Classical mechanics Books

Book SynopsisA groundbreaking work in the field of physics and mathematics. In this monumental work, Newton formulated the laws of motion and universal gravitation, laying the foundation for classical mechanics and revolutionizing our understanding of the physical world. The Principia remains one of the most significant scientific books ever written, influencing generations of scientists, and shaping the course of modern physics and mathematics. The Groundbreaking Work of Sir Isaac Newton Mathematical proofs and equations. Comprehensive coverage of planetary motion. Helps in understanding the principles of motion. Logical and rigorous approach to scientific inquiry. Studied and revered as a seminal work in the field of science.

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Book Synopsis''Beautifully clear explanations of famously difficult things ... It almost makes you think you could have been a Newton yourself'' John Gribbin Here is the ultimate master class in modern physics. World-class physicist and father of string theory Leonard Susskind and citizen-scientist George Hrabovsky combine forces in a primer that teaches the skills you need to do physics yourself.Combining crystal-clear explanations of the laws of the universe with basic exercises (including essential equations and maths), the authors cover the minimum that readers should master. They introduce the key concepts of modern physics, from classical mechanics to general relativity to quantum theory, and provide a practical toolkit that you won''t find in any other popular science book. ''A good and noble book'' Sunday Times ''A wonderful and unique resource. For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start'' Sean Carroll, physicist and author of The Particle at the End of the Universe''Very readable ... provides a clear description of advanced classical physics concepts, and gives readers who want a challenge the opportunity to exercise their brain'' Physics WorldTrade ReviewSo what do you do if you enjoyed science at school or college but ended up with a different career and are still wondering what makes the universe tick? . . . The Theoretical Minimum is the book for you. -- John Gribbin * Wall Street Journal *A pleasure to read....a beautiful, high-level overview of the entire subject * Physics Today *What a wonderful and unique resource. For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start. It gets directly to the important points, with nuggets of deep insight scattered along the way. * Sean Carroll, author of The Particle at the End of the Universe *

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Book SynopsisPhilosophic, less formalistic approach to perennially important field of analytical mechanics. Model of clear, scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography.

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Book SynopsisDescribes the acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. This title deals with the fundamental three laws of motion and the law of universal gravity. It is suitable for scientists, scholars, and students.Table of ContentsPreface A GUIDE TO NEWTON'S PRINCIPIA Contents of the Guide Abbreviations CHAPTER ONE: A Brief History of the Principia CHAPTER TWO: Translating the Principia CHAPTER THREE: Some General Aspects of the Principia CHAPTER FOUR: Some Fundamental Concepts of the Principia CHAPTER FIVE : Axioms, or the Laws of Motion CHAPTER SIX: The Structure of Book 1 CHAPTER SEVEN: The Structure of Book 2 CHAPTER EIGHT: The Structure of Book 3 CHAPTER NINE : The Concluding General Scholium CHAPTER TEN: How to Read the Principia CHAPTER ELEVEN : Conclusion THE PRINCIPIA (Mathematical Principles of Natural Philosophy) Halley's Ode to Newton Newton's Preface to the First Edition Newton's Preface to the Second Edition Cotes s Preface to the Second Edition Newton's Preface to the Third Edition Definitions Axioms, or the Laws of Motion BOOK 1: THE MOTION OF BODIES BOOK 2: THE MOTION OF BODIES BOOK 3: THE SYSTEM OF THE WORLD General Scholium Index

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Book SynopsisVery Short Introductions: Brilliant, Sharp, Inspiring Fluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. A quintessential interdisciplinary field of science, it interacts with many other scientific disciplines, from chemistry and biology to mathematics and engineering.This Very Short Introduction presents the field of fluid mechanics by focusing on the underlying physical ideas and using everyday phenomena to demonstrate them, from dripping taps to swimming ducks. Eric Lauga shows how this set of fundamental physical concepts can be applied to a wide range of flow behaviours and highlights the role of fluid motion in both the natural and industrial worlds. This book also considers future applications of fluid mechanics in science.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewOverall, the book should definitely be an individual's go-to source when seeking an authoritative perspective on the field of fluid mechanics. * Anita T. Layton, Society for Industrial and Applied Mathematics Vol 65.4 *Table of Contents1: Fluids 2: Viscosity 3: Pipes 4: Dimensions 5: Boundary layers 6: Vortices 7: Instabilities 8: Researching fluids and flows Further Reading Index

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Book SynopsisAll atomic particles have a particular spin, analagous to the rotation of the Earth about its axis. This mysterious quality has vast practical importance to topics as wide-ranging as the stability of atoms and stars and magnetic resonance imaging. This is an accessible treatment of the subject.

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Book SynopsisThis textbook provides details of the derivation of Lagrange's planetary equations and of the closely related Gauss's variational equations, thereby covering a sorely needed topic in existing literature. Analytical solutions can help verify the results of numerical work, giving one confidence that his or her analysis is correct. The authors—all experienced experts in astrodynamics and space missions—take on the massive derivation problem step by step in order to help readers identify and understand possible analytical solutions in their own endeavors. The stages are elementary yet rigorous; suggested student research project topics are provided.After deriving the variational equations, the authors apply them to many interesting problems, including the Earth-Moon system, the effect of an oblate planet, the perturbation of Mercury's orbit due to General Relativity, and the perturbation due to atmospheric drag. Along the way, they introduce several useful techniques such as averaging, Poincaré's method of small parameters, and variation of parameters. In the end, this textbook will help students, practicing engineers, and professionals across the fields of astrodynamics, astronomy, dynamics, physics, planetary science, spacecraft missions, and others. “An extensive, detailed, yet still easy-to-follow presentation of the field of orbital perturbations.” - Prof. Hanspeter Schaub, Smead Aerospace Engineering Sciences Department, University of Colorado, Boulder “This book, based on decades of teaching experience, is an invaluable resource for aerospace engineering students and practitioners alike who need an in-depth understanding of the equations they use.” - Dr. Jean Albert Kéchichian, The Aerospace Corporation, Retired “Today we look at perturbations through the lens of the modern computer. But knowing the why and the how is equally important. In this well organized and thorough compendium of equations and derivations, the authors bring some of the relevant gems from the past back into the contemporary literature.” - Dr. David A Vallado, Senior Research Astrodynamicist, COMSPOC “The book presentation is with the thoroughness that one always sees with these authors. Their theoretical development is followed with a set of Earth orbiting and Solar System examples demonstrating the application of Lagrange’s planetary equations for systems with both conservative and nonconservative forces, some of which are not seen in orbital mechanics books.” - Prof. Kyle T. Alfriend, University Distinguished Professor, Texas A&M UniversityTable of Contents1 The n-Body Problem2 General Perturbations 3 Evaluation of Lagrange’s Brackets 4 Lagrange’s Planetary Equations 5 Expansion of the Perturbation Function 6 The Earth-Moon System 7 Potential of an Oblate Spheroid8 Effects of General Relativity9 Perturbations due to Atmospheric Drag 10 Periodic Solutions in Nonlinear OscillationsBibliography Projects

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Book SynopsisSupplementary textbook for all levels of undergraduate physics courses in classical mechanics.Trade Review'This textbook serves as an introduction to standard undergraduate classical mechanics topics, including Newton's laws, energy, momentum, oscillators, rotational dynamics and angular momentum. … The real value of this book, however, lies in the extensive set of problems and worked solutions that many students tend to crave and as such is sure to be warmly welcomed.' Contemporary PhysicsTable of ContentsPreface; 1. Strategies for solving problems; 2. Statics; 3. Using F=ma; 4. Oscillations; 5. Conservation of energy and momentum; 6. The Lagrangian model; 7. Central forces; 8. Angular momentum, Part I (constant L); 9. Angular momentum, Part II (general L); 10. Accelerating frames of reference; 11. Relativity (kinematics); 12. Relativity (dynamics); 13. 4-vectors; 14. General relativity; Appendices; References; Index.

