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This classic text enables students to make connections between classical and modern physics - an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the text to include the latest topics, applications, and notation, to reflect today's physics curriculum. They introduce students to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help students to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the text remains fully accessible to students who have not had an intermediate course in classical mechanics For 30 years, this classic text has been the acknowledged standard in classical mechanics courses. Classical Mechanics enables students to make connections between classical and modern physics an indispensable part of a physicist s education. The authors have updated the topics, applications, and notations to reflect today s physics curriculum. They introduce students to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help students develop skills in the use of computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the text remains fully accessible to students who have not had an intermediate course in classical mechanics. Features The classical approach of this leading text book has been revised and updated A section on the Euler and Lagrange exact solutions to the three-body problem A section on the damped driven oscillator as an example of the workings of the Josephson junction Chapter on canonical perturbation theory has been streamlined and the mathematics has been simplified Approximately 45 new problems, mostly in Chapters 1 8 and 11. Problems sets are now divided into Derivations and Exercises Solutions for 19 select problems have been provided in Appendix C Table Of Contents: Survey of the Elementary Principles Variational Principles and Lagrange s Equations The Central Force Problem The Kinematics of Rigid Body Motion The Rigid Body Equations of Motion Oscillations The Classical Mechanics of the Special Theory of Relativity The Hamilton Equations of Motion Canonical Transformations Hamilton Jacobi Theory and Action-Angle Variables Classical Chaos Canonical Perturbation Theory Introduction to the Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields Appendix A Euler Angles in Alternate Conventions and Cayley Klein Parameters Appendix B Groups and Algebras Appendix C Solutions to Select Exercises Selected Bibliography Author Index Subject Index ** Cover 1 Title 2 Copyright 3 Contents 4 Preface to the Third Edition 10 Preface to the Second Edition 13 Preface to the First Edition 17 CHAPTER 1_Survey of the Elementary Principles 20 1.1 MECHANICS OF A PARTICLE 20 1.2 MECHANICS OF A SYSTEM OF PARTICLES 24 1.3 CONSTRAINTS 31 1.4 D’ALEMBERT’S PRINCIPLE AND LAGRANGE’S EQUATIONS 35 1.5 VELOCITY-DEPENDENT POTENTIALSAND THE DISSIPATION FUNCTION 40 1.6 SIMPLE APPLICATIONS OF THE LAGRANGIAN FORMULATION 43 CHAPTER 2_Variational Principles