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Classical Mechanics, 2nd Ed. / Edition 2
     

Classical Mechanics, 2nd Ed. / Edition 2

5.0 1
by Herbert Goldstein
 

ISBN-10: 0201029189

ISBN-13: 9780201029185

Pub. Date: 01/01/1980

Publisher: Addison-Wesley

The prospect of a second edition of Classical Mechanics, almost thirty years after initial publication, has given rise to two nearly contradictory sets of reactions.

Overview

The prospect of a second edition of Classical Mechanics, almost thirty years after initial publication, has given rise to two nearly contradictory sets of reactions.

Product Details

ISBN-13:
9780201029185
Publisher:
Addison-Wesley
Publication date:
01/01/1980
Series:
Addison-Wesley Series in Physics
Edition description:
Older Edition
Pages:
600
Product dimensions:
6.72(w) x 9.52(h) x 1.23(d)

Table of Contents

PREFACE vii
CHAPTER 1 SURVEY OF THE ELEMENTARY PRINCIPLES
1(34)
1-1 Mechanics of a particle
1(4)
1-2 Mechanics of a system of particles
5(6)
1-3 Constraints
11(6)
1-4 D'Alembert's principle and Lagrange's equations
17(4)
1-5 Velocity-dependent potentials and the dissipation function
21(4)
1-6 Simple applications of the Lagrangian formulation
25(10)
CHAPTER 2 VARIATIONAL PRINCIPLES AND LAGRANGE'S EQUATIONS
35(35)
2-1 Hamilton's principle
35(2)
2-2 Some techniques of the calculus of variations
37(6)
2-3 Derivation of Lagrange's equations from Hamilton's principle
43(2)
2-4 Extension of Hamilton's principle to nonholonomic systems
45(6)
2-5 Advantages of a variational principle formulation
51(3)
2-6 Conservation theorems and symmetry properties
54(16)
CHAPTER 3 THE TWO-BODY CENTRAL FORCE PROBLEM
70(58)
3-1 Reduction to the equivalent one-body problem
70(1)
3-2 The equations of motion and first integrals
71(6)
3-3 The equivalent one-dimensional problem, and classification of orbits
77(5)
3-4 The virial theorem
82(3)
3-5 The differential equation for the orbit, and integrable power-law potentials
85(5)
3-6 Conditions for closed orbits (Bertrand's theorem)
90(4)
3-7 The Kepler problem: Inverse square law of force
94(4)
3-8 The motion in time in the Kepler problem
98(4)
3-9 The Laplace-Runge-Lenz vector
102(3)
3-10 Scattering in a central force field
105(9)
3-11 Transformation of the scattering problem to laboratory coordinates
114(14)
CHAPTER 4 THE KINEMATICS OF RIGID BODY MOTION
128(60)
4-1 The independent coordinates of a rigid body
128(4)
4-2 Orthogonal transformations
132(5)
4-3 Formal properties of the transformation matrix
137(6)
4-4 The Euler angles
143(5)
4-5 The Cayley-Klein parameters and related quantities
148(10)
4-6 Euler's theorem on the motion of a rigid body
158(6)
4-7 Finite rotations
164(2)
4-8 Infinitesimal rotations
166(8)
4-9 Rate of change of a vector
174(3)
4-10 The Coriolis force
177(11)
CHAPTER 5 THE RIGID BODY EQUATIONS OF MOTION
188(55)
5-1 Angular momentum and kinetic energy of motion about a point
188(4)
5-2 Tensors and dyadics
192(3)
5-3 The inertia tensor and the moment of inertia
195(3)
5-4 The eigenvalues of the inertia tensor and the principal axis transformation
198(5)
5-5 Methods of solving rigid body problems and the Euler equations of motion
203(2)
5-6 Torque-free motion of a rigid body
205(8)
5-7 The heavy symmetrical top with one point fixed
213(12)
5-8 Precession of the equinoxes and of satellite orbits
225(7)
5-9 Precession of systems of charges in a magnetic field
232(11)
CHAPTER 6 SMALL OSCILLATIONS
243(32)
6-1 Formulation of the problem
243(3)
6-2 The eigenvalue equation and the principal axis transformation
246(7)
6-3 Frequencies of free vibration, and normal coordinates
253(5)
6-4 Free vibrations of a linear triatomic molecule
258(5)
6-5 Forced vibrations and the effect of dissipative forces
263(12)
CHAPTER 7 SPECIAL RELATIVITY IN CLASSICAL MECHANICS
275(64)
