experimental data on which to base them. Agus, Leong and Rahardjo (Singapore) present a large number of experimental soil-water characteristic curves determined for two types of residual soil from Sigapore. They present data for eight different sites. This data set allows them to relate the parameters of the soil-water characteristic curves to index properties. They conclude that the relationships derived are suitable to pro vide a quick preliminary estimate of a soil-water characteristic curve. The importance of soil-water characteristic curves is emphasized by another con tribution dealing with this topic. Aung, Rahardjo, Leong and Toll (Singapore) inves tigate the relationship between mercury intrusion porosimetry measurements and soil-water characteristic curves. The porosimetry measurements are presented as soil-air characteristic curves. The slopes of the soil-air characteristic curves are found to be similar to the slopes of the soil-water characteristic curves. The equiv alent pore diameters calculated from the mercury entry value and the air entry value appear to be related. Therefore, it is suggested that porosimetry data can be used to construct an estimate of the soil-water characteristic curve."

This monograph addresses the systematic representation of the methods of analysis developed by the authors as applied to such systems. Particular features of dynamic processes in such systems are studied. Special attention is given to an analysis of different resonant phenomena taking unusual and diverse forms.

There has been a growing interest in the foundation of the theory of th- walled composite beams and of their incorporation in aeronautical/aerospace, automotive, helicopter and turbomachinery rotor blades, mechanical, civil and naval constructions inthe last two decades or so. The proliferation of the specialized literature, mainly in the form of journal/ proceedings papers, and the activity in terms of workshops devoted to this topic attest this interest. A decisive factor that has fueled thisgrowing activity was generatedby highdiversity and severity ofdemandsand operating conditions imposed on structural elements involvedintheadvanced technology. In order to beable to survive andful?ll theirmission inthe extreme environmental conditions inwhich they operate, new materialsand new structural paradigms are required. The new exotic structures have to provide higher performances, unatta- able bytheclassical structures builtof traditional materials. Theadvent of advanced composite materials, of smart materialsandfunctionally graded - terials (FGMs), have constituted the strongest stimuli for suchdevelopments. Moreover, their incorporation is likely to expand the use and capabilities of thin-walledbeam structures. Thenew and stringent requirements imposed on aeronautical/aerospace, turbomachinery and shaft structural systems will be best met by such new types of material structures

1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di?erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to ?nd a complete dynamics of a nonlinear di?erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is known for some para- ters, the persistence or bifurcations of solutions from that family is studied as parameters are changing. There are several approaches to handle such nonl- ear bifurcation problems. One of them is a topological degree method, which is rather powerful in cases when nonlinearities are not enough smooth. The aim of this book is to present several original bifurcation results achieved by the author using the topological degree theory. The scope of the results is rather broad from showing periodic and chaotic behavior of non-smooth mechanical systems through the existence of traveling waves for ordinary di?erential eq- tions on in?nite lattices up to study periodic oscillations of undamped abstract waveequationsonHilbertspaceswithapplicationstononlinearbeamandstring partial di?erential equations. 1.

The contributions in this book were presented at the sixth international symposium on Advances in Robot Kinematics organised in June/July 1998 in Strobl/Salzburg in Austria. The preceding symposia of the series took place in Ljubljana (1988), Linz (1990), Ferrara (1992), Ljubljana (1994), and Piran (1996). Ever since its first event, ARK has attracted the most outstanding authors in the area and managed to create a perfect combination of professionalism and friendly athmosphere. We are glad to observe that, in spite of a strong competition of many international conferences and meetings, ARK is continuing to grow in terms of the number of participants and in terms of its scientific impact. In its ten years, ARK has contributed to develop a remarkable scientific community in the area of robot kinematics. The last four symposia were organised under the patronage of the International Federation for the Theory of Machines and Mechanisms -IFToMM. interest to researchers, doctoral students and teachers, The book is of engineers and mathematicians specialising in kinematics of robots and mechanisms, mathematical modelling, simulation, design, and control of robots. It is divided into sections that were found as the prevalent areas of the contemporary kinematics research. As it can easily be noticed, an important part of the book is dedicated to various aspects of the kinematics of parallel mechanisms that persist to be one of the most attractive areas of research in robot kinematics.

Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc.

The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time.

