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The Principle Of Least Action
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Book Synopsis The Principle of Least Action by : Alberto Rojo
Download or read book The Principle of Least Action written by Alberto Rojo and published by Cambridge University Press. This book was released on 2018-03-29 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text brings history and the key fields of physics together to present a unique technical discussion of the principles of least action.
Book Synopsis The Feynman lectures on physics: Mainly electromagnetism and matter by :
Download or read book The Feynman lectures on physics: Mainly electromagnetism and matter written by and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Karl Friedrich Siburg Publisher :Springer Science & Business Media ISBN 13 :9783540219446 Total Pages :148 pages Book Rating :4.2/5 (194 download)
Book Synopsis The Principle of Least Action in Geometry and Dynamics by : Karl Friedrich Siburg
Download or read book The Principle of Least Action in Geometry and Dynamics written by Karl Friedrich Siburg and published by Springer Science & Business Media. This book was released on 2004-05-17 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.
Book Synopsis The Lazy Universe by : Jennifer Coopersmith
Download or read book The Lazy Universe written by Jennifer Coopersmith and published by Oxford University Press. This book was released on 2017-04-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.
Book Synopsis Feynman's Thesis by : Richard Phillips Feynman
Download or read book Feynman's Thesis written by Richard Phillips Feynman and published by World Scientific. This book was released on 2005 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.
Book Synopsis Variational Principles in Dynamics and Quantum Theory by : Wolfgang Yourgrau
Download or read book Variational Principles in Dynamics and Quantum Theory written by Wolfgang Yourgrau and published by Courier Corporation. This book was released on 2012-04-26 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div
Book Synopsis Variational Principles in Classical Mechanics by : Douglas Cline
Download or read book Variational Principles in Classical Mechanics written by Douglas Cline and published by . This book was released on 2018-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.
Book Synopsis The Theoretical Minimum by : Leonard Susskind
Download or read book The Theoretical Minimum written by Leonard Susskind and published by Basic Books. This book was released on 2014-04-22 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: A master teacher presents the ultimate introduction to classical mechanics for people who are serious about learning physics "Beautifully clear explanations of famously 'difficult' things," -- Wall Street Journal If you ever regretted not taking physics in college -- or simply want to know how to think like a physicist -- this is the book for you. In this bestselling introduction to classical mechanics, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.
Book Synopsis The Development of the Action Principle by : Walter Dittrich
Download or read book The Development of the Action Principle written by Walter Dittrich and published by Springer Nature. This book was released on 2021-05-29 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book Mechanics written by L D Landau and published by Elsevier. This book was released on 1982-01-29 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics.The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Book Synopsis Variational Principles of Continuum Mechanics by : Victor Berdichevsky
Download or read book Variational Principles of Continuum Mechanics written by Victor Berdichevsky and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.
Book Synopsis An Introduction to the Calculus of Variations by : L.A. Pars
Download or read book An Introduction to the Calculus of Variations written by L.A. Pars and published by Courier Corporation. This book was released on 2013-12-10 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.
