The numerous applications of optimal control theory have given an incentive to the development of approximate techniques aimed at the construction of control laws and the optimization of dynamical systems. These constructive approaches rely on small parameter methods (averaging, regular and singular perturbations), which are well-known and have been proven to be efficient in nonlinear mechanics and optimal control theory (maximum principle, variational calculus and dynamic programming). An essential feature of the procedures for solving optimal control problems consists in the necessity for dealing with two-point boundary-value problems for nonlinear and, as a rule, nonsmooth multi-dimensional sets of differential equations. This circumstance complicates direct applications of the above-mentioned perturbation methods which have been developed mostly for investigating initial-value (Cauchy) problems. There is now a need for a systematic presentation of constructive analytical per turbation methods relevant to optimal control problems for nonlinear systems. The purpose of this book is to meet this need in the English language scientific literature and to present consistently small parameter techniques relating to the constructive investigation of some classes of optimal control problems which often arise in prac tice. This book is based on a revised and modified version of the monograph: L. D. Akulenko "Asymptotic methods in optimal control." Moscow: Nauka, 366 p. (in Russian)."

Problems involving synthesis of mathematical models of various physical systems, making use of these models in practice and verifying them qualitatively has - come an especially important area of research since more and more physical - periments are being replaced by computer simulations. Such simulations should make it possible to carry out a comprehensive analysis of the various properties of the system being modelled. Most importantly its dynamic properties can be - dressed in a situation where this would be difficult or even impossible to achieve through a direct physical experiment. To carry out a simulation of a real, phy- cally existing system it is necessary to have its mathematical description; the s- tem being described mathematically by equations, which include certain variables, their derivatives and integrals. If a single independent variable is sufficient in - der to describe the system, then derivatives and integrals with respect to only that variable will appear in the equations. Differentiation of the equation allows the integrals to be eliminated and produces an equation which includes derivatives with respect to only one independent variable i. e. an ordinary differential equation. In practice, most physical systems can be described with sufficient accuracy by linear differential equations with time invariant coefficients. Chapter 2 is devoted to the description of models by such equations, with time as the independent va- able.

Most practical processes such as chemical reactor, industrial furnace, heat exchanger, etc., are nonlinear stochastic systems, which makes their con trol in general a hard problem. Currently, there is no successful design method for this class of systems in the literature. One common alterna tive consists of linearizing the nonlinear dynamical stochastic system in the neighborhood of an operating point and then using the techniques for linear systems to design the controller. The resulting model is in general an approximation of the real behavior of a dynamical system. The inclusion of the uncertainties in the model is therefore necessary and will certainly improve the performance of the dynamical system we want to control. The control of uncertain systems has attracted a lot of researchers from the control community. This topic has in fact dominated the research effort of the control community during the last two decades, and many contributions have been reported in the literature. Some practical dynamical systems have time delay in their dynamics, which makes their control a complicated task even in the deterministic case. Recently, the class ofuncertain dynamical deterministic systems with time delay has attracted some researchers, and some interesting results have been reported in both deterministic and stochastic cases. But wecan't claim that the control problem ofthis class ofsystems is completely solved; more work must be done for this class of systems.

Random Vibration in Spacecraft Structures Design is based on the lecture notes "Spacecraft structures" and "Special topics concerning vibration in spacecraft structures" from courses given at Delft University of Technology. The monograph, which deals with low and high frequency mechanical, acoustic random vibrations is of interest to graduate students and engineers working in aerospace engineering, particularly in spacecraft and launch vehicle structures design.

This book presents the latest research results in the area of applied nonlinear dynamics and chaos theory. Papers by three academic generations address new applications of nonlinear dynamics to mechanics, including fluid-structure interaction, machining and mechanics of solids, and many other applications.

This volume covers the interdisciplinary field of disaster mitigatition against earthquakes with special emphasis on prevention of total collapse of existing low rise buildings towards reduction of life losses and economical assets. Rehabilitation of thousands of low-rise buildings in many big cities located in earthquake prone areas, is practically impossible even though there are experimentally and analytically approved intervention techniques to protect these existing buildings. It is simply not possible to find a proper way and proper amount of financial support to do this job. It will be more realistic to change the target to be achieved in a relatively short time, especially if time shortage starts to become the most critical issue. The new target can be specified as the prevention of total collapse of low-rise low-cost existing buildings, at least to save as much lives and property as possible. Simple prescriptive techniques, which can be implemented by the building owners, should be prepared. The cost of the improvement techniques, all kinds of legal, economical and social issues for convincing people, and promotions such as tax exemptions should be discussed in detail. Writers of all chapters are leading researchers and engineers working in the field of structural and earthquake engineering. The book will start with an introduction chapter written by Prof. Helmut Krawinkler of Stanford University. In this chapter, past and present of studies towards seismically safe design and construction will be introduced, as well as potential future trends in structural and earthquake engineering. In other chapters, different subjects will be presented under three main titles, namely; determination of seismic risks, seismic safety assessment of existing buildings, and measures for prevention of total collapse.

