A Modern Approach to Classical Mechanics

Second Edition

Author: Harald Iro

Publisher: World Scientific Publishing Company

ISBN: 9814696307

Category: Science

Page: 528

View: 1207

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

A Modern Approach to Quantum Mechanics

Author: John S. Townsend

Publisher: University Science Books

ISBN: 9781891389139

Category: Science

Page: 476

View: 764

This text allows lecturers to involve their undergraduates in the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound.

Classical Mechanics with Mathematica®

Author: Antonio Romano

Publisher: Springer Science & Business Media

ISBN: 0817683526

Category: Mathematics

Page: 506

View: 9455

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.​ Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica​. The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

A Radically Modern Approach to Introductory Physics

Author: David J. Raymond

Publisher: Dog Ear Publishing

ISBN: 0983039461

Category: Electromagnetism

Page: 442

View: 9308

This nontraditional text arose from the conviction that science and engineering students would benefit from an introductory course which covers all of physics from a modern point of view. The text takes the perspective of a modern particle physicist and is based more on wave dynamics and relativity than on classical mechanics. The subject matter is split into two volumes of twelve chapters each: Volume 1 - Waves, including geometrical optics - Theory of relativity - Relativistic matter waves and quantum mechanics - Classical mechanics as the geometric optics limit of quantum mechanics Volume 2 - Gravity - A treatment of electromagnetism which builds on relativity - Atomic, nuclear, and particle physics - Statistical mechanics and thermodynamics The result is a conceptually challenging but mathematically simple text which can be covered in two semesters or three quarters without omitting any content. Such a course has been offered for over ten years at New Mexico Tech to incoming physics majors and other interested students who are well prepared in high school physics and mathematics. David J. Raymond received a Ph.D. in high energy physics from Stanford University in 1970. He has taught physics and performed research in atmospheric physics at New Mexico Tech since 1973. The publisher will donate a portion of the price of this book to New Mexico Tech for scholarships.

A Modern Approach to Functional Integration

Author: John R. Klauder

Publisher: Springer Science & Business Media

ISBN: 0817647910

Category: Mathematics

Page: 282

View: 6468

This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.

A Modern Approach to Critical Phenomena

Author: Igor Herbut

Publisher: Cambridge University Press

ISBN: 1139460129

Category: Science

Page: N.A

View: 2890

Critical phenomena is one of the most exciting areas of modern physics. This 2007 book provides a thorough but economic introduction into the principles and techniques of the theory of critical phenomena and the renormalization group, from the perspective of modern condensed matter physics. Assuming basic knowledge of quantum and statistical mechanics, the book discusses phase transitions in magnets, superfluids, superconductors, and gauge field theories. Particular attention is given to topics such as gauge field fluctuations in superconductors, the Kosterlitz-Thouless transition, duality transformations, and quantum phase transitions - all of which are at the forefront of physics research. This book contains numerous problems of varying degrees of difficulty, with solutions. These problems provide readers with a wealth of material to test their understanding of the subject. It is ideal for graduate students and more experienced researchers in the fields of condensed matter physics, statistical physics, and many-body physics.

Classical Mechanics

From Newton to Einstein: A Modern Introduction

Author: Martin W. McCall

Publisher: John Wiley & Sons

ISBN: 1119956129

Category: Science

Page: 250

View: 8092

This new edition of Classical Mechanics, aimed at undergraduate physics and engineering students, presents ina user-friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity. The text starts with a careful look at Newton's Laws, before applying them in one dimension to oscillations and collisions. More advanced applications - including gravitational orbits and rigid body dynamics - are discussed after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. Examples given throughout are often unusual for an elementary text, but are made accessible to the reader through discussion and diagrams. Updates and additions for this new edition include: New vector notation in Chapter 1 An enhanced discussion of equilibria in Chapter 2 A new section on a body falling a large distance towards a gravitational source in Chapter 2 New sections in Chapter 8 on general rotation about a fixed principal axes, simple examples of principal axes and principal moments of inertia and kinetic energy of a body rotating about a fixed axis New sections in chapter 9: Foucault pendulum and free rotation of a rigid body; the latter including the famous tennis racquet theorem Enhanced chapter summaries at the end of each chapter Novel problems with numerical answers A solutions manual is available at: www.wiley.com/go/mccall

Geometric Mechanics: Dynamics and symmetry

Author: Darryl D. Holm

Publisher: Imperial College Press

ISBN: 1848161956

Category: Mathematics

Page: 354

View: 3884

Advanced undergraduate and graduate students in mathematics, physics and engineering.

