Classical Mechanics - 3rd ed. - Goldstein, Poole & Safko Ebook download

Classical Mechanics - 3rd ed. - Goldstein, Poole & Safko

 Textbook information

• Text book title            : Classical Mechanics(3rd ed.)
• Author                         : Goldstein, Poole & Safko
• ISBN                           : 0201657023

File information

• File size                     :8.95 Mb
• File format                : DjVu File
• Total No. of pages    : 636 pages

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 Text book Content page titles 

Survey of the Elementary Principles 1

• 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

Variational Principles and Lagrange's Equations 34

• 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

The Central Force Problem 70

• 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 134

• 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 184

• 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 238

• 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 276

• 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 i
• Systems 300 !
• 7.8 Relativistic Angular Momentum 309
• 7.9 The Lagrangian Formulation of Relativistic Mechanics 312
• 7.10 Co variant Lagrangian Formulations 318
• 7.11 Introduction to the General Theory of Relativity 324

8  The Hamilton Equations of Motion 334

• 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 368

• 9.1 The Equations of Canonical Transformation 368
• 9.2 Examples of Canonical Transformations 375
• 9.3 The Harmonic Oscillator 377
• 9.4 The Symplcctic 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-Jacobi Theory and Action-Angle Variables 430

• 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 483

• 11.1 Periodic Motion 484
• 11.2 Perturbations and the Kolmogorov-Amold-Moser Theorem 487
• 11.3 Attractors 489
• 11.4 Chaotic Trajectories and Liapunov Exponents 491
• 11.5 PoincareMaps 494
• 11.6 Henon-Heiles Harniltonian 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 526

• 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 Hamiltonian
Formulations for Continuous Systems and Fields 558

• 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 601
Appendix B ¦ Groups and Algebras 605
Selected Bibliography 617
Author Index 623
Subject Index 625

Solution manual of Goldstein classical mechanics 2nd edition available...!!!
 

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