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Classical Mechanics: A Computational Approach with Examples Using Mathematica and Python
by Vasilis Pagonis Christopher W. KulpClassical Mechanics: A Computational Approach with Examples using Python and Mathematica provides a unique, contemporary introduction to classical mechanics, with a focus on computational methods. In addition to providing clear and thorough coverage of key topics, this textbook includes integrated instructions and treatments of computation.This newly updated and revised second edition includes two new appendices instructing the reader in both the Python and Mathematica languages. All worked example problems in the second edition contain both Python and Mathematica code. New end-of-chapter problems explore the application of computational methods to classical mechanics problems.Full of pedagogy, it contains both analytical and computational example problems within the body of each chapter. The example problems teach readers both analytical methods and how to use computer algebra systems and computer programming to solve problems in classical mechanics. End-of-chapter problems allow students to hone their skills in problem solving with and without the use of a computer. The methods presented in this book can then be used by students when solving problems in other fields both within and outside of physics.It is an ideal textbook for undergraduate students in physics, mathematics, and engineering studying classical mechanics.Key Features: Gives readers the "big picture" of classical mechanics and the importance of computation in the solution of problems in physics Numerous example problems using both analytical and computational methods, as well as explanations as to how and why specific techniques were used Online resources containing specific example codes to help students learn computational methods and write their own algorithms A solutions manual is available via the Routledge Instructor Hub and all example codes in the book are available via the Support Material tab, and at the book’s GitHub page: https://github.com/vpagonis/Classical_Mechanics_2nd_Edition
Classical Mechanics: From Particles to Continua and Regularity to Chaos (Texts and Readings in Physical Sciences #22)
by Govind S. KrishnaswamiThis well-rounded and self-contained treatment of classical mechanics strikes a balance between examples, concepts, phenomena and formalism. While addressed to graduate students and their teachers, the minimal prerequisites and ground covered should make it useful also to undergraduates and researchers. Starting with conceptual context, physical principles guide the development. Chapters are modular and the presentation is precise yet accessible, with numerous remarks, footnotes and problems enriching the learning experience. Essentials such as Galilean and Newtonian mechanics, the Kepler problem, Lagrangian and Hamiltonian mechanics, oscillations, rigid bodies and motion in noninertial frames lead up to discussions of canonical transformations, angle-action variables, Hamilton-Jacobi and linear stability theory. Bifurcations, nonlinear and chaotic dynamics as well as the wave, heat and fluid equations receive substantial coverage. Techniques from linear algebra, differential equations, manifolds, vector and tensor calculus, groups, Lie and Poisson algebras and symplectic and Riemannian geometry are gently introduced. A dynamical systems viewpoint pervades the presentation. A salient feature is that classical mechanics is viewed as part of the wider fabric of physics with connections to quantum, thermal, electromagnetic, optical and relativistic physics highlighted. Thus, this book will also be useful in allied areas and serve as a stepping stone for embarking on research.
Classical Mechanics: Hamiltonian and Lagrangian Formalism
by Alexei DeriglazovThe revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.
Classical Mechanics: Hamiltonian and Lagrangian Formalism
by Alexei DeriglazovFormalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.
Classical Mechanics: Including an Introduction to the Theory of Elasticity (Undergraduate Lecture Notes in Physics)
by Reinhard HentschkeThis textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e. g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory chapter compiles all essential mathematical tools, ranging from coordinates to complex numbers. Completely solved problems and examples facilitate a thorough understanding of the material.
Classical Mechanics: Kinematics and Statics (Advances in Mechanics and Mathematics #28)
by Jan AwrejcewiczThis is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.
Classical Mechanics: Lectures on Theoretical Physics
by David TongAny education in theoretical physics begins with the laws of classical mechanics. The basics of the subject were laid down long ago by Galileo and Newton and are enshrined in the famous equation F=ma that we all learn in school. But there is much more to the subject and, in the intervening centuries, the laws of classical mechanics were reformulated to emphasis deeper concepts such as energy, symmetry, and action. This textbook describes these different approaches to classical mechanics, starting with Newton's laws before turning to subsequent developments such as the Lagrangian and Hamiltonian approaches. The book emphasises Noether's profound insights into symmetries and conservation laws, as well as Einstein's vision of spacetime, encapsulated in the theory of special relativity. Classical mechanics is not the last word on theoretical physics. But it is the foundation for all that follows. The purpose of this book is to provide this foundation.
