《CLASSICAL MECHANICS》
作者 | 编者 |
---|---|
出版 | ADDISON-WESLEY |
参考页数 | 672 |
出版时间 | 1980(求助前请核对) 目录预览 |
ISBN号 | 0201029189 — 求助条款 |
PDF编号 | 813123328(仅供预览,未存储实际文件) |
求助格式 | 扫描PDF(若分多册发行,每次仅能受理1册) |

CHAPTER1 SURVEY OF THE ELEMENTARY PRINCIPLES1
1-1 Mechanics of a particle1
1-2 Mechanics of a system of particles5
1-3 Constraints11
1-4 D’Alembert’s principle and Lagrange’s equations17
1-5 Velocity-dependent potentials and the dissipation function21
1-6 Simple applications of the Lagrangian formulation25
CHAPTER 2VARIATIONAL PRINCIPLES AND LAGRANGE’S EQUATIONS35
2-1 Hamilton’s principle35
2-2 Some techniques of the calculus of variations37
2-3 Derivation of Lagrange’s equations from Hamilton’s principle43
2-4 Extension of Hamilton’s principle to nonholonomic systems45
2-5 Advantages of a variational principle formulation51
2-6 Conservation theorems and symmetry properties54
CHAPTER 3THE TWO-BODY CENTRAL FORCE PROBLEM70
3-1 Reduction to the equivalent one-body problem70
3-2 The equations of motion and first integrals71
3-3 The equivalent one-dimensional problem,and classification of orbits77
3-4 The virial theorem82
3-5 The differential equation for the orbit,and integrable power-law potentials85
3-6 Conditions for closed orbits (Bertrand’s theorem)90
3-7 The Kepler problem:Inverse square law of force94
3-8 The motion in time in the Kepler problem98
3-9 The Laplace-Runge-Lenz vector102
3-10 Scattering in a central force field105
3-11 Transformation of the scattering problem to laboratory coordinates114
CHAPTER 4THE KINEMATICS OF RIGID BODY MOTION128
4-1 The independent coordinates of a rigid body128
4-2 Orthogonal transformations132
4-3 Formal properties of the transformation matrix137
4-4 The Euler angles143
4-5 The Cayley-Klein parameters and related quantities148
4-6 Euler’s theorem on the motion of a rigid body158
4-7 Finite rotations164
4-8 Infinitesimal rotations166
4-9 Rate of change of a vector174
4-10 The Coriolis force177
CHAPTER 5THE RIGID BODY EQUATIONS OF MOTION188
5-1 Angular momentum and kinetic energy of motion about a point188
5-2 Tensors and dyadics192
5-3 The inertia tensor and the moment of inertia195
5-4 The eigenvalues of the inertia tensor and the principal axis transformation198
5-5 Methods of solving rigid body problems and the Euler equations of motion203
5-6 Torque-free motion of a rigid body205
5-7 The heavy symmetrical top with one point fixed213
5-8 Precession of the equinoxes and of satellite orbits225
5-9 Precession of systems of charges in a magnetic field232
CHAPTER 6SMALL OSCILLATIONS243
6-1 Formulation of the problem243
6-2 The eigenvalue of equation and the principal axis transformation246
6-3 Frequencies of free vibration,and normal coordinates253
6-4 Free vibrations of a linear triatomic molecule258
6-5 Forced vibrations and the effect of dissipative forces263
CHAPTER 7SPECIAL RELATIVITY IN CLASSICAL MECHANICS275
7-1 The basic program of special relativity275
7-2 The Lorentz transformation278
7-3 Lorentz transformations in real four dimensional spaces288
7-4 Further descriptions of the Lorentz transformation293
7-5 Covariant four-dimensional formulations298
7-6 The force and energy equations in relativistic mechanics303
7-7 Relativistic kinematics of collisions and many-particle systems309
7-8 The Lagrangian formulation of relativistic mechanics320
7-9 Covariant Lagrangian formulations326
CHAPTER 8 THE HAMILTON EQUATIONS OF MOTION339
8-1Legendre transformations and the Hamilton equations of motion339
8-2 Cyclic coordinates and conservation theorems347
8-3 Routh’s procedure and oscillations about steady motion351
8-4 The Hamiltonian formulation of relativistic mechanics356
8-5 Derivation of Hamilton’s equations from a variational principle362
8-6 The principle of least action365
CHAPTER 9CANONICAL TRANSFORMATIONS378
9-1 The equations of canonical transformation378
9-2 Examples of canonical transformations386
9-3 The symplectic approach to canonical transformations391
9-4 Poisson brackets and other canonical invariants397
9-5 Equations of motion,infinitesimal canonical transformations,and conservations theorems in the Poisson bracket formulation405
9-6 The angular momentum Poisson bracket relations416
9-7 Symmetry groups of mechanical systems420
9-8 Liouville’stheorem426
CHAPTER 10HAMILTON-JACOBI THEORY438
10-1 The Hamilton-Jacobi equation for Hamilton’s principal function438
10-2 The harmonic oscillator problem as an example of the Hamilton-Jacobi method442
10-3 The Hamilton-Jacobi equation for Hamilton’s characteristic function445
10-4 Separation of variables in the Hamilton-Jacobi equation449
10-5 Action-angle variables in systems of one degree of freedom457
10-6 Action-angle variables for completely separable systems463
10-7 The Kepler problem in action-angle variables472
10-8 Hamilton-Jacobi theory,geometrical optics,and wave mechanics484
CHAPTER 11CANONICAL PERTURBATION THEORY499
11-1 Introduction499
11-2 Time-dependent perturbation (variation of constants)500
11-3 Illustrations of time-dependent perturbation theory506
11-4 Time-independent perturbation theory in first order with one degree of freedom515
11-5 Time-independent perturbation theory to higher order519
11-6 Specialized perturbation techniques in celestial and space mechanics527
11-7 Adiabatic invariants531
CHAPTER 12 INTRODUCTION TO THE LAGRANGIAN AND HAMILTONIAN FORMULATIONS FOR CONTINUOUS SYSTEMS AND FIELDS545
12-1The transition from a discrete to a continuous system545
12-2 The Lagrangian formulation for continuous systems548
12-3 The stress-energy tensor and conservation theorems555
12-4 Hamiltonian formulation,Poisson brackets and the momentum representation562
12-5 Relativistic field theory570
12-6 Examples of relativistic field theories575
12-7 Noetner’s theorem588
APPENDIXES601
AProof of Bertrand’s Theorem601
B Euler Angles in Alternate Conventions606
C Transformatio?Properties of dΩ611
D The Staeckel Conditions for Separability of the Hamilton-Jacobi Equation613
E Lagrangian Formulation of the Acoustic Field in Gases616
BIBLIOGRAPHY621
INDEX OF SYMBQLS631
INDEX643
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