力学 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

力学 英文PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1．Elementary Newtonian Mechanics1

1.1 Newton's Laws（1687）and Their Interpretation1

1.2 Uniform Rectilinear Motion and Inertial Systems4

1.3 Inertial Frames in Relative Motion6

1.4 Momentum and Force6

1.5 Typical Forces.A Remark About Units8

1.6 Space，Time，and Forces10

1.7 The Two-Body System with Internal Forces11

1.7.1 Center-of-Mass and Relative Motion11

1.7.2 Example:The Gravitational Force Between Two Celestial Bodies（Kepler's Problem）13

1.7.3 Center-of-Mass and Relative Momentum in the Two-Body System19

1.8 Systems of Finitely Many Particles20

1.9 The Principle of Center-of-Mass Motion21

1.10 The Principle of Angular-Momentum Conservation21

1.11 The Principle of Energy Conservation22

1.12 The Closed n-Particle System23

1.13 Galilei Transformations24

1.14 Space and Time with Galilei Invariance27

1.15 Conservative Force Fields29

1.16 One-Dimensional Motion of a Point Particle32

1.17 Examples of Motion in One Dimension34

1.17.1 The Harmonic Oscillator34

1.17.2 The Planar Mathematical Pendulum36

1.18 Phase Space for the n-Particle System（in R3）37

1.19 Existence and Uniqueness of the Solutions of？＝？（？，t）38

1.20 Physical Consequences of the Existence and Uniqueness Theorem40

1.21 Linear Systems42

1.21.1 Linear，Homogeneous Systems42

1.21.2 Linear，Inhomogeneous Systems43

1.22 Integrating One-Dimensional Equations of Motion43

1.23 Example:The Planar Pendulum for Arbitrary Deviations from the Vertical45

1.24 Example:The Two-Body System with a Central Force48

1.25 Rotating Reference Systems:Coriolis and Centrifugal Forces55

1.26 Examples of Rotating Reference Systems56

1.27 Scattering of Two Particles that Interact via a Central Force:Kinematics64

1.28 Two-Particle Scattering with a Central Force:Dynamics68

1.29 Example:Coulomb Scattering of Two Particles with Equal Mass and Charge72

1.30 Mechanical Bodies of Finite Extension76

1.31 Time Averages and the Virial Theorem80

Appendix:Practical Examples82

2．The Principles of Canonical Mechanics89

2.1 Constraints and Generalized Coordinates89

2.1.1 Definition of Constraints89

2.1.2 Generalized Coordinates91

2.2 D'Alembert's Principle91

2.2.1 Definition of Virtual Displacements91

2.2.2 The Static Case92

2.2.3 The Dynamical Case92

2.3 Lagrange's Equations94

2.4 Examples of the Use of Lagrange's Equations95

2.5 A Digression on Variational Principles97

2.6 Hamilton's Variational Principle（1834）100

2.7 The Euler-Lagrange Equations100

2.8 Further Examples of the Use of Lagrange's Equations101

2.9 A Remark About Nonuniqueness of the Lagrangian Function103

2.10 Gauge Transformations of the Lagrangian Function104

2.11 Admissible Transformations of the Generalized Coordinates105

2.12 The Hamiltonian Function and Its Relation to the Lagrangian Function L106

2.13 The Legendre Transformation for the Case of One Variable107

2.14 The Legendre Transformation for the Case of Several Variables109

2.15 Canonical Systems110

2.16 Examples of Canonical Systems111

2.17 The Variational Principle Applied to the Hamiltonian Function113

2.18 Symmetries and Conservation Laws114

2.19 Noether's Theorem115

2.20 The Generator for Infinitesimal Rotations About an Axis117

2.21 More About the Rotation Group119

2.22 Infinitesimal Rotations and Their Generators121

2.23 Canonical Transformations123

2.24 Examples of Canonical Transformations127

