Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!

This volume provides valuable insight into diverse topics related to mechanical engineering and presents state-of-the-art work on sustainable development being carried out throughout the world by budding researchers and scientists. Divided into three sections, the volume covers machine design, materials and manufacturing, and thermal engineering. It presents innovative research work on machine design that is of relevance to such varied fields as the automotive industry, agriculture, and human anatomy. The second section addresses materials characterization, an important tool in assessing proper materials for application-oriented jobs, and emerging unconventional machining processes that are important in design engineering for new products and tools. The section on thermal engineering broadly covers the use of viable alternate fuels, such as HHO, biodiesel, etc., with the objective of reducing the burden on petroleum reserves and the environment.

Starting from an undergraduate level, this book systematically develops the basics of * Calculus on manifolds, vector bundles, vector fields and differential forms, * Lie groups and Lie group actions, * Linear symplectic algebra and symplectic geometry, * Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

This book covers main properties of the excitation spectrum in superfluid 4He and the thermodynamics determined by the spectrum. It deals with hydrodynamics and describes that quantitative results should be insignificantly modified with processes of phonon decay taken into account.

Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such systems? Written by international experts, Nonlinear Dynamics and Chaos: Where Do We Go from Here? assesses what the future holds for dynamics and chaos. The chapters address one or more of the broad and interconnected main themes: neural and biological systems, spatially extended systems, and experimentation in the physical sciences. The contributors offer suggestions as to what they see as the way forward, often in the form of open questions for future research.

The book gives a general introduction to classical theoretical physics, in the fields of mechanics, relativity and electromagnetism. It is analytical in approach and detailed in the derivations of physical consequences from the fundamental principles in each of the fields. The book is aimed at physics students in the last year of their undergraduate or first year of their graduate studies.The text is illustrated with many figures, most of these in color. There are many useful examples and exercises which complement the derivations in the text.

This book is a collection of research papers selected for presentation at the International Conference on Smart Computational Methods in Continuum Mechanics 2021, organized by Moscow Institute of Physics and Technology and the Institute for Computer Aided Design of Russian Academy of Sciences. The work is presented in two volumes. The primary objective of the book is to report the state-of-the-art on smart computational paradigms in continuum mechanics and explore the use of artificial intelligence paradigms such as neural nets and machine learning for improving the performance of the designed engineering systems. The book includes up-to-date smart computational methods which are used to solve problems in continuum mechanics, engineering, seismic prospecting, non-destructive testing, and so on. The main features of the book are the research papers on the application of novel smart methods including neural nets and machine learning, computational algorithms, smart software systems, and high-performance computer systems for solving complex engineering problems. The case studies pertaining to the real-world applications in the above fields are included. The book presents a collection of best research papers in English language from some of the world leaders in the field of smart system modelling and design of engineering systems.

Originally published in 1980. More so than any other energy resource, nuclear power has the capacity to provide much of our energy needs but is highly controversial. This book discusses the major British decisions in the civil nuclear field, and the way they were made, between 1953 and 1978. It spans the period between the decision to construct Calder Hall - claimed as the world's first nuclear power station - and the Windscale Inquiry - claimed as the world's most thorough study of a nuclear project. For the period up to 1974 this involves a study of the internal processes of British central government. The private issues include the technical selection of nuclear reactors, the economic arguments about nuclear power and the political clashes between institutions and individuals. The public issues concern nuclear safety and the environment and the rights and opportunities for individuals and groups to protest about nuclear development. The book demonstrates that British civil nuclear power decision making had many shortcomings and concludes that it was hampered by outdated political and administrative attitudes and machinery and that some of the central issues in the nuclear power debate were misunderstood by the decision makers themselves.

Originally published in 1981. Examining in detail the best evidence on the likely level of domestic and overseas demand for British coal over the following 20 years, this study raised questions about the declared development and investment strategy of the National Coal Board. It exposes a central dilemma facing both the management and the unions of the British coal industry consequent upon their commitment to production objectives substantially out of line with likely market opportunities. It also poses questions for government and the EEC regarding the industry's finances and market prospects. The study concludes that Britain is unlikely to need both the scale of investment proposed for the coal industry and the nuclear programme endorsed by both the government and the electricity supply industry. The author argues for a rigorous reinterpretation of the prospects and a revision of the plans of Western Europe's largest coal industry. This is a fascinating snapshot of a changing industry and is interesting to those in geography, economics and industrial management and anyone interested in energy.

Originally published in 1988. This book considers why some public policies succeed and others do not. It looks at the entrepreneurial process that creates public policies and examines whether they prosper or falter because of their political consequences. The programs and personnel of the Atomic Energy Commission are the empirical foundation for these arguments. The data generated by that agency's annual budget-making cycles, collected over time and organised by program, are used as evidence to test some propositions about policy formation within the executive branch of government. The author's concern is with questions of where and how priorities are established in a complex institutional environment. To answer the more fundamental causal question of why some programs prosper while others wither or die, use is made of more historical analysis and comparison of the fortunes of several of AEC's efforts to develop applied nuclear technology.