Book Synopsis Human Behavior and the Principle of Least Effort by : George Kingsley Zipf
Download or read book Human Behavior and the Principle of Least Effort written by George Kingsley Zipf and published by Ravenio Books. This book was released on 2016-01-27 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic is arranged as follows: Preface 1. The Question of Practical Application. 2. The Question of Natural Science. 1. Introduction and Orientation I. The Selection of a Path II. The “Singleness of the Superlative” III. The Principle of Least Effort IV. The Scope of the Principle: “Tools-and-Jobs” V. Previous Studies VI. Prospectus 2. On the Economy of Words I. In Medias Res: Vocabulary Usage, and the Forces of Unification and Diversification II. The Question of Vocabulary Balance III. The Orderly Distribution of Meanings IV. The Integrality of Frequencies V. The Integrality of Rank VI. The Length of Intervals Between Repetitions VII. The Problem of Spreading Work Over Time (The Even Distribution of Work Over Time) 3. Formal Semantic Balance and the Economy of Evolutionary Process I. The “Minimum Equation” Of Arrangement II. The Law of Abbreviation of Words III. The Law of Diminishing Returns of Tools IV. The Law of Diminishing Returns of Words 4. Children’s Verbalizations and the “Origin of Speech” I. The Problem II. Quantitative Data III. Theoretical Discussion of the “Origin” Of Speech IV. Summary 5. Language as Sensation and Mentation I. The Comparative Conservatism of Tools in the Risks and Opportunities of the Environment II. The Economy of Sensation III. Mentation: The Correlation of Sensory Data IV. A Mind as a Unit Semantic System V. Intellectual Rigidity and Death: Miscellanea V. Summary: The N Minimum 6. The Ego as the “Origin” Of a Frame of Reference I. A Definition of an Organism II. The Biosocial Population of Organisms III. The Economy of Procreation IV. The Synchrony of the Biosocial Continuum 7. Mind and the Economy of Symbolic Process: Sex, Culture, and Schizophrenia I. Human Sexual Activity II. The Economy of Symbolic Process (Substitution III. Culture, Society, and the Superego IV. Autism and the Confusion of Kinds of Reality V. On Schizophrenic Speech VI. Semantic Dynamics: Summary VI. Language and the Structure of the Personality 8. The Language of Dreams and of Art I. The Language of Dreams II. The Language of Art III. Language and the Structure of the Personality: Mary of Part One 9. The Economy of Geography I. A Lemma in Which a Number of Human Beings Becomes Increasingly More Organized II. The Hypothesis of the “Minimum Equation” III. Empiric Tests IV. Concluding Remarks 10. Intranational and International Cooperation and Conflict I. Canadian Data II. Unstable and Stable Intranational Conditions III. Stable and Unstable International Equilibria 11. The Distribution of Economic Power and Social Status I. Theoretical Considerations II. Empiric Data III. The Interaction Between Individuals: Dominance and Submission IV. Summary 12. Prestige Symbols and Cultural Vogues I. Theoretical Considerations II. Pioneer Empiric Data III. Musical Composers and Compositions IV. Samples of Congressional Action V. Summary
Book Synopsis Energy, the Subtle Concept by : Jennifer Coopersmith
Download or read book Energy, the Subtle Concept written by Jennifer Coopersmith and published by OUP Oxford. This book was released on 2015-05-14 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy is at the heart of physics and of huge importance to society and yet no book exists specifically to explain it, and in simple terms. In tracking the history of energy, this book is filled with the thrill of the chase, the mystery of smoke and mirrors, and presents a fascinating human-interest story. Moreover, following the history provides a crucial aid to understanding: this book explains the intellectual revolutions required to comprehend energy, revolutions as profound as those stemming from Relativity and Quantum Theory. Texts by Descartes, Leibniz, Bernoulli, d'Alembert, Lagrange, Hamilton, Boltzmann, Clausius, Carnot and others are made accessible, and the engines of Watt and Joule are explained. Many fascinating questions are covered, including: - Why just kinetic and potential energies - is one more fundamental than the other? - What are heat, temperature and action? - What is the Hamiltonian? - What have engines to do with physics? - Why did the steam-engine evolve only in England? - Why S=klogW works and why temperature is IT. Using only a minimum of mathematics, this book explains the emergence of the modern concept of energy, in all its forms: Hamilton's mechanics and how it shaped twentieth-century physics, and the meaning of kinetic energy, potential energy, temperature, action, and entropy. It is as much an explanation of fundamental physics as a history of the fascinating discoveries that lie behind our knowledge today.
Book Synopsis Structure and Interpretation of Classical Mechanics, second edition by : Gerald Jay Sussman
Download or read book Structure and Interpretation of Classical Mechanics, second edition written by Gerald Jay Sussman and published by MIT Press. This book was released on 2015-02-06 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.
Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