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Book SynopsisPhysics on Your Feet (2nd Edition) is a significantly expanded collection of physics problems covering the broad range of topics in classical and modern physics that were, or could have been, asked at oral PhD exams.Trade ReviewReview from previous edition The inventive and challenging puzzles in this book are guaranteed to make you think, and they will probably also make you glad you are not encountering them on your feet in an exam! * Physics World *This practical study book for university students will help every student in the preparation of their exams. * Jan M. Broders, Optische Fenomenen *Table of Contents1: Mechanics, heat, and general physics 2: Fluids 3: Gravitation, astrophysics, cosmology 4: Electromagnetism 5: Optics 6: Quantum, atomic, and molecular 7: Nuclear and elementary-particle physics 8: Condensed-matter physics Appendix A Maxwell's equations and electromagnetic field boundary Appendix B Symbols and useful constants Free

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Book SynopsisOne of the clearest and most straightforward texts ever published, Understanding Mechanics covers all the topics required in the single-subject A Level. It is equally appropriate for those preparing for other Mathematics examinations at A Level and for students on technical courses in further and higher education. Key Points: Principles are introduced in a simple and direct manner and all have worked examples Ample opportunity is given for practice with questions and exercises carefully graded to provide a steady progression Each chapter closes with a comprehensive selection of recent examination questions Answers are given at the back of the bookTrade ReviewA lucid text with many sets of questions... make the whole a most acceptable work. * TES *Table of Contents1. Vectors ; 2. Distance, velocity and acceleration ; 3. Force and Newton's laws ; 4. Resultants and components of forces ; 5. Equilibrium and acceleration under concurrent forces ; 6. Friction ; 7. Moments ; 8. Centre of gravity ; 9. General equilibrium of a rigid body ; 10. Resultant velocity and relative velocity ; 11. Work, energy and power ; 12. Projectiles ; 13. Circular motion ; 14. Momentum and impulse ; 15. Elasticity ; 16. Use of calculus ; 17. Simple harmonic motion ; 18. Compound bodies and frameworks

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Book SynopsisThis volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems.Trade ReviewFrom the reviews: "Russian physicist Kosyakov has written an introduction to classical gauge theory for students of high energy or particle physics. … Extensive reference list. A valuable addition to a university library supporting a program in high energy theory; highly mathematical, so most useful as a resource for undergraduate programs. Summing Up: Recommended. Graduate students; professionals." (R. L. Stearns, CHOICE, Vol. 44 (10), June, 2007) "The classical theory of gauge fields is an important subject that has numerous applications in modern physics. … A nice feature of this book is that this is self contained. All the necessary definitions as well as the technical tools are provided by the author in the main body of the book. … I enjoyed reading the book. … Overall the monograph … can be warmly recommended to any serious student of electrodynamics and gauge theory and to their instructors alike." (Yuri N. Obukhov, Annalen der Physik, Vol. 16 (12), 2007) "Each chapter contains problems and final notes, a useful guide to the history of the subject. … The volume is intended to be an introduction for advanced undergraduate and graduate students in high energy physics. … We mention that it is timely elaborate a unified view of the classical self-interaction problems in classical gauge theories with particular reference to the electrodynamics of point electrons and Yang-Mills interaction of point quarks. The present work is a valuable contribution to this task." (Petre P. Teodorescu, Zentralblatt MATH, Vol. 1114 (16), 2007) "This book is an introduction to classical field theory. Although it was designed for advanced undergraduate and graduate students, researchers could also benefit from this book. It is intended for mathematical physicists and theoretical physicists. Classical gauge theories are discussed in detail, with great emphasis on self-interactions. … In summary, this is a useful introduction to classical gauge theories that can be recommended both to students (theoretical or mathematical physics), and to specialists and researchers, as a reference book." (Giuseppe Nardelli, Mathematical Reviews, Issue 2008 c)Table of ContentsGeometry of Minkowski Space.- Relativistic Mechanics.- Electromagnetic Field.- Solutions to Maxwell's Equations.- Lagrangian Formalism in Electrodynamics.- Self-Interaction in Electrodynamics.- Lagrangian Formalism for Gauge Theories.- Solutions to the Yang?Mills Equations.- Self-Interaction in Gauge Theories.- Generalizations.- Mathematical Appendices.

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Book SynopsisThis book is the second edition of an excellent undergraduate-level overview of classical and modern physics, intended for students of physics and related subjects, and also perfectly suited for the education of physics teachers. The twelve-chapter book begins with Newton’s laws of motion and subsequently covers topics such as thermodynamics and statistical physics, electrodynamics, special and general relativity, quantum mechanics and cosmology , the standard model and quantum chromodynamics. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with standard mathematics.An important addition in this second edition is a set of exercises and problems, distributed throughout the book. Some of the problems aim to complement the text, others to provide readers with additional useful tools for tackling new or more advanced topics. Furthermore, new topics have been added in several chapters; for example, the discovery of extra-solar planets from the wobble of their mother stars, a discussion of the Landauer principle relating information erasure to an increase of entropy, quantum logic, first order quantum corrections to the ideal gas equation of state due to the Fermi-Dirac and Bose-Einstein statistics. Both gravitational lensing and the time-correction in geo-positioning satellites are explained as theoretical applications of special and general relativity. The discovery of gravitational waves, one of the most important achievements of physical sciences, is presented as well. Professional scientists, teachers, and researchers will also want to have this book on their bookshelves, as it provides an excellent refresher on a wide range of topics and serves as an ideal starting point for expanding one’s knowledge of new or unfamiliar fields. Readers of this book will not only learn much about physics, they will also learn to love it.Trade ReviewFrom the reviews of the first edition:Selected by Choice magazine as an "Outstanding Academic Title" for 2014“This is a very high-quality presentation. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with the mathematics. … the work is a valuable addition to college libraries. Professionals and researchers will also want it on their bookshelves; it provides an excellent refresher on a wide range of topics and can serve as a good starting point for expanding knowledge of new or unfamiliar subjects. Summing Up: Highly recommended. Lower-division undergraduates and above.” (A. Spero, Choice, Vol. 51 (9), May, 2014)“It describes all the major developments and theories regarding the description of the universe we live on, from the very small to the very large. … I highly recommend this book to any physicist. It will not only be a fun and an easy read but also a useful revision of all the main concepts in physics. Undergraduate and graduate physics students definitely should read it. … appropriate for scientists in other fields who have a genuine interest for physics.” (Monica Pierri-Galvao, Contemporary Physics, April, 2014)Table of ContentsGravitation and Newton Laws.- Entropy, Statistical Physics and Information.- Electromagnetism and Maxwell's Equations.- Electromagnetic Waves.- Special Theory of Relativity.- Atoms and Quantum Theory.- Quantum Electrodynamics.- Fermi-Dirac and Bose-Einstein Statistics.- Four Fundamental Forces.- General Relativity and Cosmology.- Unification of the Forces of Nature.- Physics and Life.