Classical Mechanics with Applications

Author: Porter Wear Johnson

Publisher: World Scientific Publishing Company

ISBN: 9813107863

Category: Science

Page: 296

View: 943

This textbook — appropriate for a one-semester course in classical mechanics at the late undergraduate or early graduate level — presents a fresh, modern approach to mechanics. About 150 exercises, covering a wide variety of topics and applications, have solutions roughly outlined for enhanced understanding. Unique to this text is the versatile application of programming language Mathematica™ throughout to analyze systems and generate results. Coverage is also devoted to the topic on one dimensional continuum systems. The extensive discussions on inverse problems of mechanical systems and the detailed analysis of stability of classical systems certainly make this an outstanding textbook.

Klassische Mechanik

Author: Herbert Goldstein,Charles P. Poole, Jr.,John L. Safko, Sr.

Publisher: John Wiley & Sons

ISBN: 3527662073

Category: Science

Page: 700

View: 9729

Der Goldstein gehört zu den Standardwerken für die Vorlesung in Klassischer Mechanik, die Pflichtvorlesung und Teil des Theorie-Lehrplans jedes Physik-Studienganges ist. Für diese aktuelle Ausgabe haben Charles Poole und John Safko die Texte überarbeitet und neueste Themen, Anwendungen und Notationen eingearbeitet und sind damit auf moderne Trends in der Theoretischen Mechanik eingegangen. Neue numerische Übungen verhelfen den Studenten zur Fähigkeit, Computeranwendungen für die Lösung von Physikproblemen zu benutzen. Mathematische Techniken werden detailliert eingeführt, so daß der Text auch für Studenten ohne den entsprechenden Hintergrund der Theoretischen Mechanik verständlich ist.

Computer Algebra Recipes for Classical Mechanics

Author: Richard H. Enns,George C. McGuire

Publisher: Springer Science & Business Media

ISBN: 146120013X

Category: Mathematics

Page: 265

View: 2525

This is a standalone, but the recipes are correlated with topics found in standard texts, and make use of MAPLE (Release 7). As a reference text, or self-study guide this book is useful for science professionals and engineers.; Good for the classroom correlates with topics found in standard classical mechanics texts.; This book makes use of the powerful computer algebra system MAPLE (Release 7) but no prior knowledge of MAPLE is presumed.; The relevant command structures are explained on a need-to-know basis as the recipes are developed, thus making this a standalone text.

Physics of Optoelectronics

Author: Michael A. Parker

Publisher: CRC Press

ISBN: 1420027719

Category: Technology & Engineering

Page: 798

View: 2826

Physics of Optoelectronics focuses on the properties of optical fields and their interaction with matter. Understanding that lasers, LEDs, and photodetectors clearly exemplify this interaction, the author begins with an introduction to lasers, LEDs, and the rate equations, then describes the emission and detection processes. The book summarizes and reviews the mathematical background of the quantum theory embodied in the Hilbert space. These concepts highlight the abstract form of the linear algebra for vectors and operators, supplying the "pictures" that make the subject more intuitive. A chapter on dynamics includes a brief review of the formalism for discrete sets of particles and continuous media. It also covers the quantum theory necessary for the study of optical fields, transitions, and semiconductor gain. This volume supplements the description of lasers and LEDs by examining the fundamental nature of the light that these devices produce. It includes an analysis of quantized electromagnetic fields and illustrates inherent quantum noise in terms of Poisson and sub-Poisson statistics. It explains matter-light interaction in terms of time-dependent perturbation theory and Fermi's golden rule, and concludes with a detailed discussion of semiconductor emitters and detectors.

