力学（第4版）

　　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 knowl- edge of general mechanics.

暂缺《力学（第4版）》作者简介

1. Elementary Newtonian Mechanics
1.1 Newton's Laws （1687） and Their Interpretation
1.2 Uniform Rectilinear Motion and Inertial Systems
1.3 Inertial Frames in Relative Motion
!.4 Momentum and Force
1.5 Typical Forces. A Remark About Units
1.6 Space, Time, and Forces
1.7 The Two-Body System with Internal Forces
1.7.1 Center-of-Mass and Relative Motion
1.7.2 Example: The Gravitational Force Between Two Celestial Bodies （Kepler's Problem）
1.7.3 Center-of-Mass and Relative Momentum in the Two-Body System
1.8 Systems of Finitely Many Particles
1.9 The Principle of Center-of-Mass Motion
1.10 The Principle of Angular-Momentum Conservation
1.11 The Principle of Energy Conservation
1.12 The Closed n-Particle System
1.13 Galilei Transformations
1.14 Space and Time with Galilei Invariance
1.15 Conservative Force Fields
1.16 One-Dimensional Motion of a Point Particle
1.17 Examples of Motion in One Dimension
1.17.1 The Harmonic Oscillator
1.17.2 The Planar Mathematical Pendulum
1.18 Phase Space for the n-Particle System （in R3）
1.19 Existence and Uniqueness of the Solutions of x=F（x, t）
1.20 Physical Consequences of the Existence and Uniqueness Theorem
1.21 Linear Systems
1.21.1 Linear, Homogeneous Systems
1.21.2 Linear, Inhomogeneous Systems
1.22 Integrating One-Dimensional Equations of Motion
1.23 Example: The Planar Pendulum for Arbitrary Deviations from the Vertical
1.24 Example: The Two-Body System with a Central Force
1.25 Rotating Reference Systems: Coriolis and Centrifugal Forces
1.26 Examples of Rotating Reference Systems
1.27 Scattering of Two Particles that Interact via a Central Force Kinematics
1.28 Two-Particle Scattering with a Central Force: Dynamics
1.29 Example: Coulomb Scattering of Two Particles with Equal Mass and Charge
1.30 Mechanical Bodies of Finite Extension
1.31 Time Averages and the Virial Theorem
Appendix: Practical Examples
2. The Principles of Canonieal Mechanics
2.1 Constraints and Generalized Coordinates
2.1.1 Definition of Constraints
2.1.2 Generalized Coordinates
2.2 D'Alembert's Principle
2.2.1 Definition of Virtual Displacements
2.2.2 The Static Case
2.2.3 The Dynamical Case
2.3 Lagrange's Equations
2.4 Examples of the Use of Lagrange's Equations
2.5 A Digression on Variational Principles
2.6 Hamilton's Variational Principle （1834）
2.7 The Euler-Lagrange Equations
2.8 Further Examples of the Use of Lagrange's Equations
2.9 A Remark About Nonuniqueness of the Lagrangian Function .
2.10 Gauge Transformations of the Lagrangian Function
2.11 Admissible Transformations of the Generalized Coordinates
2.12 The Hamiltonian Function and Its Relation to the Lagrangian Function L
2.13 The Legendre Transformation for the Case of One Variable
2.14 The Legendre Transformation for the Case of Several Variables
2.15 Canonical Systems
2.16 Examples of Canonical Systems
2.17 The Variational Principle Applied to the Hamiltonian Function
2.18 Symmetries and Conservation Laws
2.19 Noether's Theorem
2.20 The Generator for Infinitesimal Rotations About an Axis
2.21 More About the Rotation Group
2.22 Infinitesimal Rotations and Their Generators
2.23 Canonical Transformations
2.24 Examples of Canonical Transformations
2.25 The Structure of the Canonical Equations
2.26 Example: Linear Autonomous Systems in One Dimension