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Book SynopsisEndorsed by Cambridge Assessment International Education to provide full support for Paper 4 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the Boost eBook.**To have full access to the eBook and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.com/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. This book covers the syllabus content for Mechanics, including forces and equilibrium, kinematics of motion in a straight line, momentum, Newton's laws of motion, and energy, work and power.

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Book SynopsisThe book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.Table of ContentsPart I: Newtonian Mechanics 1: Introduction 2: Newton's Three Laws 3: Energy and Work 4: Introductory Rotational Dynamics 5: The Harmonic Oscillator 6: Wave Mechanics & Elements of Mathematical Physics Part II: Langrangian Mechanics 7: Introduction 8: Coordinates & Constraints 9: The Stationary Action Principle 10: Constrained Langrangian Mechanics 11: Point Transformations in Langrangian Mechanics 12: The Jacobi Energy Function 13: Symmetries & Langrangian-Hamiltonian-Jacobi Theory 14: Near-Equilibrium Oscillations 15: Virtual Work & d'Alembert's Principle Part III: Canonical Mechanics 16: Introduction 17: The Hamiltonian & Phase Space 18: Hamiltonian's equations & Routhian Reduction 19: Poisson Brackets & Angular momentum 20: Canonical & Gauge Transformations 21: Hamilton-Jacobi Theory 22: Liouville's Theorem & Classical Statistical Mechanics 23: Constrained Hamiltonian Dynamics 24: Autonomous Geometrical Mehcanics 25: The Structure of Phase Space 26: Near-Integrable Systems Part IV: Classical Field Theory 27: Introduction 28: Langrangian Field Theory 29: Hamiltonian Field Theory 30: Clssical Electromagnetism 31: Neother's Theorem for Fields 32: Classical Path-Integrals Part V: Preliminary Mathematics 33: The (Not so?) Basics 34: Matrices 35: Partial Differentiation 36: Legendre Transformations 37: Vector Calculus 38: Differential equations 39: Calculus of Variations Part VI: Advanced Mathematics 40: Linear Algebra 41: Differential Geometry Part VII: Exam Style Questions Appendix A: Noether's Theorem Explored Appendix B: The Action Principle Explored Appendix C: Useful Relations Appendxi D: Poisson & Nambu Brackets Explored Appendix: Canonical Transformations Explored Appendix F: Action-Angle Variables Explored Appendix G: Statistical Mechanics Explored Appendix H: Biographies

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Book SynopsisPhysics on Your Feet (2nd Edition) is a significantly expanded collection of physics problems covering the broad range of topics in classical and modern physics that were, or could have been, asked at oral PhD exams at University of California at Berkeley. The questions are easy to formulate, but some of them can only be answered using an outside-of-the box approach. Detailed solutions are provided, from which the reader is guaranteed to learn a lot about the physicists'' way of thinking. The book is also packed full of cartoons and dry humor to help take the edge off the stress and anxiety surrounding exams. This is a helpful guide for students preparing for their exams, as well as a resource for university lecturers looking for good instructive problems. No exams are necessary to enjoy the book!Trade ReviewReview from previous edition The inventive and challenging puzzles in this book are guaranteed to make you think, and they will probably also make you glad you are not encountering them on your feet in an exam! * Physics World *This practical study book for university students will help every student in the preparation of their exams. * Jan M. Broders, Optische Fenomenen *Table of Contents1: Mechanics, heat, and general physics 2: Fluids 3: Gravitation, astrophysics, cosmology 4: Electromagnetism 5: Optics 6: Quantum, atomic, and molecular 7: Nuclear and elementary-particle physics 8: Condensed-matter physics Appendix A Maxwell's equations and electromagnetic field boundary Appendix B Symbols and useful constants Free

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Book SynopsisThis classical mechanics text provides a complete account of the classical mechanics of particles, systems of particles, and rigid bodies. The authors make extensive use of vector calculus to explore topics; coverage also includes the Lagrangian formulation of mechanics.

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Book Synopsis

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Book SynopsisThis hands-on text demystifies numerical modelling for early-stage physics and engineering students, with each chapter focusing on an intriguing physics problem. Developed over many years of teaching a computational modelling course, this stand-alone book gives students an essential numerical modelling toolkit for today's data-driven landscape.Table of ContentsPreface; How to use this book; First steps; 1. Rectangular finite quantum well – Stationary Schrödinger Equation in 1D; 2. Diffraction of light on a slit; 3. Pendulum as a standard unit of time; 4. Planetary system; 5. Gravitation inside a star; 6. Normal modes in a cylindrical waveguide; 7. Thermal insulation properties of a wall; 8. Cylindrical capacitor; 9. Coupled harmonic oscillators; 10. The Fermi-Pasta-Ulam problem; 11. Cold hydrogen star; 12. Rectangular quantum well filled with electrons – The idea of self-consistent calculations; 13. Time dependent Schrödinger Equation Dawid Dworzański; 14. Poisson equation in 2D; Appendices; Further Reading; Index.

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Book SynopsisThis series has been developed specifically for the Cambridge International AS & A Level Mathematics (9709) syllabus to be examined from 2020.Table of ContentsIntroduction; 1. Velocity and acceleration; 2. Force and motion in one dimension; 3. Forces in two dimensions; 4. Friction; 5. Connected particles; 6. General motion in a straight line; 7. Momentum; 8. Work and energy; 9. The work–energy principle and power; Answers

