经典力学

章节摘录

插图：Suppose acharged particle drifts in the direction ofincreasing B；by Eq.（12.117），the kinetic energy of rotation increases.As the total kinetic energy iS conserved.the kinetic energy of longitudinal drift，along the lines of force must de.crease.Eventually,the drift velocity  goes to zero and the motion reverses in direction.If it can be arranged that B eventually increases in the other direction.the charged particle will remain confined，drifting back and forth between the two ends——tlle principle 0f the SO-called mirror confinement.The mirror principle is  used to contain hot plasmas for thermonuclear energy generation.The complete story iS of course more complicated.but the significance Of the adiabatic invari.ance Of M is clearly demonstrated.We have seen that almost all phenomena of small oscillations about steady.state or steady motion can be described in terms of harmonic oscillators.In con.sequence.there iS a good deal of practicalinterest in questions of the invariance Of J for a harmonic oscillator under slow，and not SO slow，variations of a parameter.The study of oscillations in charged particle accelerators，for example，has led to a number of new insights.It has been possible to sketch here only the highlights of the subject of adia.batic invariants.The ramifications of the field go into many areas of classical and quantum physics and of mathematics.

前言

The first edition of this text appeared in 1950, and it was so well received thatit went through a second printing the very next year. Throughout the next threedecades it maintained its position as the acknowledged standard text for the intro-duciory Classical Mechanics course in graduate level physics curricula through-out the United States, and in many other countries around the world. Some majorinstitutions also used it for senior level undergraduate Mechanics. Thirty yearslater, in 1980, a second edition appeared which was "a through-going revision ofthe first edition？' The preface to the second edition contains the following state-ment: "I have tried to retain, as much as possible, the advantages of the first editionwhile taking into account the developments of the subject itself, its position in thecurriculum, and its applications to other fields." This is the philosophy which hasguided the preparation of this third edition twenty more years later.   The second edition introduced one additional chapter on Perturbation Theory,and changed the ordering of the chapter on Small Oscillations. In addition it addeda significant amount of new material which increased the number of pages byabout 68%. This third edition adds still one more new chapter on Nonlinear Dy-namics or Chaos, but counterbalances this by reducing the amount of material inseveral of the other chapters, by shortening the space allocated to appendices, byconsiderably reducing the bibliography, and by omitting the long lists of symbols.Thus the third edition is comparable in size to the second.