2.27 Canonical Transformations in Compact Notation
2.28 On the Symplectic Structure of Phase Space
2.29 Liouville's Theorem
2.29.1 The Local Form
2.29.2 The Global Form
2.30 Examples for the Use of Liouviile's Theorem
2.31 Poisson Brackets
2.32 Properties of Poisson Brackets
2.33 Infinitesimal Canonical Transformations
2.34 Integrals of the Motion
2.35 The Hamilton-Jacobi Differential Equation
2.36 Examples for the Use of the Hamilton-Jacobi Equation
2.37 The Hamilton-Jacobi Equation and Integrable Systems
2.37.1 Local Rectification of Hamiltonian Systems
2.37.2 Integrable Systems
2.37.3 Angle and Action Variables
2.38 Perturbing Quasiperiodic Hamiltonian Systems
2.39 Autonomous, Nondegenerate Hamiltonian Systems in the Neighborhood of Integrable Systems
2.40 Examples. The Averaging Principle
2.40.1 The Anharmonic Oscillator
2.40.2 Averaging of Perturbations
2.41 Generalized Theorem of Noether
Appendix: Practical Examples
3. The Mechanics of Rigid Bodies
3.1 Definition of Rigid Body
3.2 Infinitesimal Displacement of a Rigid Body
3.3 Kinetic Energy and the Inertia Tensor
3.4 Properties of the Inertia Tensor
3.5 Steiner's Theorem
3.6 Examples of the Use of Steiner's Theorem
3.7 Angular Momentum of a Rigid Body
3.8 Force-Free Motion of Rigid Bodies
3.9 Another Parametrization of Rotations: The Euler Angles
3.10 Definition of Eulerian Angles
3.11 Equations of Motion of Rigid Bodies
3.12 Euler's Equations of Motion
3.13 Euler's Equations Applied to a Force-Free Top
3.14 The Motion of a Free Top and Geometric Constructions
3.15 The Rigid Body in the Framework of Canonical Mechanics
3.16 Example: The Symmetric Children's Top in a Gravitational Field
3.17 More About the Spinning Top
3.18 Spherical Top with Friction: The "Tippe Top"
3.18.1 Conservation Law and Energy Considerations
3.18.2 Equations of Motion and Solutions with Constant Energy
Appendix：PracticaI Examples
4. Relativistic Mechanics
4.1 Failures of Nonrelativistic Mechanics
4.2 Constancy of the Speed of Light
4.3 The Lorentz Transformations
4.4 Analysis or Lorentz and Poincar6 Transformations
4.4.1 Rotations and Specia!Lorentz Tranformations （“Boosts”）
4.4.2 Interpretation of Specia!Lorentz Transformations
4.5 Decomposition 0f Lorentz Transformations into 7heir Components
4.5.1 Proposition on Orthochronous Proper Lorentz Transformations
4.5.2 Corollary of the Decomposition Theorem and Some Consequences
4.6 Addition of Relativistic VeIocities
4.7 Galilean and Lorentzian Space-Time ManifoIds
4.8 Orbita!Curves and Proper Time
4.9 Relativistic Dynamics
4.9.1 Newton’S Equation
4.9.2 The Energy-Momentum Vector
4.9.3 The Lorentz Force
4.10 Time Dilatation and Scale Contraction
4.11 More About the Motion of Free Particles
4.12 The Conformal Group
5. Geometric Aspects of Mechanics
5.1 Manifoids of Generalized COOrdinates
5.2 Differentiable ManifoIds
5.2.1 The Euclidean Space R
5.2.2 Smooth or Differentiable Manifoids
5.2.3 Examples of Smooth ManifoIds
5.3 GeometricalObiects on ManifoIds
5.3.1 Functions and Curves on ManifoIds
5.3.2 Tangent Vectors on a Smooth ManifoId
5.3.3 The Tangent Bundle of a Manifoid
5.3.4 Vector Fields on Smooth ManifoIds
5.3.5 Exterior Forms
5.4 Caiculus on ManifoIds
5.4.1 Differentiable Mappings of ManifoIds
5.4.2 Integra!Curves of Vector Fields
Stability and Chaod
Exercises
Solution of Exercises
Author Index
Subject Index