How is free will possible in the light of the physical and chemical underpinnings of brain activity and recent neurobiological experiments? How can the emergence of complexity in hierarchical systems such as the brain, based at the lower levels in physical interactions, lead to something like genuine free will? The nature of our understanding of free will in the light of present-day neuroscience is becoming increasingly important because of remarkable discoveries on the topic being made by neuroscientists at the present time, on the one hand, and its crucial importance for the way we view ourselves as human beings, on the other. A key tool in understanding how free will may arise in this context is the idea of downward causation in complex systems, happening coterminously with bottom up causation, to form an integral whole. Top-down causation is usually neglected, and is therefore emphasized in the other part of the book's title. The concept is explored in depth, as are the ethical and legal implications of our understanding of free will. This book arises out of a workshop held in California in April of 2007, which was chaired by Dr. Christof Koch. It was unusual in terms of the breadth of people involved: they included physicists, neuroscientists, psychiatrists, philosophers, and theologians. This enabled the meeting, and hence the resulting book, to attain a rather broader perspective on the issue than is often attained at academic symposia. The book includes contributions by Sarah-Jayne Blakemore, George F. R. Ellis , Christopher D. Frith, Mark Hallett, David Hodgson, Owen D. Jones, Alicia Juarrero, J. A. Scott Kelso, Christof Koch, Hans Kung, Hakwan C. Lau, Dean Mobbs, Nancey Murphy, William Newsome, Timothy O'Connor, Sean A.. Spence, and Evan Thompson.

The paradigm of complexity is pervading both science and engineering, le- ing to the emergence of novel approaches oriented at the development of a systemic view of the phenomena under study; the de?nition of powerful tools for modelling, estimation, and control; and the cross-fertilization of di?erent disciplines and approaches. One of the most promising paradigms to cope with complexity is that of networked systems. Complex, dynamical networks are powerful tools to model, estimate, and control many interesting phenomena, like agent coordination, synch- nization, social and economics events, networks of critical infrastructures, resourcesallocation, informationprocessing, controlovercommunicationn- works, etc. Advances in this ?eld are highlighting approaches that are more and more oftenbasedondynamicalandtime-varyingnetworks, i.e.networksconsisting of dynamical nodes with links that can change over time. Moreover, recent technological advances in wireless communication and decreasing cost and size of electronic devices are promoting the appearance of large inexpensive interconnected systems, each with computational, sensing and mobile ca- bilities. This is fostering the development of many engineering applications, which exploit the availability of these systems of systems to monitor and control very large-scale phenomena with ?ne resoluti

Performance-based Earthquake Engineering has emerged before the turn of the century as the most important development in the field of Earthquake Engineering during the last three decades. It has since then started penetrating codes and standards on seismic assessment and retrofitting and making headway towards seismic design standards for new structures as well. The US have been a leader in Performance-based Earthquake Engineering, but also Europe is a major contributor. Two Workshops on Performance-based Earthquake Engineering, held in Bled (Slovenia) in 1997 and 2004 are considered as milestones. The ACES Workshop in Corfu (Greece) of July 2009 builds on them, attracting as contributors world-leaders in Performance-based Earthquake Engineering from North America, Europe and the Pacific rim (Japan, New Zealand, Taiwan, China). It covers the entire scope of Performance-based Earthquake Engineering: Ground motions for performance-based earthquake engineering; Methodologies for Performance-based seismic design and retrofitting; Implementation of Performance-based seismic design and retrofitting; and Advanced seismic testing for performance-based earthquake engineering. Audience: This volume will be of interest to scientists and advanced practitioners in structural earthquake engineering, geotechnical earthquake engineering, engineering seismology, and experimental dynamics.

Time series with mixed spectra are characterized by hidden periodic components buried in random noise. Despite strong interest in the statistical and signal processing communities, no book offers a comprehensive and up-to-date treatment of the subject. Filling this void, Time Series with Mixed Spectra focuses on the methods and theory for the statistical analysis of time series with mixed spectra. It presents detailed theoretical and empirical analyses of important methods and algorithms. Using both simulated and real-world data to illustrate the analyses, the book discusses periodogram analysis, autoregression, maximum likelihood, and covariance analysis. It considers real- and complex-valued time series, with and without the Gaussian assumption. The author also includes the most recent results on the Laplace and quantile periodograms as extensions of the traditional periodogram. Complete in breadth and depth, this book explains how to perform the spectral analysis of time series data to detect and estimate the hidden periodicities represented by the sinusoidal functions. The book not only extends results from the existing literature but also contains original material, including the asymptotic theory for closely spaced frequencies and the proof of asymptotic normality of the nonlinear least-absolute-deviations frequency estimator.