Exploring the Limits of Preclassical Mechanics

A Study of Conceptual Development in Early Modern Science: Free Fall and Compounded Motion in the Work of Descartes, Galileo and Beeckman

Author: Peter Damerow,Gideon Freudenthal,Peter McLaughlin,Jürgen Renn

Publisher: Springer Science & Business Media

ISBN: 9780387205731

Category: Mathematics

Page: 412

View: 7779

The question of when and how the basic concepts that characterize modern science arose in Western Europe has long been central to the history of science. This book examines the transition from Renaissance engineering and philosophy of nature to classical mechanics oriented on the central concept of velocity. Descartes, Galileo, and other protagonists of what the authors call "preclassical mechanics" struggled with fundamental concepts and contributed crucial insights to classical mechanics, but it is not clear that they actually realized these insights themselves. This book argues that the emergence of classical mechanics was neither a cumulative change nor an abrupt revolution, but rather that the transformation was the result of exploring the limits and exhausting the possibilities of the existing, largely Aristotelian conceptual system. In the dozen years that have passed since the appearance of the first edition, significant research has been done on Descartes and Galileo and the origins of modern science. There have also been important advances in the accessibility of sources and in technology for analyzing them. For this new edition, the authors take account of the most important new results. They include a new discussion of the doctrine of proportions, an analysis of the role of traditional statics in the construction of Descartes' impact rules, and go deeper into the debate between Descartes and Hobbes on the explanation of refraction. They also provide significant new material on the early development of Galileo's work on mechanics and the law of fall. All translations have been reviewed and revised for consistency of terminology and several new documents have been added. The bibliography has been updated to take account of new literature.

Classical Mechanics, Second Edition

Author: Tai L. Chow

Publisher: CRC Press

ISBN: 1466570008

Category: Science

Page: 639

View: 1142

Classical Mechanics, Second Edition presents a complete account of the classical mechanics of particles and systems for physics students at the advanced undergraduate level. The book evolved from a set of lecture notes for a course on the subject taught by the author at California State University, Stanislaus, for many years. It assumes the reader has been exposed to a course in calculus and a calculus-based general physics course. However, no prior knowledge of differential equations is required. Differential equations and new mathematical methods are developed in the text as the occasion demands. The book begins by describing fundamental concepts, such as velocity and acceleration, upon which subsequent chapters build. The second edition has been updated with two new sections added to the chapter on Hamiltonian formulations, and the chapter on collisions and scattering has been rewritten. The book also contains three new chapters covering Newtonian gravity, the Hamilton-Jacobi theory of dynamics, and an introduction to Lagrangian and Hamiltonian formulations for continuous systems and classical fields. To help students develop more familiarity with Lagrangian and Hamiltonian formulations, these essential methods are introduced relatively early in the text. The topics discussed emphasize a modern perspective, with special note given to concepts that were instrumental in the development of modern physics, for example, the relationship between symmetries and the laws of conservation. Applications to other branches of physics are also included wherever possible. The author provides detailed mathematical manipulations, while limiting the inclusion of the more lengthy and tedious ones. Each chapter contains homework problems of varying degrees of difficulty to enhance understanding of the material in the text. This edition also contains four new appendices on D'Alembert's principle and Lagrange's equations, derivation of Hamilton’s principle, Noether’s theorem, and conic sections.

Translations. Ser. 2, 168. Dynamical systems in classical mechanics

Author: Valeriĭ Viktorovich Kozlov

Publisher: American Mathematical Soc.

ISBN: 9780821804278

Category: Differentiable dynamical systems.