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Book SynopsisWINNER of the 2023 CHOICE Outstanding Academic Title Award Follows the fascinating story of musical timekeeping, beginning in an age before the existence of external measuring devices and continuing to the present-day use of the Smartphone app. The book opens with an exploration of musical time keeping as expressed in the artwork and musical writing of the Renaissance, sources that inform our early understanding of an age when music making was bound up with motions of the body and the pulsing of the human heart. With the adoption of the simple pendulum and the subsequent incorporation of tempo-related language, musicians gained the ability to communicate concepts of speed and slowness with ever-increasing precision. The seventeenth and eighteenth centuries witnessed the development of a diverse array of musical time-keeping devices, yet it was not until the nineteenth century that a single device combined the critical elements of accuracy, functionality and affordability. Enter the metronome: portable and affordable, a triumph of innovation that enabled musicians to establish and faithfully reproduce musical time with accuracy and ease. From Beethoven to Ligeti, Moskovitz looks to a number of distinguished composers who used or refused this revolutionary machine and explores the complicated relationship that unfolded between the metronome, the musical world and practitioners in other disciplines who sought to exploit its potential. Engagingly written, Measure: In Pursuit of Musical Time will appeal to professionals and amateurs alike.Trade ReviewThrough its historical depth, vivid explanations, and engaging narrative, Measure provides a valuable resource for those seeking to think more pointedly about the history of and ideas surrounding musical time. With this book, readers will find a captivating journey into the heartbeat of music itself. -- Katie Bank * H-NET REVIEWS *This is a fascinating study of the history of keeping time in music, from pulse to pendulum to metronome. It reminds us that such seemingly dry and rigorous methods were developed to preserve a composer's intentions or to perfect a performer's rhythm, thus allowing for maximum freedom and faithful inspiration in performance. * Stephen Hough, pianist, composer, writer. *Table of ContentsIntroduction HANDS 1 Hand and Heart 2 Motion and Rest PENDULUMS 3 A Logically Ordered Universe 4 A Line, a Weight and a Nail 5 Court and Académie 6 New Systems 7 Curiosities and Chronometers 8 Revolutionary Minds 9 Clockwork 10 Hammers, Dials and Barrels METRONOMES 11 Winkel's Prototype 12 Maelzel's Metronome 13 Composer's Calibrations 14 An Incomparable Lack of Judgement 15 New Currents 16 Metronome Sense Afterword: Last Object Works Cited

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Book SynopsisThis is the fifth edition of a well-established textbook. It is intended to provide a thorough coverage of the fundamental principles and techniques of classical mechanics, an old subject that is at the base of all of physics, but in which there has also in recent years been rapid development. The book is aimed at undergraduate students of physics and applied mathematics. It emphasizes the basic principles, and aims to progress rapidly to the point of being able to handle physically and mathematically interesting problems, without getting bogged down in excessive formalism. Lagrangian methods are introduced at a relatively early stage, to get students to appreciate their use in simple contexts. Later chapters use Lagrangian and Hamiltonian methods extensively, but in a way that aims to be accessible to undergraduates, while including modern developments at the appropriate level of detail. The subject has been developed considerably recently while retaining a truly central role for all students of physics and applied mathematics.This edition retains all the main features of the fourth edition, including the two chapters on geometry of dynamical systems and on order and chaos, and the new appendices on conics and on dynamical systems near a critical point. The material has been somewhat expanded, in particular to contrast continuous and discrete behaviours. A further appendix has been added on routes to chaos (period-doubling) and related discrete maps. The new edition has also been revised to give more emphasis to specific examples worked out in detail.Classical Mechanics is written for undergraduate students of physics or applied mathematics. It assumes some basic prior knowledge of the fundamental concepts and reasonable familiarity with elementary differential and integral calculus.Trade Review"Classical Mechanics by T Kibble and F Berkshire is tailor-made for budding theoreticians. It lays the groundwork for relativity and quantum theory, quickly progressing beyond Newtonian mechanics to the alternative formulations of Joseph Lagrange and William Hamilton." New Scientist "... the student who requires a good book on the older aspects of Classical Mechanics together with a brief introduction to newer ideas will find the third edition useful." Contemporary Physics "This volume, by Kibble and Berkshire, has proved to be a successful book ... the written content and presentation are all excellent." European Journal of Physics