2.25 The Structure of the Canonical Equations128

2.26 Example:Linear Autonomous Systems in One Dimension129

2.27 Canonical Transformations in Compact Notation131

2.28 On the Symplectic Structure of Phase Space133

2.29 Liouville's Theorem136

2.29.1 The Local Form137

2.29.2 The Global Form138

2.30 Examples for the Use of Liouville's Theorem139

2.31 Poisson Brackets142

2.32 Properties of Poisson Brackets145

2.33 Infinitesimal Canonical Transformations147

2.34 Integrals of the Motion148

2.35 The Hamilton-Jacobi Differential Equation151

2.36 Examples for the Use of the Hamilton-Jacobi Equation152

2.37 The Hamilton-Jacobi Equation and Integrable Systems156

2.37.1 Local Rectification of Hamiltonian Systems156

2.37.2 Integrable Systems160

2.37.3 Angle and Action Variables165

2.38 Perturbing Quasiperiodic Hamiltonian Systems166

2.39 Autonomous，Nondegenerate Hamiltonian Systems in the Neighborhood of Integrable Systems169

2.40 Examples.The Averaging Principle170

2.40.1 The Anharmonic Oscillator170

2.40.2 Averaging of Perturbations172

2.41 Generalized Theorem of Noether174

Appendix:Practical Examples182

3．The Mechanics of Rigid Bodies187

3.1 Definition of Rigid Body187

3.2 Infinitesimal Displacement of a Rigid Body189

3.3 Kinetic Energy and the Inertia Tensor191

3.4 Properties of the Inertia Tensor193

3.5 Steiner's Theorem197

3.6 Examples of the Use of Steiner's Theorem198

3.7 Angular Momentum of a Rigid Body203

3.8 Force-Free Motion of Rigid Bodies205

3.9 Another Parametrization of Rotations:The Euler Angles207

3.10 Definition of Eulerian Angles209

3.11 Equations of Motion of Rigid Bodies210

3.12 Euler's Equations of Motion213

3.13 Euler's Equations Applied to a Force-Free Top216

3.14 The Motion of a Free Top and Geometric Constructions220

3.15 The Rigid Body in the Framework of Canonical Mechanics223

3.16 Example:The Symmetric Children's Top in a Gravitational Field227

3.17 More About the Spinning Top229

3.18 Spherical Top with Friction:The"Tippe Top"231

3.18.1 Conservation Law and Energy Considerations232

3.18.2 Equations of Motion and Solutions with Constant Energy234

Appendix:Practical Examples238

4．Relativistic Mechanics241

4.1 Failures of Nonrelativistic Mechanics242

4.2 Constancy of the Speed of Light245

4.3 The Lorentz Transformations246

4.4 Analysis of Lorentz and Poincaré Transformations252

4.4.1 Rotations and Special Lorentz Tranformations（"Boosts"）254

4.4.2 Interpretation of Special Lorentz Transformations258

4.5 Decomposition of Lorentz Transformations into Their Components259

4.5.1 Proposition on Orthochronous，Proper Lorentz Transformations259

4.5.2 Corollary of the Decomposition Theorem and Some Consequences261

4.6 Addition of Relativistic Velocities264

4.7 Galilean and Lorentzian Space-Time Manifolds266

4.8 Orbital Curves and Proper Time270

4.9 Relativistic Dynamics272

4.9.1 Newton's Equation272

4.9.2 The Energy-Momentum Vector274

4.9.3 The Lorentz Force277

4.10 Time Dilatation and Scale Contraction279

4.11 More About the Motion of Free Particles281

4.12 The Conformal Group284

5．Geometric Aspects of Mechanics285

5.1 Manifolds of Generalized Coordinates286

5.2 Differentiable Manifolds289

5.2.1 The Euclidean Space Rn289

5.2.2 Smooth or Differentiable Manifolds291

5.2.3 Examples of Smooth Manifolds293

5.3 Geometrical Objects on Manifolds297

5.3.1 Functions and Curves on Manifolds298

5.3.2 Tangent Vectors on a Smooth Manifold300