Classical Mechanics: Problems and Solutions
by Carolina C. Ilie Zachariah S. Schrecengost Elina M. van KempenThis book of problems and solutions in classical mechanics is dedicated to junior or senior undergraduate students in physics, engineering, applied mathematics, astronomy, or chemistry who may want to improve their problems solving skills, or to freshman graduate students who may be seeking a refresh of the material. The book is structured in ten chapters, starting with Newton’s laws, motion with air resistance, conservation laws, oscillations, and the Lagrangian and Hamiltonian Formalisms. The last two chapters introduce some ideas in nonlinear dynamics, chaos, and special relativity. Each chapter starts with a brief theoretical outline, and continues with problems and detailed solutions. A concise presentation of differential equations can be found in the appendix. A variety of problems are presented, from the standard classical mechanics problems, to context rich problems and more challenging problems. Key features: Presents a theoretical outline for each chapter. Motivates the students with standard mechanics problems with step-by-step explanations. Challenges the students with more complex problems with detailed solutions.
Classical Mechanics: Theory and Mathematical Modeling (Cornerstones)
by Emmanuele Dibenedetto* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries
Classical Methods in Structure Elucidation of Natural Products
by Reinhard W. HoffmannOrganic chemistry as we know it today originated from a preoccupation with substances isolated from nature. In the period from 1860 to 1960, the main task was to elucidate their molecular structure by way of degradation and synthesis. In light of the limited experimental methods available and the lack of established reference compounds, this represented an unparalleled intellectual challenge. This book makes use of twenty-five representative examples to retrace the great accomplishments made by the generation of chemists during this era. At the same time, it questions the reliability of the experimental results when judged by today's criteria, particularly since the structures for numerous natural products are stated as established facts in standard text books. With each chapter devoted to one organic compound, the author combines results from historic experiments to trace a line of evidence that may follow the path put forward by the original contributors. However, in some cases the experimental facts have been combined to form another, hopefully shorter, line of evidence. As a result, readers are able to determine for themselves the 'facts behind the established structure assignments' of a number of important natural products.
Classical Mirror Symmetry (SpringerBriefs In Mathematical Physics #29)
by Masao JinzenjiThis book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold.First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold.On the B-model side, the process of construction of a pair of mirror Calabi–Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard–Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis.On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given.The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.
Classical Mythology of the Constellations: Timeless Tales of the Starry Night Sky
by Annette GieseckeA retelling of the classic myths and timeless tales by bestselling author Annette Giesecke that underlie the 88 named constellations in the night sky--from Andromeda to Orion to Ursa Major.Classical Mythology of the Constellations is a stargazer's guide to the wondrous stories of the gods, heroes, and monsters that populate the night sky. As long as humans have lived on Earth, they have gazed up at the starry sky with fascination and longing. For the ancient Greeks and Romans, the Sun, Moon, and Earth were gods. The stars beyond our Solar System, however, represented heroes, animals, and monsters that the gods placed in the sky after their death. These include the great hunter Orion and the scorpion who killed him with its sting, the beautiful maiden Callisto who was turned into a bear (Ursa Major) by the goddess Hera, Perseus, the slayer of Medusa, and many more. In this beautifully designed work, stunningly illustrated by Jim Tierney, Giesecke tells the origin stories of the 48 constellations, first catalogued by the astronomer Ptolemy in the second century CE. A final section covers the names, locations, and brief descriptions of the remaining 40 constellations catalogued by astronomers in the sixteenth, seventeenth, and eighteenth centuries, which are not named for Classical figures. Organized by hemisphere and celestial quadrant, the book also includes two illustrated star maps to help guide the reader to the location of each constellation, as well as 48 color plates throughout.