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Book SynopsisThis is an advanced modern textbook on thermal stresses. It serves a wide range of readers, in particular, graduate and postgraduate students, scientists, researchers in various industrial and government institutes, and engineers working in mechanical, civil, and aerospace engineering. This volume covers diverse areas of applied mathematics, continuum mechanics, stress analysis, and mechanical design. This work treats a number of topics not presented in other books on thermal stresses, for example: theory of coupled and generalized thermoelasticity, finite and boundary element method in generalized thermoelasticity, thermal stresses in functionally graded structures, and thermal expansions of piping systems.The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic knowledge on the part of the reader is expected in classical mechanics, stress analysis, and mathematics, including vector and cartesian tensor analysis.This 2nd enhanced edition includes a new chapter on Thermally Induced Vibrations. The method of stiffness is added to Chapter 7. The variational principle for the Green-Lindsay and Green-Naghdi models have been added to Chapter 2 and equations of motion and compatibility equations in spherical coordinates to Chapter 3. Additional problems at the end of chapters were added. Table of ContentsChapter 1: Basic Laws of Thermoelasticity.- 1 Introduction.- 2 Stresses and Tractions.- 3 Equations of Motion.- 4 Coordinate Transformation. Principal Axes.- 5 Principal Stresses and Stress Invariants.- 6 Displacement and Strain Tensor.- 7 Compatibility Equations. Simply Connected Region.- 8 Compatibility Conditions. Multiply Connected Regions.- 9 Constitutive Laws of Linear Thermoelasticity.- 10 Displacement Formulation of Thermoelasticity.- 11 Stress Formulation of Thermoelasticity.- 12 Two-Dimensional Thermoelasticity.- 13 Michell Conditions.- 14 Problems.- Chapter 2: Thermodynamics of Elastic Continuum.- 1 Introduction.- 2 Thermodynamics Definitions.- 3 First Law of Thermodynamics.- 4 Second Law of Thermodynamics.- 5 Variational Formulation of Thermodynamics.- 6 Thermodynamics of Elastic Continuum.- 7 General Theory of Thermoelasticity.- 8 Free Energy Function of Hookean Materials.- 9 Fourier’s Law and Heat Conduction Equation.- 10 Generalized Thermoelasticity, Second Sound.- 11 Thermoelasticity without Energy Dissipation.- 12 A Unified Generalized Thermoelasticity.- 13 Uniqueness Theorem.- 14 Variational Principle of Thermoelasticity.- 15 Reciprocity Theorem.- 16 Initial and Boundary Conditions.- 17 Problems.- Chapter 3: Basic Problems of Thermoelasticity.- 1 Introduction.- 2 Temperature Distribution for Zero Thermal Stress.- 3 Analogy of Thermal Gradient with Body Forces.- 4 General Solution of Thermoelastic Problems.- 5 Solution of Two-Dimensional Navier Equations.- 6 General Solution in Cylindrical Coordinates.- 7 Solution of Problems in Spherical Coordinates.- 8 Problems.- Chapter 4: Heat Conduction Problems.- 1 Introduction.- 2 Problems in Rectangular Cartesian Coordinates.- 3 Problems in Cylindrical Coordinates.- 4 Problems in Spherical Coordinates.- 5 Problems.- Chapter 5: Thermal Stresses in Beams.- 1 Introduction.- 2 Thermal Stresses in Beams.- 3 Deflection Equation of Beams.- 4 Boundary Conditions.- 5 Shear Stress in a Beam.- 6 Beams of Rectangular Cross Section.- 7 Transient Stresses in Rectangular Beams.- 8 Beam with Internal Heat Generation.- 9 Bimetallic Beam.- 10 Functionally Graded Beams.- 11 Transient Stresses in FGM Beams.- 12 Thermal Stresses in Thin Curved Beams and Rings.- 13 Deflection of Thin Curved Beams and Rings.- 14 Problems.- Chapter 6: Disks, Cylinders, and Spheres 2591 Introduction.- 2 Cylinders with Radial Temperature Variation.- 3 Thermal Stresses in Disks.- 4 Thick Spheres.- 5 Thermal Stresses in a Rotating Disk.- 6 Non-axisymmetrically Heated Cylinders.- 7 Method of Complex Variables.- 8 Functionally Graded Thick Cylinders.- 9 Axisymmetric Stresses in FGM Cylinders.- 10 Transient Thermal Stresses in Thick Spheres.- 11 Functionally Graded Spheres .- 12 Problems.- Chapter 7: Thermal Expansion in Piping Systems.- 1 Introduction.- 2 Definition of the Elastic Center.- 3 Piping Systems in Two Dimensions.- 4 Piping Systems in Three Dimensions.- 5 Pipelines with Large Radius Elbows.- 6 Stiffness Method.- 7 Rotation Matrix.- 8 Transformation Matrix.- 9 Flexibility Matrix of a Single Member.- 10 Flexibility Matrix of a Branch.- 11 Flexibility Matrix of a Straight Member.- 12 Flexibility Matrix of a Bend Member.- 13 Problems.- Chapter 8: Coupled and Generalized Thermoelasticity.- 1 Introduction.- 2 Governing Equations of Coupled Thermoelasticity.- 3 Coupled Thermoelasticity for Infinite Space.- 4 Variable Heat Source.- 5 One-Dimensional Coupled Problem.- 6 Propagation of Discontinuities.- 7 Half-Space Subjected to a Harmonic Temperature.- 8 Coupled Thermoelasticity of Thick Cylinders.- 9 Green–Naghdi Model of a Layer.- 10 Generalized Thermoelasticity of Layers.- 11 Generalized Thermoelasticity in Spheres and Cylinders.- 12 Problems.- Chapter 9: Finite and Boundary Element Methods.- 1 Introduction.- 2 Galerkin Finite Element.- 3 Functionally Graded Layers.- 4 Coupled Thermoelasticity of Thick Spheres.- 5 Generalized Thermoelasticity of FG Spheres.- 6 Generalized Thermoelasticity of FG Disk.- 7 Higher Order Elements.- 8 Functionally Graded Beams.- 9 Thermally Nonlinear GeneralizedThermoelasticity.- 10 Boundary Element Formulation.- Chapter 10: Thermally Induced Vibrations.- 1 Introduction.- 2 Thermally Induced Vibrations of Isotropic Beams.- 3 Thermally Induced Vibration of FGM Beams.- 4 Thermally Induced Vibration of Shallow Arches.- Chapter 11: Creep Analysis.- 1 Introduction.- 2 Creep of Metals.- 3 Constitutive Equation of Uniaxial Creep.- 4 Creep Relaxation, Linear Rheological Models.- 5 Three-Dimensional Governing Equations.- 6 Creep Potential, General Theory of Creep.- 7 Stress Function for Creep Problems.- 8 Creep Linearization.- 9 Creep Relaxation of Axisymmetric Stresses.- 10 Creep Relaxation of Non-axisymmetric Stresses.- 11 Thermoelastic Creep Relaxation in Beams.12 Problems.- Subject Index.

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Book SynopsisThe 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.

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Book SynopsisDescribes the acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. This title deals with the fundamental three laws of motion and the law of universal gravity, and more. It is suitable for scientists, scholars, and students.

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Book SynopsisThis textbook provides a modern introduction to linear algebra, a mathematical discipline every first year undergraduate student in physics and engineering must learn. A rigorous introduction into the mathematics is combined with many examples, solved problems, and exercises as well as scientific applications of linear algebra. These include applications to contemporary topics such as internet search, artificial intelligence, neural networks, and quantum computing, as well as a number of more advanced topics, such as Jordan normal form, singular value decomposition, and tensors, which will make it a useful reference for a more experienced practitioner. Structured into 27 chapters, it is designed as a basis for a lecture course and combines a rigorous mathematical development of the subject with a range of concisely presented scientific applications. The main text contains many examples and solved problems to help the reader develop a working knowledge of the subject and every chapter comes with exercises.Trade ReviewThe authors are uniquely well qualified to produce a textbook suitable for first-year university students. * David Matravers, University of Portsmouth *Linear Algebra is a core undergraduate course not only in Mathematics but also in Physics, Chemistry, Biology and Computer Science. This textbook brilliantly succeeds in catering to such a wide audience by covering a broad range of formal developments along with concrete applications and is unique in its presentation of the topic. * Richard Joseph Szabo, Heriot-Watt University *Lukas has written an impressive mathematical textbook that covers standard introductory linear algebra topics along with advanced concepts that will appeal to many readers. * Choice *Table of Contents1: Linearity - an informal introduction 2: Sets and functions 3: Groups 4: Fields 5: Coordinate vectors 6: Vector spaces 7: Elementary vector space properties 8: Vector subspaces 9: The dot product 10: Vector and triple product 11: Lines and planes 12: Introduction to linear maps 13: Matrices 14: The structure of linear maps 15: Linear maps in terms of matrices 16: Computing with matrices 17: Linear systems 18: Determinants 19: Basics of eigenvalues 20: Diagonalising linear maps 21: The Jordan normal form 22: Scalar products 23: Adjoint and unitary maps 24: Diagonalisation - again 25: Bi-linear and sesqui-linear forms 26: The dual vector space 27: Tensors

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Book SynopsisCovariant Physics: From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed. Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance. The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.Trade ReviewIntroduces and progresses with the subject in ways that are very conducive to good learning and understanding, and fills a real (and currently unmet) need in an undergraduate's education in preparation for some of modern physics' most fascinating areas. * S. Leslie Blatt, Clark University, Worcester, Massachusetts *Stresses Einstein's legacy of using the symmetry principle to discover new physics, and introduces the relevant mathematics in a very gradual way. * Ta-Pei Cheng, University of Missouri - St Louis *Table of Contents1: Coordinate Systems and Vectors 2: Tensors 3: Classical Covariance 4: Special Covariance 5: General Covariance 6: Physics in curved spacetime 7: Riemann and Einstein 8: Least action and classical fields 9: Differential forms 10: Generalizing general relativity