It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua.

The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.

This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.

There are many monographs in the existing literature devoted to the static and dynamic behavior of plates and shells. Plates and shells are enco- tered often in engineering applications being integralparts of a wide range of constructions, such as machines, vehicles, airplanes, rockets, ships, bridges, buildings, and containers, to name a few. In addition to the usual requi- ments posedby engineersrelatedtolightweightness, su?cientrigidityor?- ibility, and robust stability properties, there is an additional class ofapriori dynamicalpropertiesrequiredbymodernengineeringapplicationswheren- homogeneity and non-uniformity of structural components is often the norm incertainapplications. Inaddition, strictoperationalrequirementsinmodern engineering applications towards higher speeds, lighter construction, robust andreliableperformance, dictatessmallermarginsoferrorordeviationsfrom prescribed performances in adverse or uncertain forcing environments. This, in turn, requires the development of new analytical and computational tools capable of addressing challenging and not very well developed topics, such as, nonlinearities a?ecting the system performance, the e?ects of unmodeled dynamics on the stability of operation, and the role of uncertainties in the systemparametersonthestructuralresponse. Asaresult, thereisanongoing e?ort to address such issues, leading to the development of new analytical and computational tools, some of which are discussed in this monograph. The monograph follows an approach based on an integrated treatment of analysis and computation. Such a hybrid approach, coupled with computer algebra, can lead to results that cannot be obtained by other standard th- ries in the ?eld. We show, that in a wide class of problems only a carefully prepared numerical experiment followed by purely mathematical conside- tionscan?nallyleadtothesoughtresults. Thenumerousanalyticalconstr- tions are illustrated by examples of application and computational resu

The area of analysis and control of mechanical systems using differential geometry is flourishing.

This book collects many results over the last decade and provides a comprehensive introduction to the area.

The ECCOMAS Thematic Conference Multibody Dynamics 2005 was held in Madrid, representing the second edition of a series which began in Lisbon 2003. This book contains the revised and extended versions of selected conference communications, representing the state-of-the-art in the advances on computational multibody models, from the most abstract mathematical developments to practical engineering applications.

Servo Motors and Industrial Control Theory presents the fundamentals of servo motors and control theory in a manner that is accessible to undergraduate students, as well as practitioners who may need updated information on the subject. Graphical methods for classical control theory have been replaced with examples using mathematical software, such as MathCad and MatLab, to solve real-life engineering control problems. State variable feedback control theory, which is generally not introduced until the Masters level, is introduced clearly and simply for students to approach complicated problems and examples.

The International Symposium on History of Machines and Mechanisms is a new initiative to promote explicitly researches and publications in the field of the History of TMM (Theory of Machines and Mechanisms). It was held at the University of Cassino, Italy, from 11 to 13 May 2000. The Symposium was devoted mainly to the technical aspects of historical developments and therefore it has been addressed mainly to the IFToMM Community. In fact, most the authors of the contributed papers are experts in TMM and related topics. This has been, indeed, a challenge: convincing technical experts to go further in-depth into the background of their topics of expertise. We have received a very positive response, as can be seen by the fact that these Proceedings contain contributions by authors from all around the world. We received about 50 papers, and after review about 40 papers were accepted for both presentation and publishing in the Proceedings. This means also that the History of TMM is of interest everywhere and, indeed, an in-depth knowledge of the past can be of great help in working on the present and in shaping the future with new ideas. I believe that a reader will take advantage of the papers in these Proceedings with further satisfaction and motivation for her or his work (historical or not). These papers cover the wide field of the History of Mechanical Engineering and particularly the History of TMM.

Cybernetical physics borrows methods from both theoretical physics and control engineering. It deals with the control of complex systems is one of the most important aspects in dealing with systems exhibiting nonlinear behavior or similar features that defy traditional control techniques. This book fully details this new discipline.

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.

Following the recent developments in the field of absolute stability, Prof. Xiaoxin Liao, in conjunction with Prof. Pei Yu, has created a second edition of his seminal work on the subject. Liao begins with an introduction to the Lurie problem and Lurie control system, before moving on to the simple algebraic sufficient conditions for the absolute stability of autonomous and non-autonomous ODE systems, as well as several special classes of Lurie-type systems. The focus of the book then shifts toward the new results and research that have appeared in the decade since the first edition was published. This book is aimed to be used by undergraduates in the areas of applied mathematics, nonlinear control systems, and chaos control and synchronisation, but may also be useful as a reference for researchers and engineers. The book is self-contained, though a basic knowledge of calculus, linear system and matrix theory, and ordinary differential equations is a prerequisite.