Classical Newtonian Gravity: A Comprehensive Introduction, with Examples and Exercises (UNITEXT for Physics)
by Roberto A. Capuzzo DolcettaThis textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.
Classical Optics and its Applications
by Masud MansuripurCovering a broad range of fundamental topics in classical optics and electro-magnetism, this book is ideal for graduate-level courses in optics, providing supplementary reading materials for teachers and students alike. Industrial scientists and engineers developing modern optical systems will also find it an invaluable resource. Now in color, this second edition contains 13 new chapters, covering optical pulse compression, the Hanbury Brown-Twiss experiment, the Sagnac effect, Doppler shift and stellar aberration, and optics of semiconductor diode lasers. The first half of the book deals primarily with the basic concepts of optics, while the second half describes how these concepts can be used in a variety of technological applications. Each chapter is concerned with a single topic, developing an understanding through the use of diagrams, examples, numerical simulations, and logical arguments. The mathematical content is kept to a minimum to provide the reader with insightful discussions of optical phenomena.
Classical Pendulum Feels Quantum Back-Action (Springer Theses)
by Nobuyuki MatsumotoIn this thesis, ultimate sensitive measurement forweak force imposed on a suspended mirror is performed with the help of a laserand an optical cavity for the development of gravitational-wave detectors. According to the Heisenberg uncertainty principle, such measurements aresubject to a fundamental noise called quantum noise, which arises from thequantum nature of a probe (light) and a measured object (mirror). One of thesources of quantum noise is the quantum back-action, which arises from thevacuum fluctuation of the light. It sways the mirror via the momentumtransferred to the mirror upon its reflection for the measurement. The authordiscusses a fundamental trade-off between sensitivity and stability in themacroscopic system, and suggests using a triangular cavity that can avoid thistrade-off. The development of an optical triangular cavity is described and itscharacterization of the optomechanical effect in the triangular cavity isdemonstrated. As a result, for the first time in the world the quantum back-actionimposed on the 5-mg suspended mirror is significantly evaluated. This workcontributes to overcoming the standard quantum limit in the future.
Classical Physics of Matter (Malvern Physics Series)
by J BoltonClassical Physics of Matter explores the properties of matter that can be explained more or less directly in terms of classical physics. Among the topics discussed are the principles of flight and the operation of engines and refrigerators. The discussion introduces ideas such as temperature, heat, and entropy that will take you beyond Newtonian me
Classical Probability in the Enlightenment
by Lorraine DastonWhat did it mean to be reasonable in the Age of Reason? Classical probabilists from Jakob Bernouli through Pierre Simon Laplace intended their theory as an answer to this question--as "nothing more at bottom than good sense reduced to a calculus," in Laplace's words. In terms that can be easily grasped by nonmathematicians, Lorraine Daston demonstrates how this view profoundly shaped the internal development of probability theory and defined its applications.
Classical Probability in the Enlightenment, New Edition
by Lorraine DastonAn award-winning history of the Enlightenment quest to devise a mathematical model of rationalityWhat did it mean to be reasonable in the Age of Reason? Enlightenment mathematicians such as Blaise Pascal, Jakob Bernoulli, and Pierre Simon Laplace sought to answer this question, laboring over a theory of rational decision, action, and belief under conditions of uncertainty. Lorraine Daston brings to life their debates and philosophical arguments, charting the development and application of probability theory by some of the greatest thinkers of the age. Now with an incisive new preface, Classical Probability in the Enlightenment traces the emergence of new kind of mathematics designed to turn good sense into a reasonable calculus.
Classical Recording: A Practical Guide in the Decca Tradition (Audio Engineering Society Presents)
by Mark Rogers Caroline Haigh John DunkerleyClassical Recording: A Practical Guide in the Decca Tradition is the authoritative guide to all aspects of recording acoustic classical music. Offering detailed descriptions, diagrams, and photographs of fundamental recording techniques such as the Decca tree, this book offers a comprehensive overview of the essential skills involved in successfully producing a classical recording. Written by engineers with years of experience working for Decca and Abbey Road Studios and as freelancers, Classical Recording equips the student, the interested amateur, and the practising professional with the required knowledge and confidence to tackle everything from solo piano to opera.