andLagrange’s Equations 53 2.1 HAMILTON’S PRINCIPLE 53 2.2 SOME TECHNIQUES OF THE CALCULUS OF VARIATIONS 55 2.3 DERIVATION OF LAGRANGE’S EQUATIONSFROM HAMILTON’S PRINCIPLE 63 2.4 EXTENDING HAMILTON’S PRINCIPLE TO SYSTEMS WITH CONSTRAINTS 64 2.5 ADVANTAGES OF A VARIATIONAL PRINCIPLE FORMULATION 70 2.6 CONSERVATION THEOREMS AND SYMMETRY PROPERTIES 74 2.7 ENERGY FUNCTION AND THE CONSERVATION OF ENERGY 80 CHAPTER 3_The Central Force Problem 89 3.1 REDUCTION TO THE EQUIVALENT ONE-BODY PROBLEM 89 3.2 THE EQUATIONS OF MOTION AND FIRST INTEGRALS 91 3.3 THE EQUIVALENT ONE-DIMENSIONAL PROBLEM,AND CLASSIFICATION OF ORBITS 95 3.4 THE VIRIAL THEOREM 102 3.5 THE DIFFERENTIAL EQUATION FOR THE ORBIT,AND INTEGRABLE POWER-LAW POTENTIALS 105 3.6 CONDITIONS FOR CLOSED ORBITS (BERTRAND’S THEOREM 108 3.7 THE KEPLER PROBLEM: INVERSE-SQUARE LAW OF FORCE 111 3.8 THE MOTION IN TIME IN THE KEPLER PROBLEM 117 3.9 THE LAPLACE–RUNGE–LENZ VECTOR 121 3.10 SCATTERING IN A CENTRAL FORCE FIELD 125 3.11 TRANSFORMATION OF THE SCATTERING PROBLEM TO LABORATORY COORDINATES 133 3.12 THE THREE-BODY PROBLEM 140 CHAPTER 4_The Kinematics ofRigid Body Motion 153 4.1 THE INDEPENDENT COORDINATES OF A RIGID BODY 153 4.2 ORTHOGONAL TRANSFORMATIONS 158 4.3 FORMAL PROPERTIES OF THE TRANSFORMATION MATRIX 163 4.4 THE EULER ANGLES 169 4.5 THE CAYLEY–KLEIN PARAMETERS AND RELATED QUANTITIES 173 4.6 EULER’S THEOREM ON THE MOTION OF A RIGID BODY 174 4.7 FINITE ROTATIONS 180 4.8 INFINITESIMAL ROTATIONS 182 4.9 RATE OF CHANGE OF A VECTOR 190 4.10 THE CORIOLIS EFFECT 193 CHAPTER 5_The Rigid Body Equationsof Motion 203 5.1 ANGULAR MOMENTUM AND KINETIC ENERGY OF MOTION ABOUT A POINT 203 5.2 TENSORS 207 5.3 THE INERTIA TENSOR AND THE MOMENT OF INERTIA 210 5.4 THE EIGENVALUES OF THE INERTIA TENSORAND THE PRINCIPAL AXIS TRANSFORMATION 213 5.5 SOLVING RIGID BODY PROBLEMS AND THE EULER EQUATIONS OF MOTION 217 5.6 TORQUE-FREE MOTION OF A RIGID BODY 219 5.7 THE HEAVY SYMMETRICAL TOP WITH ONE POINT FIXED 227 5.8 PRECESSION OF THE EQUINOXES AND OF SATELLITE ORBITS 242 5.9 PRECESSION OF SYSTEMS OF CHARGES IN A MAGNETIC FIELD 249 CHAPTER 6_Oscillations 257 6.1 FORMULATION OF THE PROBLEM 257 6.2 THE EIGENVALUE EQUATIONAND THE PRINCIPAL AXIS TRANSFORMATION 260 6.3 FREQUENCIES OF FREE VIBRATION, AND NORMAL COORDINATES 269 6.4 FREE VIBRATIONS OF A LINEAR TRIATOMIC MOLECULE 272 6.5 FORCED VIBRATIONS AND THE EFFECT OF DISSIPATIVE FORCES 277 6.6 BEYOND SMALL OSCILLATIONS: THE DAMPED DRIVEN PENDULUM AND THE JOSEPHSON JUNCTION 284 CHAPTER 7_The Classical Mechanics of theSpecial Theory of Relativity 295 7.1 BASIC POSTULATES OF THE SPECIAL THEORY 296 7.2 LORENTZ TRANSFORMATIONS 299 7.3 VELOCITY ADDITION AND THOMAS PRECESSION 301 7.4 VECTORS AND THE METRIC TENSOR 305 7.5 1-FORMS AND TENSORS∗ 308 7.6 FORCES IN THE SPECIAL THEORY; ELECTROMAGNETISM 316 7.7 RELATIVISTIC KINEMATICS OF COLLISIONS AND MANY-PARTICLE SYSTEMS 319 7.8 RELATIVISTIC ANGULAR MOMENTUM 328 7.9 THE LAGRANGIAN