7-1 The basic program of special relativity
275(3)
7-2 The Lorentz transformation
278(10)
7-3 Lorentz transformations in real four dimensional spaces
288(5)
7-4 Further descriptions of the Lorentz transformation
293(5)
7-5 Covariant four-dimensional formulations
298(5)
7-6 The force and energy equations in relativistic mechanics
303(6)
7-7 Relativistic kinematics of collisions and many-particle systems
309(11)
7-8 The Lagrangian formulation of relativistic mechanics
320(6)
7-9 Covariant Lagrangian formulations
326(13)
CHAPTER 8 THE HAMILTON EQUATIONS OF MOTION
339(39)
8-1 Legendre transformations and the Hamilton equations of motion
339(8)
8-2 Cyclic coordinates and conservation theorems
347(4)
8-3 Routh's procedure and oscillations about steady motion
351(5)
8-4 The Hamiltonian formulation of relativistic mechanics
356(6)
8-5 Derivation of Hamilton's equations from a variational principle
362(3)
8-6 The principle of least action
365(13)
CHAPTER 9 CANONICAL TRANSFORMATIONS
378(60)
9-1 The equations of canonical transformation
378(8)
9-2 Examples of canonical transformations
386(5)
9-3 The symplectic approach to canonical transformations
391(6)
9-4 Poisson brackets and other canonical invariants
397(8)
9-5 Equations of motion, infinitesimal canonical transformations, and conservation theorems in the Poisson bracket formulation
405(11)
9-6 The angular momentum Poisson bracket relations
416(4)
9-7 Symmetry groups of mechanical systems
420(6)
9-8 Liouville's theorem
426(12)
CHAPTER 10 HAMILTON-JACOBI THEORY
438(61)
10-1 The Hamilton-Jacobi equation for Hamilton's principal function
438(4)
10-2 The harmonic oscillator problem as an example of the Hamilton-Jacobi method
442(3)
10-3 The Hamilton-Jacobi equation for Hamilton's characteristic function
445(4)
10-4 Separation of variables in the Hamilton-Jacobi equation
449(8)
10-5 Action-angle variables in systems of one degree of freedom
457(6)
10-6 Action-angle variables for completely separable systems
463(9)
10-7 The Kepler problem in action-angle variables
472(12)
10-8 Hamilton-Jacobi theory, geometrical optics, and wave mechanics
484(15)
CHAPTER 11 CANONICAL PERTURBATION THEORY
499(46)
11-1 Introduction
499(1)
11-2 Time-dependent perturbation (variation of constants)
500(6)
11-3 Illustrations of time-dependent perturbation theory
506(9)
11-4 Time-independent perturbation theory in first order with one degree of freedom
515(4)
11-5 Time-independent perturbation theory to higher order
519(8)
11-6 Specialized perturbation techniques in celestial and space mechanics
527(4)
11-7 Adiabatic invariants
531(14)
CHAPTER 12 INTRODUCTION TO THE LAGRANGIAN AND HAMILTONIAN FORMULATIONS FOR CONTINUOUS SYSTEMS AND FIELDS
545(56)
12-1 The transition from a discrete to a continuous system
545(3)
12-2 The Lagrangian formulation for continuous systems
548(7)
12-3 The stress-energy tensor and conservation theorems
555(7)
12-4 Hamiltonian formulation, Poisson brackets and the momentum representation
562(8)
12-5 Relativistic field theory
570(5)
12-6 Examples of relativistic field theories
575(13)
12-7 Noether's theorem
588(13)
APPENDIXES 601(20)
A Proof of Bertrand's Theorem 601(5)
B Euler Angles in Alternate Conventions 606(5)
C Transformation Properties of d(XXX) 611(2)
D The Staeckel Conditions for Separability of the Hamilton-Jacobi Equation 613(3)
E Lagrangian Formulation of the Acoustic Field in Gases 616(5)
BIBLIOGRAPHY 621(10)
INDEX OF SYMBOLS 631(12)
INDEX 643

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Classical Mechanics, 2nd Ed. 5 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
There's a reason this book has been used continuously as a text since its original publication in 1950. Covers the basics in enough detail to be understandable as well as enough depth to provide a springboard into advanced topics.