Classical Relaxation Phenomenology
by Ian M. HodgeThis book serves as a self-contained reference source for engineers, materials scientists, and physicists with an interest in relaxation phenomena. It is made accessible to students and those new to the field by the inclusion of both elementary and advanced math techniques, as well as chapter opening summaries that cover relevant background information and enhance the book's pedagogical value. These summaries cover a wide gamut from elementary to advanced topics.The book is divided into three parts. The opening part, on mathematics, presents the core techniques and approaches. Parts II and III then apply the mathematics to electrical relaxation and structural relaxation, respectively. Part II discusses relaxation of polarization at both constant electric field (dielectric relaxation) and constant displacement (conductivity relaxation), topics that are not often discussed together. Part III primarily discusses enthalpy relaxation of amorphous materials within and below the glass transition temperature range. It takes a practical approach inspired by applied mathematics in which detailed rigorous proofs are eschewed in favor of describing practical tools that are useful to scientists and engineers. Derivations are however given when these provide physical insight and/or connections to other material.A self-contained reference on relaxation phenomenaDetails both the mathematical basis and applicationsFor engineers, materials scientists, and physicists
Classical Solutions in Quantum Field Theory
by Erick J. WeinbergClassical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang-Mills instantons and on bounce solutions.
Classical Statistical Mechanics with Nested Sampling (Springer Theses)
by Robert John Nicholas BaldockThis thesis develops a nested sampling algorithm into a black box tool for directly calculating the partition function, and thus the complete phase diagram of a material, from the interatomic potential energy function. It represents a significant step forward in our ability to accurately describe the finite temperature properties of materials. In principle, the macroscopic phases of matter are related to the microscopic interactions of atoms by statistical mechanics and the partition function. In practice, direct calculation of the partition function has proved infeasible for realistic models of atomic interactions, even with modern atomistic simulation methods. The thesis also shows how the output of nested sampling calculations can be processed to calculate the complete PVT (pressure-volume-temperature) equation of state for a material, and applies the nested sampling algorithm to calculate the pressure-temperature phase diagrams of aluminium and a model binary alloy.
Classical Systems in Quantum Mechanics
by Pavel BónaThis book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".
Classical Theory of Electricity and Magnetism: A Course of Lectures (Texts and Readings in Physical Sciences #21)
by Amal Kumar RaychaudhuriThis book examines the topics of magnetohydrodynamics and plasma oscillations, in addition to the standard topics discussed to cover courses in electromagnestism, electrodynamics, and fundamentals of physics, to name a few. This textbook on electricity and magnetism is primarily targeted at graduate students of physics. The undergraduate students of physics also find the treatment of the subject useful. The treatment of the special theory of relativity clearly emphasises the Lorentz covariance of Maxwell's equations. The rather abstruse topic of radiation reaction is covered at an elementary level, and the Wheeler–Feynman absorber theory has been dwelt upon briefly in the book.
Classical Thermodynamics of Fluid Systems: Principles and Applications
by Juan H. Vera Grazyna Wilczek-VeraThis text explores the connections between different thermodynamic subjects related to fluid systems. Emphasis is placed on the clarification of concepts by returning to the conceptual foundation of thermodynamics and special effort is directed to the use of a simple nomenclature and algebra. The book presents the structural elements of classical thermodynamics of fluid systems, covers the treatment of mixtures, and shows via examples and references both the usefulness and the limitations of classical thermodynamics for the treatment of practical problems related to fluid systems. It also includes diverse selected topics of interest to researchers and advanced students and four practical appendices, including an introduction to material balances and step-by-step procedures for using the Virial EOS and the PRSV EOS for fugacities and the ASOG-KT group method for activity coefficients. The Olivera-Fuentes table of PRSV parameters for more than 800 chemical compounds and the Gmehling-Tochigi tables of ASOG interaction parameters for 43 groups are included.