FORMULATION OF RELATIVISTIC MECHANICS 331 7.10 COVARIANT LAGRANGIAN FORMULATIONS 337 7.11 INTRODUCTION TO THE GENERAL THEORY OF RELATIVITY 343 CHAPTER 8_The Hamilton Equationsof Motion 353 8.1 LEGENDRE TRANSFORMATIONS AND THE HAMILTON EQUATIONS OF MOTION 353 8.2 CYCLIC COORDINATES AND CONSERVATION THEOREMS 362 8.3 ROUTH’S PROCEDURE 366 8.4 THE HAMILTONIAN FORMULATION OF RELATIVISTIC MECHANICS 368 8.5 DERIVATION OF HAMILTON’S EQUATIONS FROM A VARIATIONAL PRINCIPLE 372 8.6 THE PRINCIPLE OF LEAST ACTION 375 CHAPTER 9_Canonical Transformations 387 9.1 THE EQUATIONS OF CANONICAL TRANSFORMATION 387 9.2 EXAMPLES OF CANONICAL TRANSFORMATIONS 394 9.3 THE HARMONIC OSCILLATOR 396 9.4 THE SYMPLECTIC APPROACH TO CANONICAL TRANSFORMATIONS 400 9.5 POISSON BRACKETS AND OTHER CANONICAL INVARIANTS 407 9.6 EQUATIONS OF MOTION, INFINITESIMAL CANONICALTRANSFORMATIONS, AND CONSERVATION THEOREMSIN THE POISSON BRACKET FORMULATION 415 9.7 THE ANGULAR MOMENTUM POISSON BRACKET RELATIONS 427 9.8 SYMMETRY GROUPS OF MECHANICAL SYSTEMS 431 9.9 LIOUVILLE’S THEOREM 438 CHAPTER 10_Hamilton–Jacobi Theory andAction-Angle Variables 449 10.1 THE HAMILTON–JACOBI EQUATION FOR HAMILTON’S PRINCIPAL FUNCTION 449 10.2 THE HARMONIC OSCILLATOR PROBLEM AS AN EXAMPLE OF THE HAMILTON–JACOBI METHOD 453 10.3 THE HAMILTON–JACOBI EQUATION FOR HAMILTON’S CHARACTERISTIC FUNCTION 459 10.4 SEPARATION OF VARIABLES IN THE HAMILTON–JACOBI EQUATION 463 10.5 IGNORABLE COORDINATES AND THE KEPLER PROBLEM 464 10.6 ACTION-ANGLE VARIABLES IN SYSTEMS OF ONE DEGREE OF FREEDOM 471 10.7 ACTION-ANGLE VARIABLES FOR COMPLETELY SEPARABLE SYSTEMS* 476 10.8 THE KEPLER PROBLEM IN ACTION-ANGLE VARIABLES* 485 CHAPTER 11_Classical Chaos 502 11.1 PERIODIC MOTION 503 11.2 PERTURBATIONS AND THE KOLMOGOROV–ARNOLD–MOSER THEOREM 506 11.3 ATTRACTORS 508 11.4 CHAOTIC TRAJECTORIES AND LIAPUNOV EXPONENTS 510 11.5 POINCAR ́E MAPS 513 11.6 H ́ENON–HEILES HAMILTONIAN 515 11.7 BIFURCATIONS, DRIVEN-DAMPED HARMONIC OSCILLATOR, AND PARAMETRIC RESONANCE 524 11.8 THE LOGISTIC EQUATION 528 11.9 FRACTALS AND DIMENSIONALITY 535 CHAPTER 12_Canonical Perturbation Theory 545 12.1 INTRODUCTION 545 12.2 TIME-DEPENDENT PERTURBATION THEORY 546 12.3 ILLUSTRATIONS OF TIME-DEPENDENT PERTURBATION THEORY 552 12.4 TIME-INDEPENDENT PERTURBATION THEORY 560 12.5 ADIABATIC INVARIANTS 568 CHAPTER 13_Introduction to the Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields 577 13.1 THE TRANSITION FROM A DISCRETE TO A CONTINUOUS SYSTEM 577 13.2 THE LAGRANGIAN FORMULATION FOR CONTINUOUS SYSTEMS 580 13.3 THE STRESS-ENERGY TENSOR AND CONSERVATION THEOREMS 585 13.4 HAMILTONIAN FORMULATION 591 13.5 RELATIVISTIC FIELD THEORY 596 13.6 EXAMPLES OF RELATIVISTIC FIELD THEORIES 602 13.7 NOETHER’S THEOREM 608 APPENDIX A_Euler Angles in Alternate Conventions and Cayley–Klein Parameters 620 APPENDIX B_Groups and Algebras 624 APPENDIX C_Solutions to Select Exercises 636 Selected Bibliography 645 Author Index 650 Subject Index 652