This book presents 53 independently reviewed papers which embody the latest advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automation, surgery, locomotion and biomechanics. Methods used include line geometry, quaternion algebra, screw algebra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The contributors are recognised authorities in robot kinematics.

A very complete survey of different approaches adopted by Eastern and Western countries for the disposal of surplus ammunition. Incineration and other techniques for the disposal of high explosives, gun and rocket propellants are introduced and discussed in relation to environmental and safety requirements. Proposals for and examples of the re-use of military explosives in commercial applications are given. Topics discussed range from the conversion of energetic systems into chemical raw materials to the new development of energetic systems with special features for commercial use (such as producing artificial diamonds by detonation, self-propagating high-temperature synthesis, fire extinguishing, etc.).

The purpose of this book is to provide students, practicing engineers and scientists with a treatment of nonlinear phenomena occurring in physical systems. Although only mechanical models are used, the theory applies to all physical systems governed by the same equations, so that the book can be used to study nonlinear phenomena in other branches of engineering, such as electrical engineering and aerospace engineering, as well as in physics. The book consists of two volumes. Volume I is concerned with single degree-of-freedom systems and it presents the fundamental concepts of nonlinear analysis. Both analytical methods and computer simulations are included. The material is presented in such a manner that the book can be used as a graduate as well as an undergraduate textbook. Volume II deals with multi-degree-of-freedom systems. Following an introduc tion to linear systems, the volume presents fundamental concepts of geometric theory and stability of motion of general nonlinear systems, as well as a concise discussion of basic approximate methods for the response of such systems. The material represents a generalization of a series of papers on the vibration of nonlinear multi-degree-of-freedom systems, some of which were published by me and my associates during the period 1965 - 1983 and some are not yet published."

Basic models and concepts of machine dynamics and motion control are presented in the order of the principal steps of machine design. The machine is treated as a coupled dynamical system, including drive, mechanisms and controller, to reveal its behavior at different regimes through the interaction of its units under dynamic and processing loads. The main dynamic effects in machines are explained. The influence of component compliances on accuracy, stability and efficiency of the machines is analyzed. Methods for decreasing internal and external vibration activity of machines are described. The dynamic features of digital control are considered. Special attention is given to machines with intense dynamic behavior: resonant and hand-held percussion ones. Targeted to engineers as well as to lecturers and advanced students.

The interest of the media in dust explosions increased considerably following two major grain-elevator disasters in the United States in 1979. However, these were not isolated incidents and were statistically unusual only in the high loss of life involved. Any oxidizable material that is dispersed in fine powder form may be explosive, and ignition sources with sufficient energy to ignite a dust cloud are easily produced in normal industrial processing. Dust fires and minor incidents are not uncommon in many industries, but fortunately the combination of events and circumstances that must coincide for a large-scale explosion arise only rarely. Nevertheless, this is often more by luck than by good management and many potentially hazardous situations are common in industry. An explosive dust cloud and the circumstances in which it can ignite are not as simple to define as the equivalent situation in gases or flammable vapors. A large number of definitions and experimental tests have been devised to characterize the explosibility of dusts and ignition sources. The aim of this book is to provide a guide describing conditions in industry that could lead to dust explosions and the means to avoid them. Ignition sources and the way in which they can arise in powder processing are discussed and illustrated by case histories of reported incidents. The methods by which the potential hazards of a process or product can be evaluated are described, with special attention paid to the interpretation of the results of the different experimental methods.

Intended for engineers who deal with vibrations of rods and shells in their everyday practice but who also wish to understand the subject from the mathematical point-of-view, the results contained here concerning high-frequency vibrations may be new to many. The book serves equally well as an advanced textbook, while remaining of interest to mathematicians who seek applications of the variational and asymptotic methods in elasticity and piezoelectricity. Only a minimum knowledge in advanced calculus and continuum mechanics is assumed on the part of the reader.

This short but complicated book is very demanding of any reader. The scope and style employed preserve the nature of its subject: the turbulence phe nomena in gas and liquid flows which are believed to occur at sufficiently high Reynolds numbers. Since at first glance the field of interest is chaotic, time-dependent and three-dimensional, spread over a wide range of scales, sta tistical treatment is convenient rather than a description of fine details which are not of importance in the first place. When coupled to the basic conserva tion laws of fluid flow, such treatment, however, leads to an unclosed system of equations: a consequence termed, in the scientific community, the closure problem. This is the central and still unresolved issue of turbulence which emphasizes its chief peculiarity: our inability to do reliable predictions even on the global flow behavior. The book attempts to cope with this difficult task by introducing promising mathematical tools which permit an insight into the basic mechanisms involved. The prime objective is to shed enough light, but not necessarily the entire truth, on the turbulence closure problem. For many applications it is sufficient to know the direction in which to go and what to do in order to arrive at a fast and practical solution at minimum cost. The book is not written for easy and attractive reading."

