This hard bound spinoff from a special issue of the Journal of Elasticity (volume 100: 1-2) features an English translation of an important 1955 paper by Walter Noll, Die Herteitung der Grundgleichungen der Thermomechanik der Kontinua aus der statistischen Mechanik. In this paper, Noll addresses and analyses the seminal paper of Irving and Kirkwood, published five years earlier, on The Statistical Mechanical Theory of Transport Processes. IV, The Equations of Hydrodynamics. Noll gives new interpretations and provides a firm setting for ideas advanced by Irving & Kirkwood that clearly and directly relate to the basic principles of continuum mechanics. However, the original German paper of Noll seems not to have gained the attention that it deserved as the field of statistical mechanics grew both fundamentally and in applications. By providing an English translation of Noll s paper, Lehoucq & Von Lilienfeld-Toal have provided a great service to the scientific community. The Noll translation is presented here to expose fundamental ideas of statistical mechanics that are of major importance in the modeling of small-scale behavior and its link to macroscopic observations. In recent years there has been a rapidly increasing reliance upon and interest in multi scale methods in computation. This has accentuated the need to establish meaningful connections between atomistic and continuum descriptions of contact interactions such as stress and heat flux. In recognition of Noll s contribution, the translation is accompanied by four relevant and invited papers, including one, entitled Thoughts on the Concept of Stress, by Noll himself.

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects.

This second edition includes more extended coverage of the classical andabstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added.

The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics.

Reviews of first edition:

"This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. Detailed solutions of the exercises are provided in an appendix." (L Enseignment Mathematique, Vol. 49 (1-2), 2003)

"The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises test the reader s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

"

This volume shows how collective magnetic excitations determine most of the magnetic properties of itinerant electron magnets. Previous theories were mainly restricted to the Curie-Weiss law temperature dependence of magnetic susceptibilities. Based on the spin amplitude conservation idea including the zero-point fluctuation amplitude, this book shows that the entire temperature and magnetic field dependence of magnetization curves, even in the ground state, is determined by the effect of spin fluctuations. It also shows that the theoretical consequences are largely in agreement with many experimental observations. The readers will therefore gain a new comprehensive perspective of their unified understanding of itinerant electron magnetism.

This book deals with the problem of dynamics of bodies with time-variable mass and moment of inertia. Mass addition and mass separation from the body are treated. Both aspects of mass variation, continual and discontinual, are considered. Dynamic properties of the body are obtained applying principles of classical dynamics and also analytical mechanics. Advantages and disadvantages of both approaches are discussed. Dynamics of constant body is adopted, and the characteristics of the mass variation of the body is included. Special attention is given to the influence of the reactive force and the reactive torque. The vibration of the body with variable mass is presented. One and two degrees of freedom oscillators with variable mass are discussed. Rotors and the Van der Pol oscillator with variable mass are displayed. The chaotic motion of bodies with variable mass is discussed too. To support learning, some solved practical problems are included.

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization.

Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition.

The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

This book presents a history of shock compression science, including development of experimental, material modeling, and hydrodynamics code technologies over the past six decades at Sandia National Laboratories. The book is organized into a discussion of major accomplishments by decade with over 900 references, followed by a unique collection of 45 personal recollections detailing the trials, tribulations, and successes of building a world-class organization in the field. It explains some of the challenges researchers faced and the gratification they experienced when a discovery was made. Several visionary researchers made pioneering advances that integrated these three technologies into a cohesive capability to solve complex scientific and engineering problems. What approaches worked, which ones did not, and the applications of the research are described. Notable applications include the turret explosion aboard the USS Iowa and the Shoemaker-Levy comet impact on Jupiter. The personal anecdotes and recollections make for a fascinating account of building a world-renowned capability from meager beginnings. This book will be inspiring to the expert, the non expert, and the early-career scientist. Undergraduate and graduate students in science and engineering who are contemplating different fields of study should find it especially compelling.

"Statics and Dynamics of Rigid Bodies" presents an interdisciplinary approach to mechanical engineering through a close evaluation of the statics and dynamics of rigid bodies, presenting a concise introduction to both. This volume bridges the gap of interdisciplinary published texts linking fields like mechatronics and robotics with multi-body dynamics in order to provide readers with a clear path to understanding numerous sub-fields of mechanical engineering. Three-dimensional kinematics, rigid bodies in planar spaces and numerous vector and matrix operations are presented in order to provide a comprehensive understanding of mechanics through dynamics and rigid bodies.

