Classical Mechanics

, by Goldstein, Herbert; Poole, Charles P., Jr.; Safko, John L.

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ISBN: 9780201657029 | 0201657023
Cover: Hardcover
Copyright: 6/15/2001

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For thirty years this has been the acknowledged standard in advanced classical mechanics courses.This classic book enables readers to make connections between classical and modern physics - an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation, to reflect today's physics curriculum. They introduce readers to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help readers to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the book remains fully accessible to readers who have not had an intermediate course in classical mechanics.For college instructors and students.

Survey of the Elementary Principles

(33)

Mechanics of a Particle

(4)

Mechanics of a System of Particles

(7)

Constraints

(4)

D'Alembert's Principle and Lagrange's Equations

(6)

Velocity-Dependent Potentials and the Dissipation Function

(2)

Simple Applications of the Lagrangian Formulation

(10)

Variational Principles and Lagrange's Equations

(36)

Hamilton's Principle

(2)

Some Techniques of the Calculus of Variations

(8)

Derivation of Lagrange's Equations from Hamilton's Principle

(1)

Extension of Hamilton's Principle to Nonholonomic Systems

(6)

Advantages of a Variational Principle Formulation

(3)

Conservation Theorems and Symmetry Properties

(6)

Energy Function and the Conservation of Energy

(10)

The Central Force Problem

(64)

Reduction to the Equivalent One-Body Problem

(2)

The Equations of Motion and First Integrals

(4)

The Equivalent One-Dimensional Problem, and Classification of Orbits

(7)

The Virial Theorem

(3)

The Differential Equation for the Orbit, and Integrable Power-Law Potentials

(3)

Conditions for Closed Orbits (Bertrant's Theorem)

(3)

The Kepler Problem: Inverse-Square Law of Force

(4)

The Motion in Time in the Kepler Problem

(7)

The Laplace--Runge--Lenz Vector

103

(3)

Scattering in a Central Force Field

106

(9)

Transformation of the Scattering Problem to Laboratory Coordinates

115

(6)

The Three-Body Problem

121

(13)

The Kinematics of Rigid Body Motion

134

(50)

The Independent Coordinates of a Rigid Body

134

(5)

Orthogonal Transformations

139

(5)

Formal Properties of the Transformation Matrix

144

(6)

The Euler Angles

150

(4)

The Cayley--Klein Parameters and Related Quantities

154

(1)

Euler's Theorem on the Motion of a Rigid Body

155

(6)

Finite Rotations

161

(2)

Infinitesimal Rotations

163

(8)

Rate of Change of a Vector

171

(3)

The Coriolis Effect

174

(10)

The Rigid Body Equations of Motion

184

(54)

Angular Momentum and Kinetic Energy of Motion about a Point

184

(4)

Tensors

188

(3)

The Inertia Tensor and the Moment of Inertia

191

(4)

The Eigenvalues of the Inertia Tensor and the Principal Axis Transformation

195

(3)

Solving Rigid Body Problems and the Euler Equations of Motion

198

(2)

Torque-free Motion of a Rigid Body

200

(8)

The Heavy Symmetrical Top with One Point Fixed

208

(15)

Precession of the Equinoxes and of Satellite Orbits

223

(7)

Precession of Systems of Charges in a Magnetic Field

230

(8)

Oscillations

238

(38)

Formulation of the Problem

238

(3)

The Eigenvalue Equation and the Principal Axis Transformation

241

(9)

Frequencies of Free Vibration, and Normal Coordinates

250

(3)

Free Vibrations of a Linear Triatomic Molecule

253

(6)

Forced Vibrations and the Effect of Dissipative Forces

259

(6)

Beyond Small Oscillations: The Damped Driven Pendulum and the Josephson Junction

265

(11)

The Classical Mechanics of the Special Theory of Relativity

276

(58)

Basic Postulates of the Special Theory

277

(3)

Lorentz Transformations

280

(2)

Velocity Addition and Thomas Precession

282

(4)

Vectors and the Metric Tensor

286

(3)

I-Forms and Tensors

289

(8)

Forces in the Special Theory; Electromagnetism

297

(3)

Relativistic Kinematics of Collisions and Many-Particle Systems

300

(9)

Relativistic Angular Momentum

309

(3)

The Lagrangian Formulation of Relativistic Mechanics

312

(6)

Covariant Lagrangian Formulations

318

(6)

Introduction to the General Theory of Relativity

324

(10)

The Hamilton Equations of Motion

334

(34)

Legendre Transformations and the Hamilton Equations of Motion

334

(9)

Cyclic Coordinates and Conservation Theorems

343

(4)

Routh's Procedure

347

(2)

The Hamiltonian Formulation of Relativistic Mechanics

349

(4)

Derivation of Hamilton's Equations from a Variational Principle

353

(3)

The Principle of Least Action

356

(12)

Canonical Transformations

368

(62)

The Equations of Canonical Transformation

368

(7)

Examples of Canonical Transformations

375

(2)

The Harmonic Oscillator

377

(4)

The Symplectic Approach to Canonical Transformations

381

(7)

Poisson Brackets and Other Canonical Invariants

388

(8)

Equations of Motion, Infinitesimal Canonical Transformations, and Conservation Theorems in the Poisson Bracket Formulation

396

(12)

The Angular Momentum Poisson Bracket Relations

408

(4)

Symmetry Groups of Mechanical Systems

412

(7)

Liouville's Theorem

419

(11)

Hamilton--Jacobi Theory and Action-Angle Variables

430

(53)

The Hamilton--Jacobi Equation for Hamilton's Principal Function

430

(4)

The Harmonic Oscillator Problem as an Example of the Hamilton--Jacobi Method

434

(6)

The Hamilton--Jacobi Equation for Hamilton's Characteristic Function

440

(4)

Separation of Variables in the Hamilton--Jacobi Equation

444

(1)

Ignorable Coordinates and the Kepler Problem

445

(7)

Action-angle Variables in Systems of One Degree of Freedom

452

(5)

Action-angle Variables for Completely Separable Systems

457

(9)

The Kepler Problem in Action-angle Variables

466

(17)

Classical Chaos

483

(43)

Periodic Motion

484

(3)

Perturbations and the Kolmogorov--Arnold--Moser Theorem

487

(2)

Attractors

489

(2)

Chaotic Trajectories and Liapunov Exponents

491

(3)

Poincare Maps

494

(2)

Henon--Heiles Hamiltonian

496

(9)

Bifurcations, Driven-damped Harmonic Oscillator, and Parametric Resonance

505

(4)

The Logistic Equation

509

(7)

Fractals and Dimensionality

516

(10)

Canonical Perturbation Theory

526

(32)

Introduction

526

(1)

Time-dependent Perturbation Theory

527

(6)

Illustrations of Time-dependent Perturbation Theory

533

(8)

Time-independent Perturbation Theory

541

(8)

Adiabatic Invariants

549

(9)

Introduction to the Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields

558

(43)

The Transistion from a Discrete to a Continuous System

558

(3)

The Lagrangian Formulation for Continuous Systems

561

(5)

The Stress-energy Tensor and Conservation Theorems

566

(6)

Hamiltonian Formulation

572

(5)

Relativistic Field Theory

577

(6)

Examples of Relativistic Field Theories

583

(6)

Noether's Theorem

589

(12)

Appendix A Euler Angles in Alternate Conventions and Cayley--Klein Parameters

601

(4)

Appendix B Groups and Algebras

605

(12)

Selected Bibliography

617

(6)

Author Index

623

(2)

Subject Index

625

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Classical Mechanics

Summary

Table of Contents

Supplemental Materials