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Book SynopsisGovernment Cryocooler Development and Test Programs.- Space Stirling Cryocooler Developments.- Long-Life Tactical and Commercial Stirling Coolers.- Long-Life Commercial Pulse Tube Coolers.- Space Pulse Tube Cryocooler Developments.- GM-Type Pulse Tube Coolers for Low Temperatures.- Hybrid Cryocoolers Using Pulse Tubes.- Pulse Tube Analysis and Experimental Measurements.- GM Refrigerator Developments.- Regenerator Analysis and Materials Developments.- Turbo-Brayton Cryocooler Developments.- J-T and Throttle-Cycle Cryocooler Developments.- Sorption Cryocooler Developments.- Sub-Kelvin Refrigerator Developments.- Optical Refrigeration Developments.- Cryocooler Reliability Investigations and Analyses.- Cryocooler Integration Technologies and Materials.- Space Cryocooler Applications.- Commercial Cryocooler Applications.Table of ContentsGovernment Cryocooler Development and Test Programs. Space Stirling Cryocooler Developments. Long Life Tactical, and Commercial Stirling Coolers. Long Life Commercial Pulse Tube Coolers. Space Pulse Tube Cryocooler Developments. GM-Type Pulse Tube Coolers for Low Temperatures. Hybrid Cryocoolers Using Pulse Tubes. Pulse Tube Analysis and Experimental Measurements. GM Refrigerator Developments. Regenerator Analysis and Materials Developments. Turbo-Brayton Cryocooler Developments. J-T and Throttle-Cycle Cryocooler Developments. Sorption Cryocooler Developments. Sub-Kelvin Refrigerator Developments. Optical Refrigeration Developments. Cryocooler Reliability Investigations and Analyses. Cryocooler Integration Technologies and Materials. Space Cryocooler Applications. Commercial Cryocooler Applications. Indexes.

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Book SynopsisBy including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course.Trade ReviewFrom the reviews: SIAM REVIEW "This book presents a modern treatment of stability in shear flows. Stability theory has seen a number of classic treatments over the years…Schmid and Henningson’s book builds on these and offers much new material relevant to stability in shear flows…The MATLAB codes included in the appendix and a discussion of the effects of rounding error and resolution on the computations of eigenvalues of linear stability operators will be particularly helpful for students and researchers as they get started with stability computations…As the basis for a course, the first part of the book would permit students to build a solid foundation in classical and modern stability theory, while a selection of advanced topics from the second half of the book could be treated later in the course or through projects and independent study by students." ZENTRALBLATT MATH "The book addresses to graduate students as well as to a broad community of researchers with a basic knowledge of fundamental fluid dynamics…The topics are treated with mathematical rigor while the physical motivation and usefulness of mathematical concepts is kept close at hand. The work is elegantly structured, and the graphical material is very suggestive."Table of Contents1 Introduction and General Results.- 1.1 Introduction.- 1.2 Nonlinear Disturbance Equations.- 1.3 Definition of Stability and Critical Reynolds Numbers.- 1.3.1 Definition of Stability.- 1.3.2 Critical Reynolds Numbers.- 1.3.3 Spatial Evolution of Disturbances.- 1.4 The Reynolds-Orr Equation.- 1.4.1 Derivation of the Reynolds-Orr Equation.- 1.4.2 The Need for Linear Growth Mechanisms.- I Temporal Stability of Parallel Shear Flows.- 2 Linear Inviscid Analysis.- 2.1 Inviscid Linear Stability Equations.- 2.2 Modal Solutions.- 2.2.1 General Results.- 2.2.2 Dispersive Effects and Wave Packets.- 2.3 Initial Value Problem.- 2.3.1 The Inviscid Initial Value Problem.- 2.3.2 Laplace Transform Solution.- 2.3.3 Solutions to the Normal Vorticity Equation.- 2.3.4 Example: Couette Flow.- 2.3.5 Localized Disturbances.- 3 Eigensolutions to the Viscous Problem.- 3.1 Viscous Linear Stability Equations.- 3.1.1 The Velocity-Vorticity Formulation.- 3.1.2 The Orr-Sommerfeld and Squire Equations.- 3.1.3 Squire’s Transformation and Squire’s Theorem.- 3.1.4 Vector Modes.- 3.1.5 Pipe Flow.- 3.2 Spectra and Eigenfunctions.- 3.2.1 Discrete Spectrum.- 3.2.2 Neutral Curves.- 3.2.3 Continuous Spectrum.- 3.2.4 Asymptotic Results.- 3.3 Further Results on Spectra and Eigenfunctions.- 3.3.1 Adjoint Problem and Bi-Orthogonality Condition.- 3.3.2 Sensitivity of Eigenvalues.- 3.3.3 Pseudo-Eigenvalues.- 3.3.4 Bounds on Eigenvalues.- 3.3.5 Dispersive Effects and Wave Packets.- 4 The Viscous Initial Value Problem.- 4.1 The Viscous Initial Value Problem.- 4.1.1 Motivation.- 4.1.2 Derivation of the Disturbance Equations.- 4.1.3 Disturbance Measure.- 4.2 The Forced Squire Equation and Transient Growth.- 4.2.1 Eigenfunction Expansion.- 4.2.2 Blasius Boundary Layer Flow.- 4.3 The Complete Solution to the Initial Value Problem.- 4.3.1 Continuous Formulation.- 4.3.2 Discrete Formulation.- 4.4 Optimal Growth.- 4.4.1 The Matrix Exponential.- 4.4.2 Maximum Amplification.- 4.4.3 Optimal Disturbances.- 4.4.4 Reynolds Number Dependence of Optimal Growth.- 4.5 Optimal Response and Optimal Growth Rate.- 4.5.1 The Forced Problem and the Resolvent.- 4.5.2 Maximum Growth Rate.- 4.5.3 Response to Stochastic Excitation.- 4.6 Estimates of Growth.- 4.6.1 Bounds on Matrix Exponential.- 4.6.2 Conditions for No Growth.- 4.7 Localized Disturbances.- 4.7.1 Choice of Initial Disturbances.- 4.7.2 Examples.- 4.7.3 Asymptotic Behavior.- 5 Nonlinear Stability.- 5.1 Motivation.- 5.1.1 Introduction.- 5.1.2 A Model Problem.- 5.2 Nonlinear Initial Value Problem.- 5.2.1 The Velocity-Vorticity Equations.- 5.3 Weakly Nonlinear Expansion.- 5.3.1 Multiple-Scale Analysis.- 5.3.2 The Landau Equation.- 5.4 Three-Wave Interactions.- 5.4.1 Resonance Conditions.- 5.4.2 Derivation of a Dynamical System.- 5.4.3 Triad Interactions.- 5.5 Solutions to the Nonlinear Initial Value Problem.- 5.5.1 Formal Solutions to the Nonlinear Initial Value Problem.- 5.5.2 Weakly Nonlinear Solutions and the Center Manifold.- 5.5.3 Nonlinear Equilibrium States.- 5.5.4 Numerical Solutions for Localized Disturbances.- 5.6 Energy Theory.- 5.6.1 The Energy Stability Problem.- 5.6.2 Additional Constraints.- II Stability of Complex Flows and Transition.- 6 Temporal Stability of Complex Flows.- 6.1 Effect of Pressure Gradient and Crossflow.- 6.1.1 Falkner-Skan (FS) Boundary Layers.- 6.1.2 Falkner-Skan-Cooke (FSC) Boundary layers.- 6.2 Effect of Rotation and Curvature.- 6.2.1 Curved Channel Flow.- 6.2.2 Rotating Channel Flow.- 6.2.3 Combined Effect of Curvature and Rotation.- 6.3 Effect of Surface Tension.- 6.3.1 Water Table Flow.- 6.3.2 Energy and the Choice of Norm.- 6.3.3 Results.- 6.4 Stability of Unsteady Flow.- 6.4.1 Oscillatory Flow.- 6.4.2 Arbitrary Time Dependence.- 6.5 Effect of Compressibility.- 6.5.1 The Compressible Initial Value Problem.- 6.5.2 Inviscid Instabilities and Rayleigh’s Criterion.- 6.5.3 Viscous Instability.- 6.5.4 Nonmodal Growth.- 7 Growth of Disturbances in Space.- 7.1 Spatial Eigenvalue Analysis.- 7.1.1 Introduction.- 7.1.2 Spatial Spectra.- 7.1.3 Gaster’s Transformation.- 7.1.4 Harmonic Point Source.- 7.2 Absolute Instability.- 7.2.1 The Concept of Absolute Instability.- 7.2.2 Briggs’ Method.- 7.2.3 The Cusp Map.- 7.2.4 Stability of a Two-Dimensional Wake.- 7.2.5 Stability of Rotating Disk Flow.- 7.3 Spatial Initial Value Problem.- 7.3.1 Primitive Variable Formulation.- 7.3.2 Solution of the Spatial Initial Value Problem.- 7.3.3 The Vibrating Ribbon Problem.- 7.4 Nonparallel Effects.- 7.4.1 Asymptotic Methods.- 7.4.2 Parabolic Equations for Steady Disturbances.- 7.4.3 Parabolized Stability Equations (PSE).- 7.4.4 Spatial Optimal Disturbances.- 7.4.5 Global Instability.- 7.5 Nonlinear Effects.- 7.5.1 Nonlinear Wave Interactions.- 7.5.2 Nonlinear Parabolized Stability Equations.- 7.5.3 Examples.- 7.6 Disturbance Environment and Receptivity.- 7.6.1 Introduction.- 7.6.2 Nonlocalized and Localized Receptivity.- 7.6.3 An Adjoint Approach to Receptivity.- 7.6.4 Receptivity Using Parabolic Evolution Equations.- 8 Secondary Instability.- 8.1 Introduction.- 8.2 Secondary Instability of Two-Dimensional Waves.- 8.2.1 Derivation of the Equations.- 8.2.2 Numerical Results.- 8.2.3 Elliptical Instability.- 8.3 Secondary Instability of Vortices and Streaks.- 8.3.1 Governing Equations.- 8.3.2 Examples of Secondary Instability of Streaks and Vortices.- 8.4 Eckhaus Instability.- 8.4.1 Secondary Instability of Parallel Flows.- 8.4.2 Parabolic Equations for Spatial Eckhaus Instability.- 9 Transition to Turbulence.- 9.1 Transition Scenarios and Thresholds.- 9.1.1 Introduction.- 9.1.2 Three Transition Scenarios.- 9.1.3 The Most Likely Transition Scenario.- 9.1.4 Conclusions.- 9.2 Breakdown of Two-Dimensional Waves.- 9.2.1 The Zero Pressure Gradient Boundary Layer.- 9.2.2 Breakdown of Mixing Layers.- 9.3 Streak Breakdown.- 9.3.1 Streaks Forced by Blowing or Suction.- 9.3.2 Freestream Turbulence.- 9.4 Oblique Transition.- 9.4.1 Experiments and Simulations in Blasius Flow.- 9.4.2 Transition in a Separation Bubble.- 9.4.3 Compressible Oblique Transition.- 9.5 Transition of Vortex-Dominated Flows.- 9.5.1 Transition in Flows with Curvature.- 9.5.2 Direct Numerical Simulations of Secondary Instability of Crossflow Vortices.- 9.5.3 Experimental Investigations of Breakdown of Cross-flow Vortices.- 9.6 Breakdown of Localized Disturbances.- 9.6.1 Experimental Results for Boundary Layers.- 9.6.2 Direct Numerical Simulations in Boundary Layers.- 9.7 Transition Modeling.- 9.7.1 Low-Dimensional Models of Subcritical Transition.- 9.7.2 Traditional Transition Prediction Models.- 9.7.3 Transition Prediction Models Based on Nonmodal Growth.- 9.7.4 Nonlinear Transition Modeling.- III Appendix.- A Numerical Issues and Computer Programs.- A.1 Global versus Local Methods.- A.2 Runge-Kutta Methods.- A.3 Chebyshev Expansions.- A.4 Infinite Domain and Continuous Spectrum.- A.5 Chebyshev Discretization of the Orr-Sommerfeld Equation.- A.6 MATLAB Codes for Hydrodynamic Stability Calculations.- A.7 Eigenvalues of Parallel Shear Flows.- B Resonances and Degeneracies.- B.1 Resonances and Degeneracies.- B.2 Orr-Sommerfeld-Squire Resonance.- C Adjoint of the Linearized Boundary Layer Equation.- C.1 Adjoint of the Linearized Boundary Layer Equation.- D Selected Problems on Part I.

