A Modern Approach to Classical Mechanics

Second Edition

Author: Harald Iro

Publisher: World Scientific Publishing Company

ISBN: 9814696307

Category: Science

Page: 528

View: 4663


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: 370


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

From Newton to Einstein: A Modern Introduction

Author: Martin W. McCall

Publisher: John Wiley & Sons

ISBN: 1119956129

Category: Science

Page: 250

View: 9926


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

A History of Mechanics

Author: René Dugas

Publisher: Courier Corporation

ISBN: 0486173372

Category: Science

Page: 688

View: 5890


Monumental study traces the history of mechanical principles chronologically from antiquity through the early 20th century. Contributions of ancient Greeks, Leonardo, Galileo, Kepler, Lagrange, others. 116 illustrations.

Classical Mechanics with Mathematica®

Author: Antonio Romano,Addolorata Marasco

Publisher: Springer

ISBN: 3319775952

Category: Science

Page: 644

View: 600


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 authors from over 30 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 Hamilton—while also painting a clear picture of the most modern developments. The text 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. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material. Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Structure and Interpretation of Classical Mechanics

Author: Gerald Jay Sussman,Jack Wisdom

Publisher: MIT Press

ISBN: 0262028964

Category: Science

Page: 584

View: 2381


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.

Classical Mechanics

Transformations, Flows, Integrable and Chaotic Dynamics

Author: Joseph L. McCauley

Publisher: Cambridge University Press

ISBN: 9780521578820

Category: Science

Page: 469

View: 9980


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.

Classical Dynamics

A Modern Perspective

Author: E C G Sudarshan,N Mukunda

Publisher: World Scientific Publishing Company

ISBN: 9814713899

Category: Science

Page: 612

View: 3584


Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics. Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of dynamical systems is discussed in detail, and Poisson brackets are developed as a realization of Lie brackets. Other topics include treatments of classical spin, elementary relativistic systems in the classical context, irreducible realizations of the Galileo and Poincaré groups, and hydrodynamics as a Galilean field theory. Students will also find that this approach that deals with problems of manifest covariance, the no-interaction theorem in Hamiltonian mechanics and the structure of action-at-a-distance theories provides all the essential preparatory groundwork for a passage to quantum field theory. This reprinting of the original text published in 1974 is a testimony to the vitality of the contents that has remained relevant over nearly half a century.

Classical Mechanics with Applications

Author: Porter Wear Johnson

Publisher: World Scientific Publishing Company

ISBN: 9813107863

Category: Science

Page: 296

View: 8764


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.


From Newton's Laws to Deterministic Chaos

Author: Florian Scheck

Publisher: Springer Science & Business Media

ISBN: 364205370X

Category: Science

Page: 547

View: 8460


Purpose and Emphasis. Mechanics not only is the oldest branch of physics but was and still is the basis for all of theoretical physics. Quantum mechanics can hardly be understood, perhaps cannot even be formulated, without a good kno- edge of general mechanics. Field theories such as electrodynamics borrow their formal framework and many of their building principles from mechanics. In short, throughout the many modern developments of physics where one frequently turns back to the principles of classical mechanics its model character is felt. For this reason it is not surprising that the presentation of mechanics re?ects to some - tent the development of modern physics and that today this classical branch of theoretical physics is taught rather differently than at the time of Arnold S- merfeld, in the 1920s, or even in the 1950s, when more emphasis was put on the theoryandtheapplicationsofpartial-differentialequations. Today, symmetriesand invariance principles, the structure of the space–time continuum, and the geom- rical structure of mechanics play an important role. The beginner should realize that mechanics is not primarily the art of describing block-and-tackles, collisions of billiard balls, constrained motions of the cylinder in a washing machine, or - cycle riding.

Statistical Mechanics in a Nutshell

Author: Luca Peliti

Publisher: Princeton University Press

ISBN: 0691145296

Category: Science

Page: 398

View: 816


Statistical mechanics is one of the most exciting areas of physics today, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. Statistical Mechanics in a Nutshell offers the most concise, self-contained introduction to this rapidly developing field. Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to the very threshold of today's cutting-edge research. Statistical Mechanics in a Nutshell zeroes in on the most relevant and promising advances in the field, including the theory of phase transitions, generalized Brownian motion and stochastic dynamics, the methods underlying Monte Carlo simulations, complex systems--and much, much more. The essential resource on the subject, this book is the most up-to-date and accessible introduction available for graduate students and advanced undergraduates seeking a succinct primer on the core ideas of statistical mechanics. Provides the most concise, self-contained introduction to statistical mechanics Focuses on the most promising advances, not complicated calculations Requires only elementary calculus and elementary mechanics Guides readers from the basics to the threshold of modern research Highlights the broad scope of applications of statistical mechanics

Classical Mechanics with Calculus of Variations and Optimal Control

An Intuitive Introduction

Author: Mark Levi

Publisher: American Mathematical Soc.

ISBN: 0821891383

Category: Mathematics

Page: 299

View: 4068


This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Classical Mechanics

Author: John Robert Taylor

Publisher: University Science Books

ISBN: 9781891389221

Category: Science

Page: 786

View: 5237


'Classical Mechanics' is intended for students who have studied some mechanics in an introductory physics course. A particular highlight is the chapter on chaos, which focuses on a few simple systems to give truly comprehensible coverage.

Classical Mechanics Illustrated by Modern Physics

42 Problems with Solutions

Author: David Gu‚ry-Odelin,Thierry Lahaye

Publisher: World Scientific

ISBN: 1848164793

Category: Science

Page: 251

View: 7436


In many fields of modern physics, classical mechanics plays a key role. This book provides an illustration of classical mechanics in the form of problems (at the bachelor level) inspired - for most of them - by contemporary research in physics, and resulting from the teaching and research experience of the authors.

Classical Mechanics

A Modern Perspective

Author: Vernon Barger,Martin G. Olsson

Publisher: McGraw-Hill College

ISBN: 9780070037342

Category: Technology & Engineering

Page: 418

View: 6247


This outstanding volume in the McGraw-Hill International Series in Pure and Applied Physics provides solid coverage of the principles of mechanics in a well-written, accessible style. Topic coverage for the second edition of Classical Mechanics: A Modern Perspective includes linear motion, energy conservation, Lagrange's equations, momentum conservation, as well as discussions of nonlinear mechanics and relativity. The text is comprehensive and designed to be appropriate for one- or two-semester introductory mechanics courses. Drs. Barger and Olsson have taken great care to provide readers with the most understandable presentation possible, including an abundance of new and relevant examples, problems, and interesting applications. In order to develop the most up-to-date coverage of mechanics in the second edition, the authors have included modern coverage of topics in chaos and cosmology, as well as numerous discussions of numerical techniques.

Mathematical Methods of Classical Mechanics

Author: V.I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 1475720637

Category: Mathematics

Page: 520

View: 374


This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

A Radically Modern Approach to Introductory Physics

Author: David J. Raymond

Publisher: Dog Ear Publishing

ISBN: 0983039461

Category: Electromagnetism

Page: 442

View: 8263


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: 0817647902

Category: Mathematics

Page: 282

View: 6156


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.