This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble's path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble. The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations.

This book addresses a range of basic and essential topics, selected from the author's teaching and research activities, offering a comprehensive guide in three parts: Statics, Kinematics and Kinetics. Chapter 1 briefly discusses the history of classical and modern mechanics, while Chapter 2, presents preliminary knowledge, preparing readers for the subsequent chapters. Chapters 3 to 7 introduce statics, force analysis, simplification of force groups, equilibrium of the general coplanar force group, and the center of the parallel force group. The Kinematics section (Chapters 8 to 10), covers the motion of a particle, basic motion and planar motion of a rigid body. Lastly, the Kinetics section (Chapters 11 to 14) explores Newton's law of motion, theorem of momentum, theorem of angular momentum, and theorem of kinetic energy. With numerous examples from engineering, illustrations, and step-by-step tutorials, the book is suitable for both classroom use and self-study. After completing the course, students will be able to simplify complex engineering structures and perform force and motion analyses on particles and structures, preparing them for further study and research. The book can be used as a textbook for undergraduate courses on fundamental aspects of theoretical mechanics, such as aerospace, mechanical engineering, petroleum engineering, automotive and civil engineering, as well as material science and engineering.

This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.

The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

1 Grundlagen der Dynamik regelungstechnischer Systeme.- 1.1 Allgemeine Zielsetzung der Regelungstechnik.- 1.2 Regelkreis.- 1.3 Voraussetzungen fur Blockorientierung und Regelkreisbildung.- 1.4 Aufgaben der Regelungstechnik.- 1.5 UEbertragungsfunktion und Regelungssystemtheorie.- 1.6 Anfangsbedingungen und Nullstellen der UEbertragungsfunktion.- 1.7 Ausgangssignal Xa(s) bei x a(k)(0?)=0.- 1.8 Nichtverschwindende Vorgeschichte xa(k)(0?)?0.- 1.9 Analyse im Spektralbereich. Verknupfung mehrerer Elemente.- 1.10 Regelstrecke und Stoergroessen.- 1.11 Einschleifiger Standardregelkreis.- 1.12 Sensitivitat.- 1.13 Differentielle Sensitivitat fur den Standardregelkreis.- 1.14 Linearisierung.- 1.15 Regelkreis im Signalflussdiagramm.- 1.16 Spezielle Elemente regelungstechnischer Systeme.- 1.16.1 Rationale UEbertragungselemente.- 1.16.2 Totzeit-Elemente.- 1.16.3 Allpass-Elemente.- 1.16.4 Laufzeitelemente.- 2 Regelkreisanalyse im Zeitbereich.- 2.1 Regelkreis-Reaktion auf einfache Signale.- 2.2 Mehrfache Polstellen von Xa(s).- 2.3 Naherung fur kleine Zeitwerte.- 2.4 Naherung fur grosse Zeitwerte.- 2.5 Faltungsintegral und Naherung durch Faltungssumme.- 2.6 Regelungen mit Totzeitelementen.- 3 Formulierung kontinuierlicher Regelungssysteme im Zustandsraum.- 3.1 Grundlagen.- 3.2 Transitionsmatrix (Fundamentalmatrix).- 3.3 Potenzreihenentwicklung der Transitionsmatrix.- 3.4 Zustandsregler. Fuhrungs- und Stoerungsverhalten.- 3.5 Vorfilterbemessung.- 4 Analyseverfahren im Frequenzbereich.- 4.1 Frequenzgang.- 4.2 Ortskurven des Frequenzgangs.- 4.3 Ortskurven von typischen stabilen Regelkreis-Element en.- 4.4 Ortskurven instabiler Regelkreiselemente.- 4.5 Frequenzgangsortskurve des Regelkreises.- 4.6 Ermittlung von Zeitbereichssignalen aus dem Frequenzbereich.- 4.7 Ermittlung des Frequenzganges aus der gemessenen Systemantwort.- 4.8 Bode-Diagramm.- 4.9 Phasenminimum-Beziehungen.- 4.10 Knickstellen der Regelschleife und des Regelkreises.- 4.11 H?-Norm einer UEbertragungsfunktion.- 5 Regelstrecken im Regelkreis.- 5.1 Antriebe. Allgemeines.- 5.2 Stromrichtergespeiste Gleichstromantriebe.- 5.3 Stromleitverfahren.- 5.4 Begrenzungsregelung.- 5.5 Kupplungselastizitat.- 5.6 Umrichtergespeiste Asynchronmaschine.- 5.7 Thermische Regelstrecken.- 5.7.1 Durchlauferhitzer, Warmetauscher.- 5.7.2 Kessel und Turbine.- 5.8 Hydraulische Regelstrecken.- 5.9 Pneumatische Regelstrecke.- 5.10 Mechanische Positionsregelstrecken.- 5.10.1 Einfache Fahrzeuglenkung.- 5.10.2 Balancierung.- 5.10.3 Passagierflugzeug.- 5.10.4 Raketenantrieb.- 5.11 Verfahrenstechnische Regelstrecken.- 5.12 Elektronische und nachrichtentechnische Regelstrecken.- 5.12.1 Verstarkungsausgleich.- 5.12.2 Scharfabstimmung.- 5.12.3 Zeilensynchronisierung.- 5.12.4 Rauschunterdruckung.- 5.13 Phase-Locked Loops (PLL).- 5.13.1 Phase-Locked Loop in analoger Ersatzrechnung.- 5.13.2 Regelungen an einem CD-Player.- 5.14 Schaltzeichen (Sinnbilder) fur technische Regelstrecken.- 5.15 Volkswirtschaftliche Regelungen.- 5.16 Physiologische und psychische Regelkreise.- 5.17 Soziologische Regelungen.- 6 Stellglieder und Verstarker.- 6.1 Stromrichterstellglieder.- 6.2 Umrichter fur Drehfeldmaschinen.- 6.3 Stellmotoren fur mechanische Positionierung.- 6.4 Stellglieder fur Flussigkeits-, Gasstroeme u. koernige Stoffe.- 6.5 Schaltzeichen fur Stellglieder und Verstarker.- 7 Regelungstechnischer Einsatz von Sensoren und Messumformern.- 7.1 Anforderungen.- 7.2 Messrauschen.- 7.3 Leistung eines Rauschsignales.- 8 Identifikationsverfahren.- 8.1 Auswertung der Sprungantwort von PDT1-Elementen.- 8.2 Auswertung der Sprungantwort von PT2-Elementen.- 8.3 Wendetangentenmethode bei PT2-Elementen.- 8.4 Auswertung der Sprungantwort von IT1-Elementen.- 8.5 Momentenmethode an der Gewichtsfunktion.- 8.6 Identifikation mit Hilfsregler.- 8.7 Identifikation mit fiktivem Serienelement.- 8.8 Regressionsanalyse. Quadratische Ausgleichsrechnung.- 9 Regler. Ausfuhrung und Dimensionierung.- 9.1 Operationsverstarker.- 9.2 Elektr

