In this book we describe the evolution of Classical Mechanics from Newton's laws via Lagrange's and Hamilton's theories with strong emphasis on integrability versus chaotic behavior.In the second edition of the book we have added historical remarks and references to historical sources important in the evolution of classical mechanics.

In this book we describe the evolution of Classical Mechanics from Newton's laws via Lagrange's and Hamilton's theories with strong emphasis on integrability versus chaotic behavior.In the second edition of the book we have added historical remarks and references to historical sources important in the evolution of classical mechanics.

Advances in Petrochemical Engineering and Green Development is a compilation of selected papers from the 3rd International Conference on Petrochemical Engineering and Green Development (ICPEGD 2022) and focuses on the research of petrochemical engineering. The proceedings features the most cutting-edge research directions and achievements related to geology and green development. Subjects in this proceedings include: Petroleum and Petrochemical Engineering Fossil Technologies Oil & Gas Production Renewable Energy Sources and Technology Green Synergy Innovation Urban Crisis Management The collection of papers in this proceedings will promote the development of petrochemical industry and energy, resource sharing, flexibility and high efficiency. Thereby, it will promote scientific information interchange between scholars from top universities, research centers and high-tech enterprises working all around the world.

Essential Dynamics & Relativity provides students with an introduction to the core aspects of dynamics and special relativity. The author reiterates important ideas and terms throughout and covers concepts that are often missing from other textbooks at this level. He also places each topic within the wider constructs of the theory, without jumping from topic to topic to illustrate a point. The first section of the book focuses on dynamics, discussing the basic aspects of single particle motion and analyzing the motion of multi-particle systems. The book also explains the dynamical behavior of both composite bodies (rigid bodies) and objects in non-inertial frames of reference (rotating reference frames). The second section concentrates on relativity. The author describes the ideas leading to the inception of special relativity. He also formulates fundamental aspects, such as time dilation, length contraction, Lorentz transformations, and the visual aids of Minkowski diagrams, necessary to develop more sophisticated ideas. He then develops the concepts within the context of relativistic mechanics. With many examples throughout and exercises at the end of each chapter, this text makes the often daunting and confusing ideas of dynamics and special relativity accessible to undergraduate students studying the subjects for the first time.

These lecture notes cover Classical Mechanics at the level of second-year undergraduates. The book offers comprehensive as well as self-contained material that can be taught in a one-semester course for students with the minimal background knowledge acquired in preuniversity education or in the usual first-year overview. The presentation does not skip the technical details which renders the book particularly well-suited for the self-studying student.

These lecture notes cover Classical Mechanics at the level of second-year undergraduates. The book offers comprehensive as well as self-contained material that can be taught in a one-semester course for students with the minimal background knowledge acquired in preuniversity education or in the usual first-year overview. The presentation does not skip the technical details which renders the book particularly well-suited for the self-studying student.

Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author 's research group over the past forty years at the Chinese Academy of Sciences.

The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields.

Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

This book offers the first comprehensive introduction to the optical properties of the catenary function, and includes more than 200 figures. Related topics addressed here include the photonic spin Hall effect in inhomogeneous anisotropic materials, coupling of evanescent waves in complex structures, etc. After familiarizing readers with these new physical phenomena, the book highlights their applications in plasmonic nanolithography, flat optical elements, perfect electromagnetic absorbers and polarization converters. The book will appeal to a wide range of readers: while researchers will find new inspirations for historical studies combining mechanics, mathematics, and optics, students will gain a wealth of multidisciplinary knowledge required in many related areas. In fact, the catenary function was deemed to be a "true mathematical and mechanical form" in architecture by Robert Hooke in the 1670s. The discovery of the mathematical form of catenaries is attributed to Gottfried Leibniz, Christiaan Huygens and Johann Bernoulli in 1691. As the founders of wave optics, however, Hooke and Huygens did not recognize the importance of catenaries in optics. It is only in recent decades that the link between catenaries and optics has been established.

We lift a veil of obscurity from a branch of mathematical physics in a straightforward manner that can be understood by motivated and prepared undergraduate students as well as graduate students specializing in relativity. Our book on 'Einstein Fields' clarifies Einstein's very first principle of equivalence (1907) that is the basis of his theory of gravitation. This requires the exploration of homogeneous Riemannian manifolds, a program that was suggested by Elie Cartan in 'Riemannian Geometry in an Orthogonal Frame,' a 2001 World Scientific publication.Einstein's first principle of equivalence, the key to his General Relativity, interprets homogeneous fields of acceleration as gravitational fields. The general theory of these 'Einstein Fields' is given for the first time in our monograph and has never been treated in such exhaustive detail. This study has yielded significant new insights to Einstein's theory. The volume is heavily illustrated and is accessible to well-prepared undergraduate and graduate students as well as the professional physics community.