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Book SynopsisThis book describes the historical development of the principle of stationary action from the 17th to the 20th centuries. Reference is made to the most important contributors to this topic, in particular Bernoullis, Leibniz, Euler, Lagrange and Laplace. The leading theme is how the action principle is applied to problems in classical physics such as hydrodynamics, electrodynamics and gravity, extending also to the modern formulation of quantum mechanics and quantum field theory, especially quantum electrodynamics. A critical analysis of operator versus c-number field theory is given. The book contains many worked examples. In particular, the term "vacuum" is scrutinized.The book is aimed primarily at actively working researchers, graduate students and historians interested in the philosophical interpretation and evolution of physics; in particular, in understanding the action principle and its application to a wide range of natural phenomena.Table of ContentsShort Historical Introduction.- Curva Elastica.- The Curva Elastica, a Curve of Least Energy.- From Euler to Lagrange.- Laplace and the Capillary - 1807.- A Final Application in Elasticity with Jacobi Elliptic Functions.- Short List of Jacobi Elliptic Functions and Constants Used in Chapter 5.- Variational Methods for Periodic Motions; Mathieu Functions.- Lagrangian for Isentropic Irrotational Flow.- Action Principle in Classical Electrodynamics.- The Two Giants in Gravity: Einstein and Hilbert.- The Quantum Action Principle.- The Action Principle in Quantum Field Theory.- Quantum Field Theory on Space-Like Hypersurfaces.- Lagrangian Formulation of Gauge Theories.- Effective Actions (Lagrangians) in Quantum Field Theory.- Modified Photon Propagation Function, Source Theory.