5.3.3 The Tangent Bundle of a Manifold302

5.3.4 Vector Fields on Smooth Manifolds303

5.3.5 Exterior Forms307

5.4 Calculus on Manifolds309

5.4.1 Differentiable Mappings of Manifolds309

5.4.2 Integral Curves of Vector Fields311

5.4.3 Exterior Product of One-Forms313

5.4.4 The Exterior Derivative315

5.4.5 Exterior Derivative and Vectors in R3317

5.5 Hamilton-Jacobi and Lagrangian Mechanics319

5.5.1 Coordinate Manifold Q，Velocity Space TQ，and Phase Space TQ319

5.5.2 The Canonical One-Form on Phase Space323

5.5.3 The Canonical，Symplectic Two-Form on M326

5.5.4 Symplectic Two-Form and Darboux's Theorem328

5.5.5 The Canonical Equations331

5.5.6 The Poisson Bracket334

5.5.7 Time-Dependent Hamiltonian Systems337

5.6 Lagrangian Mechanics and Lagrange Equations339

5.6.1 The Relation Between the Two Formulations of Mechanics339

5.6.2 The Lagrangian Two-Form341

5.6.3 Energy Function on TQ and Lagrangian Vector Field342

5.6.4 Vector Fields on Velocity Space TQ and Lagrange Equations344

5.6.5 The Legendre Transformation and the Correspondence of Lagrangian and Hamiltonian Functions346

5.7 Riemannian Manifolds in Mechanics349

5.7.1 Affine Connection and Parallel Transport350

5.7.2 Parallel Vector Fields and Geodesics352

5.7.3 Geodesics as Solutions of Euler-Lagrange Equations353

5.7.4 Example:Force-Free Asymmetric Top354

6．Stability and Chaos357

6.1 Qualitative Dynamics357

6.2 Vector Fields as Dynamical Systems358

6.2.1 Some Definitions of Vector Fields and Their Integral Curves360

6.2.2 Equilibrium Positions and Linearization of Vector Fields362

6.2.3 Stability of Equilibrium Positions365

6.2.4 Critical Points of Hamiltonian Vector Fields369

6.2.5 Stability and Instability of the Free Top371

6.3 Long-Term Behavior of Dynamical Flows and Dependence on External Parameters373

6.3.1 Flows in Phase Space374

6.3.2 More General Criteria for Stability375

6.3.3 Attractors378

6.3.4 The Poincaré Mapping382

6.3.5 Bifurcations of Flows at Critical Points386

6.3.6 Bifurcations of Periodic Orbits390

6.4 Deterministic Chaos392

6.4.1 Iterative Mappings in One Dimension392

6.4.2 Qualitative Definitions of Deterministic Chaos394

6.4.3 An Example:The Logistic Equation398

6.5 Quantitative Measures of Deterministic Chaos403

6.5.1 Routes to Chaos403

6.5.2 Liapunov Characteristic Exponents407

6.5.3 Strange Attractors409

6.6 Chaotic Motions in Celestial Mechanics411

6.6.1 Rotational Dynamics of Planetary Satellites411

6.6.2 Orbital Dynamics of Asteroids with Chaotic Behavior417

7．Continuous Systems421

7.1 Discrete and Continuous Systems421

7.2 Transition to the Continuous System425

7.3 Hamilton's Variational Principle for Continuous Systems427

7.4 Canonically Conjugate Momentum and Hamiltonian Density429

7.5 Example:The Pendulum Chain430

7.6 Comments and Outlook434

Exercises439

Chapter 1:Elementary Newtonian Mechanics439

Chapter 2:The Principles of Canonical Mechanics446

Chapter 3:The Mechanics of Rigid Bodies454

Chapter 4:Relativistic Mechanics457

Chapter 5:Geometric Aspects of Mechanics460

Chapter 6:Stability and Chaos463

Solution of Exercises467

Chapter 1:Elementary Newtonian Mechanics467

Chapter 2:The Principles of Canonical Mechanics483

Chapter 3:The Mechanics of Rigid Bodies503

Chapter 4:Relativistic Mechanics511

Chapter 5:Geometric Aspects of Mechanics523

Chapter 6:Stability and Chaos528

Appendix537

A．Some Mathematical Notions537

B．Historical Notes540

Bibliography547

Index549