Page: 254

View: 5599

This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include ... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics

Der Wiener Kreis in Ungarn

The Vienna Circle in Hungary

Author: András Máté,Miklós Rédei,Friedrich Stadler

Publisher: Springer-Verlag

ISBN: 3709101778

Category: Philosophy

Page: 304

View: 4804

Der Einfluss des Wiener Kreises zeigt sich bis heute auf allen Gebieten der Philosophie. Mit der erzwungenen Emigration der meisten Mitglieder wurde diese logisch-empiristische Tradition in Mitteleuropa jedoch vorerst unterbrochen. Erst als der logische Empirismus nach dem 2. Weltkrieg in der angelsächsischen Welt zu einer wichtigen Denkrichtung geworden war, wirkte er von dort zurück nach Mitteleuropa. In den Beiträgen analysieren und bewerten namhafte Experten die Auswirkungen des Logischen Empirismus auf die Entwicklung der Philosophie in Ungarn.

Feynman's Thesis

A New Approach to Quantum Theory

Author: Richard Phillips Feynman,Laurie M. Brown

Publisher: World Scientific

ISBN: 9812563660

Category: Science

Page: 119

View: 5667

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.

Classical Mechanics

Transformations, Flows, Integrable and Chaotic Dynamics

Author: Joseph L. McCauley

Publisher: Cambridge University Press

ISBN: 9780521578820

Category: Science

Page: 469

View: 8519

An advanced text for first-year graduate students in physics and engineering taking a standard classical mechanics course, this is the first book to describe the subject in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability. It introduces flows in phase space and transformations early and illustrates their applications throughout the text. The standard integrable problems of elementary physics are analyzed from the standpoint of flows, transformations, and integrability. This approach allows the author to introduce most of the interesting ideas of modern nonlinear dynamics via the most elementary nonintegrable problems of Newtonian mechanics. This text will also interest specialists in nonlinear dynamics, mathematicians, engineers and system theorists.

The Logico-Algebraic Approach to Quantum Mechanics

Historical evolution. Vol. 1

Author: C.A. Hooker

Publisher: Springer Science & Business Media

ISBN: 9789027705679

Category: Philosophy

Page: 622

View: 4369

The twentieth century has witnessed a striking transformation in the un derstanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi tional opinion that one should look to the specific applications of a theory in order to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that struc ture, while to understand how a theory might be modified in light of its experimental inadequacies one must be intimately acquainted with how it is applied. Quantum theory itself has gone through a development this century which illustrates strikingly the shifting perspective. From a collection of intuitive physical maneuvers under Bohr, through a formative stage in which the mathematical framework was bifurcated (between Schrödinger and Heisenberg) to an elegant culmination in von Neumann's Hilbert space formulation the elementary theory moved, flanked even at the later stage by the ill-understood formalisms for the relativistic version and for the field-theoretic altemative; after that we have a gradual, but constant, elaboration of all these quantal theories as abstract mathematical struc tures (their point of departure being von Neumann's formalism) until at the present time theoretical work is heavily preoccupied with the manip ulation of purely abstract structures.

Semiclassical Approach to Mesoscopic Systems

Classical Trajectory Correlations and Wave Interference

Author: Daniel Waltner

Publisher: Springer Science & Business Media

ISBN: 3642245277

Category: Science

Page: 182

View: 658

This volume describes mesoscopic systems with classically chaotic dynamics using semiclassical methods which combine elements of classical dynamics and quantum interference effects. Experiments and numerical studies show that Random Matrix Theory (RMT) explains physical properties of these systems well. This was conjectured more than 25 years ago by Bohigas, Giannoni and Schmit for the spectral properties. Since then, it has been a challenge to understand this connection analytically. The author offers his readers a clearly-written and up-to-date treatment of the topics covered. He extends previous semiclassical approaches that treated spectral and conductance properties. He shows that RMT results can in general only be obtained semiclassically when taking into account classical configurations not considered previously, for example those containing multiply traversed periodic orbits. Furthermore, semiclassics is capable of describing effects beyond RMT. In this context he studies the effect of a non-zero Ehrenfest time, which is the minimal time needed for an initially spatially localized wave packet to show interference. He derives its signature on several quantities characterizing mesoscopic systems, e. g. dc and ac conductance, dc conductance variance, n-pair correlation functions of scattering matrices and the gap in the density of states of Andreev billiards.