Several consistent solutions for cooperative system control have recently been identified by the authors of the current monograph. This was achieved by solving three separate tasks that are essential for solving the problem of cooperative manipulation as a whole. The first task is related to the understanding of the physical nature of cooperative manipulation and finding a way for a sufficiently exact characterization of cooperative system statics, kinematics and dynamics. After successfully completing this task, in the frame of the second task, the problem of coordinated motion of the cooperative system is solved. Finally, as a solution to the third task, the control laws of cooperative manipulation are synthesized.

The starting point in dealing with the above three tasks of cooperative manipulation was the assumption that the problem of force uncertainty in cooperative manipulation can be resolved by introducing elastic properties into the cooperative system, at least in the part where force uncertainty appears. In static and dynamic analysis of the elastic structure of cooperative systems the finite element method is applied. In contrast to the procedure used in the major part of the available literature where deformation work is expressed by deviations from the unloaded state of fixed elastic structure, in this monograph the deformation work is expressed by internal forces as a function of the absolute coordinates of contacts of mobile elastic structure. Coordinated motion and control in cooperative manipulation are solved as the problem of coordinated motion and control of a mobile elastic structure, taking into account the specific features of cooperative manipulation. Coordinated motion and control laws in cooperative manipulation are synthesized on the basis of a non-linear model where the problem of uncertainty is solved, which is not the case in the available literature. Simple examples demonstrate the consistent procedure of mathematical modeling and synthesis of nominal coordinated motion, as well as control of the cooperative system.

This book will be useful to a wide audience of engineers, ranging from undergraduate and graduate students, new and advanced academic researchers, to practitioners (mechanical and electrical engineers, computer and system scientists). It is intended for readers whose work involves manufacturing, industrial, robotics, automation, computer and control engineering, and who wish to find out about this important new technology and its potential advantages for control engineering applications.

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.

This book deals with the class of singular systems with random abrupt changes also known as singular Markovian jump systems. Various problems and their robustness are tackled. The book examines both the theoretical and practical aspects of the control problems from the angle of the structural properties of linear systems. It can be used as a textbook as well as a reference for researchers in control or mathematics with interest in control theory.

1. Background This textbook is an introduction to and exploration of a number of core topics in the ?eld of applied mechanics. Mechanics, in both its theoretical and applied contexts, is, like all scienti?c endeavors, a human construct. It re?ects the personalities, thoughts, errors, and successes of its creators. We therefore provide some personal information about each of these individuals when their names arise for the ?rst time in this book. This should enable the reader to piece together a cultural-historical picture of the ?eld s origins and development. This does not mean that we are writing history. Nevertheless, some remarks putting individuals and ideas in context are necessary in order to make clear what we are speaking about - and what we are not speaking about. At the end of the 19th century, technical universities were established eve- where in Europe in an almost euphoric manner. But the practice of technical mechanics itself, as one of the basics of technical development, was in a desolate state, due largely to the refusal of its practitioners to recognize the in?uence of kinetics on motion. They were correct to the extend that then current mechanical systems moved with small velocities where kinetics does not play a signi?cant role. But they had failed to keep up with developments in the science underlying their craft and were unable to keep pace with the speeds of such systems as the steam engine.

Micromechanics provides a link between the structure and the properties at different scales of observation. This book deals with micromechanical analysis of interfaces and interface layers and presents several modelling tools. These range from the rigorous method of asymptotic expansions to practical finite element simulations, suitable for this class of problems. The corresponding two parts of the book are self-contained, so they can be read separately.

In this book, the major ideas behind Organic Computing are delineated, together with a sparse sample of computational projects undertaken in this new field. Biological metaphors include evolution, neural networks, gene-regulatory networks, networks of brain modules, hormone system, insect swarms, and ant colonies. Applications are as diverse as system design, optimization, artificial growth, task allocation, clustering, routing, face recognition, and sign language understanding.

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.