内容概要

编者：（美国）戈尔茨坦（Herbert Goldstein） （美国）普尔（Charles Poole） （美国）萨夫科（John Safko）

书籍目录

1 Survey of the Elementary Principles

1.1 Mechanics of a Particle 1

1.2 Mechanics of a System of Particles 5

1.3 Constraints 12

1.4 D'Alembert's Principle and Lagrange's Equations 16

1.5 Velocity-Dependent Potentials and the Dissipation Function 22

1.6 Simple Applications of the Lagrangian Formulation 24

2 Variational Principles and I.agrange's Equations

2.1 Hamilton's Principle 34

2.2 Some Techniques of the Calculus of Variations 36

2.3 Derivation of Lagrange's Equations from Hamilton's Principle 44

2.4 Extension of Hamilton's Principle to Nonholonomic Systems 45

2.5 Advantages of a Variational Principle Formulation 51

2.6 Conservation Theorems and Symmetry Properties 54

2.7 Energy Function and the Conservation of Energy 60

3 The Central Force Problem

3.1 Reduction to the Equivalent One-Body Problem 70

3.2 The Equations of Motion and First Integrals 72

3.3 The Equivalent One-Dimensional Problem, and

Classification of Orbits 76

3.4 The Virial Theorem 83

3.5 The Differential Equation for the Orbit, and Integrable

Power-Law Potentials 86

3.6 Conditions for Closed Orbits (Bertrand's Theorem) 89

3.7 The Kepler Problem: Inverse-Square Law of Force 92

3.8 The Motion in Time in the Kepler Problem 98

3.9 The Laplace-Runge-Lenz Vector 102

3.10 Scattering in a Central Force Field 106

3.11 Transformation of the Scattering Problem to Laboratory

Coordinates 114

3.12 The Three-Body Problem 121

4 The Kinematics of Rigid Body Motion

4.1 The Independent Coordinates of a Rigid Body 134

4.2 Orthogonal Transformations 139

4.3 Formal Properties of the Transformation Matrix 144

4.4 The Euler Angles 150

4.5 The Cayley-Klein Parameters and Related Quantities 154

4.6 Euler's Theorem on the Motion of a Rigid Body 155

4.7 Finite Rotations 161

4.8 Infinitesimal Rotations 163

4.9 Rate of Change of a Vector 171

4.10 The Coriolis Effect 174

5 The Rigid Body Equations of Motion

5.1 Angular Momentum and Kinetic Energy of Motion

about a Point 184

5.2 Tensors 188

5.3 The Inertia Tensor and the Moment of Inertia 191

5.4 The Eigenvalues of the Inertia Tensor and the Principal

Axis Transformation 195

5.5 Solving Rigid Body Problems and the Euler Equations of

Motion 198

5.6 Torque-free Motion of a Rigid Body 200

5.7 The Heavy Symmetrical Top with One Point Fixed 208

5.8 Precession of the Equinoxes and of Satellite Orbits 223

5.9 Precession of Systems of Charges in a Magnetic Field 230

6 Oscillations

6.1 Formulation of the Problem 238

6.2 The Eigenvalue Equation and the Principal Axis Transformation 241

6.3 Frequencies of Free Vibration, and Normal Coordinates 250

6.4 Free Vibrations of a Linear Triatomic Molecule 253

6.5 Forced Vibrations and the Effect of Dissipative Forces 259

6.6 Beyond Small Oscillations: The Damped Driven Pendulum and the

Josephson Junction 265

7 The Classical Mechanics of the

Special Theory of Relativity

7.1 Basic Postulates of the Special Theory 277

7.2 Lorentz Transformations 280

7.3 Velocity Addition and Thomas Precession 282

7.4 Vectors and the Metric Tensor 286

7.5 1-Forms and Tensors 289

7.6 Forces in the Special Theory; Electromagnetism 297

7.7 Relativistic Kinematics of Collisions and Many-Particle

Systems 300

7.8 Relativistic Angular Momentum 309

7.9 The Lagrangian Formulation of Relativistic Mechanics 312

7.10 Covariant Lagrangian Formulations 318

7.11 Introduction to the General Theory of Relativity 324

8 The Hamilton Equations of Motion

8.1 Legendre Transformations and the Hamilton Equations

of Motion 334

8.2 Cyclic Coordinates and Conservation Theorems 343

8.3 Routh's Procedure 347

8.4 The Hamiltonian Formulation of Relativistic Mechanics 349

8.5 Derivation of Hamilton's Equations from a

Variational Principle 353

8.6 The Principle of Least Action 356

9 Canonical Transformations

9.1 The Equations of Canonical Transformation 368

9.2 Examples of Canonical Transformations 375

9.3 The Harmonic Oscillator 377

9.4 The Symplectic Approach to Canonical Transformations 381

9.5 Poisson Brackets and Other Canonical Invariants 388

9.6 Equations of Motion, Infinitesimal Canonical Transformations, and

Conservation Theorems in the Poisson Bracket Formulation 396

9.7 The Angular Momentum Poisson Bracket Relations 408

9.8 Symmetry Groups of Mechanical Systems 412

9.9 Liouville's Theorem 419

10 Hamilton-lacobi Theory and Action-Angle Variables

10.1 The Hamilton-Jacobi Equation for Hamilton's Principal

Function 430

10.2 The Harmonic Oscillator Problem as an Example of the

Hamilton-Jacobi Method 434

10.3 The Hamilton-Jacobi Equation for Hamilton's Characteristic

Function 440

10.4 Separation of Variables in the Hamilton-Jacobi Equation 444

10.5 Ignorable Coordinates and the Kepler Problem 445

10.6 Action-angle Variables in Systems of One Degree of Freedom 452

10.7 Action-Angle Variables for Completely Separable Systems 457

10.8 The Kepler Problem in Action-angle Variables 466

11 Classical Chaos

11.1 Periodic Motion 484

11.2 Perturbations and the Kolmogorov-Arnold-Moser Theorem 487

11.3 Attractors 489

11.4 Chaotic Trajectories and Liapunov Exponents 491

11.5 Poincar6 Maps 494

11.6 Hrnon-Heiles Hamiltonian 496

11.7 Bifurcations, Driven-damped Harmonic Oscillator, and Parametric

Resonance 505

11.8 The Logistic Equation 509

11.9 Fractals and Dimensionality 516

12 Canonical Perturbation Theory

12.1 Introduction 526

12.2 Time-dependent Perturbation Theory 527

12.3 Illustrations of Time-dependent Perturbation Theory 533

12.4 Time-independent Perturbation Theory 541

12.5 Adiabatic Invariants 549

13 Introduction to the Lagrangian and HamUtonian

Formulations for Continuous Systems and Fields

13.1 The Transition from a Discrete to a Continuous System 558

13.2 The Lagrangian Formulation for Continuous Systems 561

13.3 The Stress-energy Tensor and Conservation Theorems 566

13.4 Hamiltonian Formulation 572

13.5 Relativistic Field Theory 577

13.6 Examples of Relativistic Field Theories 583

13.7 Noether's Theorem 589

Appendix A Euler Angles in Alternate Conventions and Cayley-Klein Parameters

Appendix B Groups and Algebras

Selected Bibliography

Author Index

Subject Index

编辑推荐

《经典力学(第3版·影印版)》：海外优秀理科类系列教材

作者简介

《经典力学(第3版·影印版)》是一本有着很高知名度的经典力学教材，长期以来被世界上多所大学选用。本影印版是2002年出版的第3版。与前两版相比，第3版在保留基本经典力学内容的基础上，做了不少调整。例如，增加了混沌一章；引入了一些对新研究问题的方法的讨论，例如张量、群论的等；对于第二版中的一些内容做了适当的压缩和调整。

全书共13章，可作为为物理类专业经典力学课程的教材，尤其适合开展双语教学的学校，对于有志出国深造的人员也是一本必不可少的参考书。

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