This book gives state-of-the-art information about recent developments in the field of computational modeling of solid materials at finite strains. It contains papers presented at the IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains. Today, computational methods and simulation techniques play a central role in advancing the understanding of complex material behavior. Material behavior is nowadays modeled in the strongly nonlinear range by taking into account finite strains, complex hysteresis effect, fracture phenomena and multiscale features. Progress in this field is of fundamental importance for many engineering disciplines, especially those concerned with material testing, safety, reliability and serviceability analyses of engineering structures. This book summarizes recent progress in the modeling of solid materials undergoing deformations large strains, where the mathematical and computational analysis is highly challenging due to the nonlinear geometry. A further key aspect of the volume is the modeling of multiscale characteristics of materials by homogenization approaches and variational methods. The volume provides a state of the art survey about theoretical and computational approaches to (i) modeling of large-strain elastic and inelastic deformations of solids on different length scales, (ii) mathematical analysis of finite inelastic deformations of solids based on incremental variational formulations for non-convex problems with microstructure developments and (iii) homogenization methods for the determination of effective overall properties of heterogeneous materials. The book allows researchers and engineers to get an excellent overview aboutthe computational methods for solid materials at finite strains.

What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n < m. For continuous time systems, the evolution rule may be a differential eq- tion: to each state x G M one associates the speed and direction in which the system is going to evolve from that state. This corresponds to a vector field X(x) in the phase space. Assuming the vector field is sufficiently regular, for instance continuously differentiable, there exists a unique curve tangent to X at every point and passing through x: we call it the orbit of x.

With a focus on modified gravity this book presents a review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. General Relativity and the CDM framework are currently the standard lore and constitute the concordance paradigm of cosmology. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology in the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. In this review all extended theories and scenarios are first examined under the light of theoretical consistency, and are then applied in various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology has been able to offer in the last two decades. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature, allowing readers to get a clear overview of the state of the art and where the field of modified gravity is likely to go. This work was performed in the framework of the COST European Action "Cosmology and Astrophysics Network for Theoretical Advances and Training Actions" - CANTATA.

The aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject -tensor, and can be used in many fields of research. Special applications are discussed in the book, to remove any confusion, and for absolute understanding of the subject. In most books, they emphasize only the theoretical development, but not the methods of presentation, to develop concepts. Without knowing how to change the dummy indices, or the real indices, the concept cannot be understood. This book takes it down a notch and simplifies the topic for easy comprehension. Features Provides a clear indication and understanding of the subject on how to change indices Describes the original evolution of symbols necessary for tensors Offers a pictorial representation of referential systems required for different kinds of tensors for physical problems Presents the correlation between critical concepts Covers general operations and concepts

This book deals with some recent advances in conservation laws and energy release rates. Unlike their conventional applications in Fracture Mechanics for single crack problems, the contents of this book are mainly concemed with the conservation lawsand energy release rates insomerelatively complex problems, i. e. , strongly interacting cracks, microcrack damage, and microcrack shielding problems in f ive kinds of materiaIs, respectively. The five kinds of materials involve four traditional structural materiaIs: brittIe solids, metallceramic bi- materiaIs, anisotropic elastic solids, and dissimilar anisotropic solids; and one functional material: piezoelectric ceramics. Although this book starts from the original concepts of the Jk vector, the Mintegral, and the L integral in sin- gle crack problems proposed by Eshelby (1956, 1970, 1975), Rice (1968a,b), Knowies and Stemberg (1972), Budiansky and Rice (1973), Berges (1974), Freund (1978), Cherepanov (1974, 1979), and Herrman and Herrman (1981), etc. , the extension from investigations of single crack problems to those of multiple crack interacting problems or microcrack damage problems is based on the author's (andlor co-workers) works published in recent years. From detailed manipulations and numerical examinations the author would like to show readers some new insights of the conservation laws and energy release rates. Readers will see that although these 'old' concepts were established more than 30 or 40 years ago, they play a quite important role in multiple crack interacting problems or microcrack damage problems of both structural and functional materials.

This book compiles historical notes and a review of the work of the author and his associates on shock compression of condensed matter (SCCM). The work includes such topics as foundational aspects of SCCM, thermodynamics, thermodynamics of defects, and plasticity as they relate to shock compression, shock-induced phase transition, and shock compaction. Also included are synthesis of refractory and hard ceramic compounds such as Ni aluminides, SiC and diamonds, method of characteristics, discrete element methods, the shock compression process at the grain scale, and modeling shock-to-detonation transition in high explosives. The book tells the story of how the author's view of shock physics came to be where it is now. and analytically discusses how the author's appreciation of shock waves has evolved in time. It offers a personal but pedagogical perspective on SCCM for young scientists and engineers who are starting their careers in the field. For experts it offers materials to nudge them reflect on their own stories, with the hope of planting a seed of motivation to write them down to be published.