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape centsn, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape centsn. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1

The subject of random vibrations of elastic systems has gained, over the past decades, great importance, specifically due to its relevance to technical problems in hydro- and aero-mechanics. Such problems involve aircraft, rockets and oil-drilling platforms; elastic vibrations of structures caused by acoustic radiation of a jet stream and by seismic disturbances must also be included. Appli cations of the theory of random vibrations are indeed numerous and the development of this theory poses a challenge to mathematicians, mechanicists and engineers. Therefore, a book on random vibrations by a leading authority such as Dr. V.V. Bolotin must be very welcome to anybody working in this field. It is not surprising that efforts were soon made to have the book translated into English. With pleasure I acknowledge the co-operation of the very competent translater, I Shenkman; of Mrs. C. Jones, who typeJ the first draft; and of Th. Brunsting, P. Keskikiikonen and R. Piche, who read it and suggested where required, corrections and changes. I express my gratitude to Martinus Nijhoff Publishers BV for entrust ing me with the task of editing the English translation, and to F.J. van Drunen, publishers of N. Nijhoff Publishers BV, who so kindly supported my endeavours. Special acknowledgement is due to Mrs. L. Strouth, Solid Mechanics Division, University of Waterloo, for her competent and efficient preparation of the final manuscript."

As robots are becoming more and more sophisticated the interest in robot dynamics is increasing. Within this field, contact problems are among the most interesting, since contacts are present in almost any robot task and introduce serious complexity to system dynamics, strongly influencing robot behavior. The book formulates dynamic models of robot interaction with different kinds of environment, from pure geometrical constraints to complex dynamic environments. It provides a number of examples. Dynamic modeling is the primary interest of the book but control issues are treated as well. Because dynamics and contact control tasks are strongly related the authors also provide a brief description of relevant control issues.
The book will be of interest to engineers working in research and development in robotics and automation and to both graduate and postgraduate students. The work will also be valuable to readers involved in manufacturing, robotics, automation, computer and control engineering.

Optical Microscanners and Microspectrometers using Thermal Bimorph Actuators shows how to design and fabricate optical microsystems using innovative technologies and and original architectures. A barcode scanner, laser projection mirror and a microspectrometer are explained in detail, starting from the system conception, discussing simulations, choice of cleanroom technologies, design, fabrication, device test, packaging all the way to the system assembly.

An advanced microscanning device capable of one- and two-dimensional scanning can be integrated in a compact barcode scanning system composed of a laser diode and adapted optics. The original design of the microscanner combines efficiently the miniaturized thermal mechanical actuator and the reflecting mirror, providing a one-dimensional scanning or an unique combination of two movements, depending on the geometry. The simplicity of the device makes it a competitive component.

The authors rethink the design of a miniaturized optical device and find a compact solution for a microspectrometer, based on a tunable filter and a single pixel detector. A porous silicon technology combines efficiently the optical filter function with a thermal mechanical actuator on chip. The methodology for design and process calibration are discussed in detail. The device is the core component of an infrared gas spectrometer.

0.1 The partial differential equation (1) (Au)(x) = L aa(x)(Dau)(x) = f(x) m lal9 is called elliptic on a set G, provided that the principal symbol a2m(X, ) = L aa(x) a lal=2m of the operator A is invertible on G X (~n \ 0); A is called elliptic on G, too. This definition works for systems of equations, for classical pseudo differential operators ("pdo), and for operators on a manifold n. Let us recall some facts concerning elliptic operators. 1 If n is closed, then for any s E ~ , is Fredholm and the following a priori estimate holds (2) 1 2 Introduction If m > 0 and A : C=(O; C') -+ L (0; C') is formally self - adjoint 2 with respect to a smooth positive density, then the closure Ao of A is a self - adjoint operator with discrete spectrum and for the distribu- tion functions of the positive and negative eigenvalues (counted with multiplicity) of Ao one has the following Weyl formula: as t -+ 00, (3) n 2m = t / II N+-(1,a2m(x,e))dxde T*O\O (on the right hand side, N+-(t,a2m(x,e))are the distribution functions of the matrix a2m(X,e) : C' -+ CU).

This book explores two important aspects of the optimal control of oscillatory systems: the initiation of optimal oscillatory regimes and control possibilities for random disturbances. The main content of the book is based upon assertions of the optimal control theory and the disturbance theory. All theoretical propositions are illustrated by examples with exact mechanical context. An appendix covers the necessary mathematical prerequisites.

At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.