This book gives a detailed, up-to-date account of the Lense-Thirring effect and its implications for physics and astrophysics. Starting from a profound intuition of Lense and Thirring in 1918, based on a simple solution to the linearized Einstein field equations, this has emerged in the past four decades as a phenomenon of extraordinary importance in cosmology, radio jets in quasars, and the physics of neutron stars and black holes, besides leading to some of the most sophisticated experiments ever performed in the space surrounding our planet. The book contains the contributions presented at the "Third William Fairbank Meeting," which have been expanded by adding a complete set of classical and prominent contemporary papers on this subject and a general introduction by R Ruffini.

This book reviews the phenomenology displayed by relativistic jets as well as the most recent theoretical efforts to understand the physical mechanisms at their origin. Relativistic jets have been observed and studied in Active Galactic Nuclei (AGN) for about half a century and are believed to be fueled by accretion onto a supermassive black hole at the center of the host galaxy. Since the first discovery of relativistic jets associated with so-called "micro-quasars" much more recently, it has seemed clear that much of the physics governing the relativistic outflows in stellar X-ray binaries harboring black holes and in AGN must be common, but acting on very different spatial and temporal scales. With new observational and theoretical results piling up every day, this book attempts to synthesize a consistent, unified physical picture of the formation and disruption of jets in accreting black-hole systems. The chapters in this book offer overviews accessible not only to specialists but also to graduate students and astrophysicists working in other areas. Covered topics comprise Relativistic jets in stellar systems Launching of AGN jets Parsec-scale AGN jets Kiloparsec-scale AGN jets Black hole magnetospheres Theory of relativistic jets The structure and dynamics of the inner accretion disk The origin of the jet magnetic field X-ray observations, phenomenology, and connection with theory