Rhythms permeate our everyday lives: they animate our bodies, and structure our experience of day and night and the seasons, time patterns of work and leisure, and the temporal organisation of mundane routine activities. Rhythms are also intrinsically about flows of energy - heat, light, motion - that run through the world, from the smallest movements of muscles, to the petrol fuelled patterns of the rush hour, the spinning of wind turbines and shifting cycles of solar radiation. Energy and Rhythm in Society sets out to energise the rhythm in Lefebvre's 'Rhythmanalysis' in order to develop a novel and far reaching polyrhythmic theorisation and exemplification of our collective living with energy in its many natural and technological forms and flows. Through so doing, it also provides a distinctive understanding of the urgent challenges and possibilities of transforming future energy systems and energy uses into more just and lower carbon configurations.

This volume collects the edited and reviewed contribution presented in the 9th iTi Conference that took place virtually, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. In the present book, the contributions have been structured according to the topics: I Experiments II Simulations and Modelling III Data Processing and Scaling IV Theory V Miscellaneous topics

This book offers a timely review of wave energy and its conversion mechanisms. Written having in mind current needs of advanced undergraduates engineering students, it covers the whole process of energy generation, from waves to electricity, in a systematic and comprehensive manner. Upon a general introduction to the field of wave energy, it presents analytical calculation methods for estimating wave energy potential in any given location. Further, it covers power-take off (PTOs), describing their mechanical and electrical aspects in detail, and control systems and algorithms. The book includes chapters written by active researchers with vast experience in their respective filed of specialization. It combines basic aspects with cutting-edge research and methods, and selected case studies. The book offers systematic and practice-oriented knowledge to students, researchers, and professionals in the wave energy sector. Chapters 17 of this book is available open access under a CC BY 4.0 license at link.springer.com

This textbook introduces readers to the detailed and methodical resolution of classical and more recent problems in analytical mechanics. This valuable learning tool includes worked examples and 40 exercises with step-by-step solutions, carefully chosen for their importance in classical, celestial and quantum mechanics. The collection comprises six chapters, offering essential exercises on: (1) Lagrange Equations; (2) Hamilton Equations; (3) the First Integral and Variational Principle; (4) Canonical Transformations; (5) Hamilton - Jacobi Equations; and (6) Phase Integral and Angular Frequencies Each chapter begins with a brief theoretical review before presenting the clearly solved exercises. The last two chapters are of particular interest, because of the importance and flexibility of the Hamilton-Jacobi method in solving many mechanical problems in classical mechanics, as well as quantum and celestial mechanics. Above all, the book provides students and teachers alike with detailed, point-by-point and step-by-step solutions of exercises in Lagrangian and Hamiltonian mechanics, which are central to most problems in classical physics, astronomy, celestial mechanics and quantum physics.

This book focuses on the way in which the problem of the motion of bodies has been viewed and approached over the course of human history. It is not another traditional history of mechanics but rather aims to enable the reader to fully understand the deeper ideas that inspired men, first in attempting to understand the mechanisms of motion and then in formulating theories with predictive as well as explanatory value. Given this objective, certain parts of the history of mechanics are neglected, such as fluid mechanics, statics and astronomy after Newton. On the other hand, due attention is paid, for example, to the history of thermodynamics, which has its own particular point of view on motion. Inspired in part by historical epistemology, the book examines the various views and theories of a given historical period (synchronic analysis) and then makes comparisons between different periods (diachronic analysis). In each period, one or two of the most meaningful contributions are selected for particular attention, instead of presenting a long inventory of scientific achievements.

Biofuels and food are dependent on the same resources for production: land, water, and energy. The conjuncture of food, energy, and climate crises demands a new direction in how to harness agriculture to the joint tasks of energy-saving, emissions reduction, and food security. Global Economic and Environmental Aspects of Biofuels focuses on the all-important question of the efficacy of biofuels as a solution to the global energy problem. Written by a distinguished team from five countries and multiple disciplines including agronomy, petroleum engineering, ecology, and meteorology, the book addresses the use of biofuels produced from crops and various organic materials as alternatives or supplements to petroleum. Key Features Discusses biofuels within the context of the world population problem, food, malnutrition, resource depletion, and climate change Asks the critical question whether the production of ethanol from corn, sugar cane, crop residues, and other organic materials has proven too costly in both economic and environmental terms Analyzes the uses and interdependencies among land, water, and fossil energy resources in food versus biofuel production Includes case studies on the economic and environmental impacts of biofuel production and use from the United States, Europe, Brazil, and tropical environments Explores the future production of biodiesel and ethanol from salt-water algae and tropical palms, while recognizing the technological problems that must be resolved in processing these materials This book examines key environmental and economic issues associated with the production of ethanol as a fuel, from corn, sugar cane, crop residues, and other organic materials. It brings together the opinions of a number of U.S. scientists and experts from Spain, Italy, the United Kingdom, and Brazil, and highlights the remarkable agreement among the contributors on the pros and cons of biofuels as an answer to future petroleum shortages. This mix of contributors and opinions presents a well-rounded view of the subject that puts a spotlight on unresolved concerns and complexities that are often overlooked.