This textbook - incorporated with many illuminating examples and exercises - is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation - by a pure mathematician's standards - is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and phenomena such as caustics.

The present book - which is the third, significantly revised edition of the textbook originally published by Elsevier Science - emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler-Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics.New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

It is estimated that a large fraction of natural gas reserves are found in locations from where transport is not economical. If these isolated natural gas reserves could be converted to synthetic fuels, they would generate around 250 billion barrels of synthetic oil-a quantity equal to one-third of the Middle East's proven oil reserves. Small-Scale Gas to Liquid Fuel Synthesis explores next-generation technologies geared toward overcoming the significant cost and technical barriers prohibiting the extensive use of conventional gas to liquid (GTL) processes for the exploitation of small and/or isolated natural gas reservoirs. The book highlights key research activities in the framework of two large European projects-Innovative Catalytic Technologies & Materials for Next Gas to Liquid Processes (NEXT-GTL) and Oxidative Coupling of Methane followed by Oligomerization to Liquids (OCMOL)-examining novel technical developments that reduce the costs associated with air fractioning and syngas production. Featuring contributions from internationally respected experts, Small-Scale Gas to Liquid Fuel Synthesis discusses innovative GTL technologies based on recent advances in catalytic membrane systems, reaction engineering, and process design. The book provides academic and industrial researchers with a concise presentation of the current state of the art of low-cost, energy-efficient GTL technologies for small-scale applications.

This book is a thoroughly up-to-date treatment of all the available technologies for biomass conversion. Each chapter looks at the viability and implementation of each technology with examples of existing equipment and plants. In addition, the text addresses the economics of biomass processing. The book could also be used as a supplementary text for senior undergraduate courses on biomass processing. Features: Provides a concise overview of all currently available biomass processing technologies Includes relatively recent technologies such as Biochar Contains numerous industry examples and case studies Covers the science and technology behind biomass processing as well as the economics, including the effect of carbon taxation

The 2014 International Conference on Energy and Environmental Engineering (ICEEE 2014) was held September 21-22, 2014 in Hong Kong. This proceedings volume assembles papers from various professionals, leading researchers, engineers, scientists and students and presents innovative ideas and research results focused on Energy and Environmental Engineering. The papers in this book group around the following topics: Energy Science and Technology, Environmental Science and Engineering, Motivation, Electrical Engineering and Automation, the Development and Utilization of Resources, Theory and Practice of Sustainable Development, as well as other related topics.

An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler-Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics.New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

This book focuses on novel electrochemical materials particularly designed for specific energy applications. It presents the relationship between materials properties, state-of-the-art processing, and device performance and sheds light on the research, development, and deployment (RD&D) trend of emerging materials and technologies in this field. Features: Emphasizes electrochemical materials applied in PEM fuel cells and water splitting Summarizes anode, cathode, electrolyte, and additive materials developed for lithium-ion batteries and reviews other batteries, including lithium-air, lithium-sulfur, sodium- and potassium-ion batteries, and multivalent-ion batteries Discusses advanced carbon materials for supercapacitors Highlights catalyst design and development for CO2RR and fundamentals of proton facilitated reduction reactions With a cross-disciplinary approach, this work will be of interest to scientists and engineers across chemical engineering, mechanical engineering, materials science, chemistry, physics, and other disciplines working to advance electrochemical energy conversion and storage capabilities and applications.

Mechanics Over Micro and Nano Scales covers the recent developments in the fields of mechanics in all forms over micro, meso and nano scales. Special emphasis is given to related novel applications and includes fundamental aspects of fluid and solid mechanics, soft matters, scaling laws, and synthetic biology. At the micro and nano scales, realization of many technologically viable ideas relies on the skillful integration of mechanics at macroscopic and molecular levels, both for solids as well as fluids. Research in the related areas is no longer confined to the understanding of the governing the physics of the system, but is also responsible for triggering a technological revolution at small scales. This book also: discusses the fundamentals of mechanics over micro and nano scales in a level accessible to multi-disciplinary researchers, with a balance of mathematical details and physical principles, covers life sciences and chemistry for use in emerging applications related to mechanics over small scales and demonstrates the explicit interconnection between various scale issues and the mechanics of miniaturized systems. Mechanics Over Micro and Nano Scales is an ideal book for researchers and engineers working in mechanics of both solids and fluids.