This book discusses the design of new space missions and their use for a better understanding of the dynamical behaviour of solar system bodies, which is an active field of astrodynamics. Space missions gather data and observations that enable new breakthroughs in our understanding of the origin, evolution and future of our solar system and Earth's place within it. Covering topics such as satellite and space mission dynamics, celestial mechanics, spacecraft navigation, space exploration applications, artificial satellites, space debris, minor bodies, and tidal evolution, the book presents a collection of contributions given by internationally respected scientists at the summer school "Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics", held in 2017 at San Martino al Cimino, Viterbo (Italy). This school aimed to teach the latest theories, tools and methods developed for satellite dynamics and space, and as such the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

This volume presents the Proceedings of the 10th International Conference on Vibration Problems, 2011, Prague, Czech Republic. ICOVP 2011 brings together again scientists from different backgrounds who are actively working on vibration-related problems of engineering both in theoretical and applied fields, thus facilitating a lively exchange of ideas, methods and results between the many different research areas. The aim is that reciprocal intellectual fertilization will take place and ensure a broad interdisciplinary research field. The topics, indeed, cover a wide variety of vibration-related subjects, from wave problems in solid mechanics to vibration problems related to biomechanics. The first ICOVP conference was held in 1990 at A.C. College, Jalpaiguri, India, under the co-chairmanship of Professor M.M. Banerjee and Professor P. Biswas. Since then it has been held every 2 years at various venues across the World.

This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations. The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects - from systems with two degrees of freedom to three-dimensional continuous objects.

This work contains the proceedings of an International Astronomical Symposium devoted to the interactions between physics and dynamics in the solar system, especially with regard to the small bodies (asteroids, comets, meteors). These two topics were traditionally considered as almost independent, but their interactions are increasingly being reviewed as the key to an understanding of the formation and evolution of the solar system. For instance, the rotational dynamics of planets have a profound influence on their climate. On the other hand, a good understanding of the complicated dynamics of asteroids and the identification of families of bodies born from the break-up of a parent body may tell us much about the formation and the evolution of the solar system. All these, and several related questions are discussed in these proceedings, which should be of interest to both physicists and dynamicists.

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of "handouts" to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.

The study of mechanics is presented as the fundamental basis of the electromagnetic theory, quantum mechanics, and all theoretical physics. Mathematical difficulty and order of historical development have determined the order of presenting the material.

Vibro-impact dynamics has occupied a wide spectrum of studies by dyn- icists, physicists, and mathematicians. These studies may be classi?ed into three main categories: modeling, mapping and applications. The main te- niques used in modeling of vibro-impact systems include phenomenological modelings, Hertzian models, and non-smooth coordinate transformations- velopedbyZhuravlevandIvanov. Oneofthemostcriticalsituationsimpeded invibro-impactsystemsisthegrazingbifurcation. Grazingbifurcationisu- ally studied through discontinuity mapping techniques, which are very useful to uncover the rich dynamics in the process of impact interaction. Note the availablemappings arevalidonly intheabsenceofnon-impactnonlinearities. Complex dynamic phenomena of vibro-impact systems include subharmonic oscillations, chaotic motion, and coexistence of di?erent attractors for the sameexcitationand systemparametersbut under di?erent initial conditions. Selectedapplicationsofvibro-impactdynamics. Theseincludelumpedand continuous systems. Lumped systems cover a bouncing ball on an oscillating barrier, mass-spring-dashpot systems, normal and inverted pendulums, the spherical pendulum, the ship roll motion against icebergs, joints with fr- play, rotor-stator rubbing in rotating machinery, vocal folds, microactuators, strings, beams, pipes conveying ?uids with end-restraints, nuclear reactors and heat exchangers, and plates. These applications are discussed within the framework of the deterministic theory. Under random excitation the tre- ment requires special tools. The techniques of equivalent linearization and stochastic averaging have been applied to limited number of problems. One of the most bene?cial outcomesof vibro-impact dynamics is the development of impact dampers, which have witnessed signi?cant activities over the last four decades and have been used in several applications. On the other hand, vibro-impacthas detrimental e?ects on the operationsof mechanicalsystems and damage of pipes and rods in nuclear reactors.