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Book SynopsisThis book addresses the needs of growing community of graduate students and researchers new to the area, for a survey that covers a wide range of pertinent topics, summarizes the current status of the field, and provides the necessary pedagogical materials for newcomers. The investigation of strongly interacting matter under the influence of macroscopic rotational motion is a new, emerging area of research that encompasses a broad range of conventional physics disciplines such as nuclear physics, astrophysics, and condensed matter physics, where the non-trivial interplay between global rotation and spin is generating many novel phenomena. Edited and authored by leading researchers in the field, this book covers the following topics: thermodynamics and equilibrium distribution of rotating matter; quantum field theory and rotation; phase structure of QCD matter under rotation; kinetic theory of relativistic rotating matter; hydrodynamics with spin; magnetic effects in fluid systems with high vorticity and charge; polarization measurements in heavy ion collisions; hydrodynamic modeling of the QCD plasma and polarization calculation in relativistic heavy ion collisions; chiral vortical effect; rotational effects and related topics in neutron stars and condensed matter systems.Trade Review“The book is interesting to everyone who wants to have the detailed and comprehensive review of recent developments in strongly interacting matter under the influence of macroscopic rotational motion.” (Dominik Strzałka, zbMATH 1480.82001, 2022)Table of Contents1. Strongly Interacting Matter under Rotation: An Overview.- 2. Quantum Field Theory and Rotation.- 3. Thermodynamics of Rotating Matter.- 4. Phase Structure of Matter under Rotation.- 5. The Spin Transport of Relativistic Rotating Matter.- 6. Relativistic Hydrodynamics with Spin.- 7. Global and Local Polarization Measurements at RHIC.- 8. Global and Local Polarization Measurements at LHC.- 9. Vorticity and Polarization in Heavy Ion Collisions: Hydrodynamic Models.- 10. Vorticity and Polarization in Heavy Ion Collisions: Transport Models.- 11. Magnetic Effects of Charged Fluid under Rotation.- 12. A Review of Chiral Vertical Effect.

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Book SynopsisThis textbook explores the working principles of all kinds of turbomachines. The same theoretical framework is used to analyze the different machine types. The order in which the different kinds are treated is chosen by the possibility of gradually building up theoretical concepts. For each of the turbomachine kinds, a balance is sought between fundamental understanding and knowledge of practical aspects. Readers are invited through challenging exercises to consider how the theory applies to particular cases. This textbook appeals to senior undergraduate and graduate students in mechanical engineering and to professional engineers seeking to understand the operation of turbomachines. Readers will gain a fundamental understanding of turbomachines and will be able to make a reasoned choice of a turbomachine for a particular application. Table of Contents1. Working Principles2. Basic Components3. Fans4. Compressible Fluids5. Performance Measurement6. Steam Turbines7. Dynamic Similitude8. Pumps9. Hydraulic Turbines10. Wind Turbines11. Power Gas Turbines12. Thrust Gas Turbines13. Axial Compressors14. Radial Compressors15. Axial and Radial Turbines for GasesReferencesIndex

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Book SynopsisIntroduction.- Deformations.- Stress .- Constitutive equations.- Exact solutions of non-linear elasticity.

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Book SynopsisThis concise treatment embraces, in four parts, all the main aspects of theoretical physics. Recent topics such as holography and quantum cryptography are included. The book summarizes what a graduate student, physicist working in industry, or a physics teacher should master during his or her degree course. It will also be useful for deepening one’s insight and it adds new dimensions to understanding of these elemental concepts.Trade ReviewFrom the reviews: "A comprehensive work covering the material that graduate students in physics typically would study in preparing for doctoral candidacy examinations. … This book would be very useful for self-study by motivated students, or for preparation for candidacy exams. … Practicing physicists may find that the brief, accessible treatments of many topics will earn this book a place on a convenient bookshelf. Summing Up: Recommended. Upper-division undergraduates through professionals." (M. C. Ogilvie, CHOICE, Vol. 45 (7), 2008) "The book, written by two … ‘working physicists’, contains what the authors regard as being ‘basic knowledge’ in the standard courses of theoretical physics (yet) held at German Universities. … is primarily intended to cover the ‘Basic Theoretical Physics’ in a single and handy volume. … Hence, the book should be considered as being a kind of ‘compendium’ of … formulas used in theoretical physics where the formulas are filled in between with some remarks." (Jürgen Tolksdorf, Zentralblatt MATH, Vol. 1134 (12), 2008)Table of ContentsFrom the contents: Part I: Mechanics and Aspects of Relativity.- Space and Time.- Force and Mass.- Basic tasks of Mechanics for one-dimensional motions.-The damped and driven harmonic oscillator.- The three fundamental conservation laws.- Motion in central force fields.- The Rutherford scattering cross section.- Lagrange formalism I : The Lagrangian and the Hamiltonian.- Relativity I: Einstein's principle of the shortest proper time and Hamilton's principle of least-action momentum.- Coupled small oscillations.- Rigid bodies.- Remarks on non-integrable systems.- Lagrange formalism II: Constraints.- Accelerated reference frames.- Relativity II: E=mc².- Part II: Electrodynamics and aspects of optics.- Opening: Literature, internet, contents, purpose.- Introduction: units and (mathematical) prelimaries.- Electrostatics and magnetostatics.- Magnetic field of steady electric currents.- The general Maxwell equations I: Faraday's 'law of induction.- Maxwell's displacement current.- The general Maxwell equations II: Electromagnetic waves.- Applications of the electrodynamics in the field of optics.- Conclusion.- Part III: Quantum mechanics.- Introductory remarks.- References and internet.- On the history of quantum mechanics.- Quantum mechanics: Foundations.- One-dimensional problems.- The harmonic oscillator in the wave mechanics.- The hydrogen atom in the wave mechanics.- Abstract quantum mechanics (algebraic methods).- Spin momentum and Pauli's principle (the spin-statistics theorem).- Spin-orbit interaction.- The minimisation principle of Ritz.- Schrödinger's perturbation theory for the statics.- Time-dependent perturbations.- Magnetism as an essentially quantum-mechanical phenomenon.- Cooper pairs.- On the interpretation of quantum mechanics.- Conclusion: Repetition and summary on the history of quantum mechanics.- Looking back and looking forward.- Appendix: On cryptography and quantum cryptography.- Part IV: Thermodynamics and Statistical Physics.- Introductionand overview.- Phenomenological thermodynamics: Temperature and heat.- The fundamental theorems I and II.- Phase transitions, van der Waals theory and related problems.- Kinetic gas theory.- Statistical Physics.- From quantum statistics to the classical statistical physics.- Deepening of the fundamental theorem II.- Shannon's information entropy.- The set of canonical ensembles in the phenomenological thermodynamics.- The relation of Clausius and Clapeyron.- Generation of low and ultralow temperatures, and the fundamental theorem III.- General statistical physics (formal completion): The statistical operator and the trace formalism.- Ideal Bose and Fermi gases.- Applications I.- Applications II.- Conclusion

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