Structure and Interpretation of Classical Mechanics, second edition PDF Download
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Author: Gerald Jay Sussman
Publisher: MIT Press
ISBN: 0262028964
Category : Science
Languages : en
Pages : 580
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Book Description
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.
Author: Gerald Jay Sussman
Publisher: MIT Press
ISBN: 0262028964
Category : Science
Languages : en
Pages : 580
Get Book Here
Book Description
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.
Author: H.C. Corben
Publisher: Courier Corporation
ISBN: 0486140784
Category : Science
Languages : en
Pages : 417
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Book Description
Applications not usually taught in physics courses include theory of space-charge limited currents, atmospheric drag, motion of meteoritic dust, variational principles in rocket motion, transfer functions, much more. 1960 edition.
Author: Harald Iro
Publisher: World Scientific Publishing Company
ISBN: 9814696307
Category : Science
Languages : en
Pages : 528
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Book Description
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.
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Category : Mathematics
Languages : en
Pages : 530
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Book Description
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.
Author: Tai L. Chow
Publisher: CRC Press
ISBN: 1466569980
Category : Science
Languages : en
Pages : 643
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Book Description
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.
Author: Vernon Barger
Publisher: McGraw-Hill College
ISBN: 9780070037342
Category : Technology & Engineering
Languages : en
Pages : 418
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Book Description
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.
Author: Douglas Cline
Publisher:
ISBN: 9780998837277
Category :
Languages : en
Pages :
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Book Description
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.
Author: Antonio Romano
Publisher: Springer
ISBN: 3319775952
Category : Science
Languages : en
Pages : 644
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Book Description
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.
Author: Ralph Abraham
Publisher: CRC Press
ISBN: 0429689047
Category : Science
Languages : en
Pages : 849
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Book Description
Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
Author: Karan S. Surana
Publisher: CRC Press
ISBN: 1000512347
Category : Science
Languages : en
Pages : 829
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Book Description
This book provides physical and mathematical foundation as well as complete derivation of the mathematical descriptions and constitutive theories for deformation of solid and fluent continua, both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contra-variant bases. Definitions of co- and contra-variant tensors and tensor calculus are introduced using curvilinear frame and then specialized for Cartesian frame. Both Galilean and non-Galilean coordinate transformations are presented and used in establishing objective tensors and objective rates. Convected time derivatives are derived using the conventional approach as well as non-Galilean transformation and their significance is illustrated in finite deformation of solid continua as well as in the case of fluent continua. Constitutive theories are derived using entropy inequality and representation theorem. Decomposition of total deformation for solid and fluent continua into volumetric and distortional deformation is essential in providing a sound, general and rigorous framework for deriving constitutive theories. Energy methods and the principle of virtual work are demonstrated to be a small isolated subset of the calculus of variations. Differential form of the mathematical models and calculus of variations preclude energy methods and the principle of virtual work. The material in this book is developed from fundamental concepts at very basic level with gradual progression to advanced topics. This book contains core scientific knowledge associated with mathematical concepts and theories for deforming continuous matter to prepare graduate students for fundamental and basic research in engineering and sciences. The book presents detailed and consistent derivations with clarity and is ideal for self-study.
