9780201657029

Classical Mechanics

by ; ;
  • ISBN13:

    9780201657029

  • ISBN10:

    0201657023

  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 6/15/2001
  • Publisher: Pearson

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Summary

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.

Table of Contents

Survey of the Elementary Principles
1(33)
Mechanics of a Particle
1(4)
Mechanics of a System of Particles
5(7)
Constraints
12(4)
D'Alembert's Principle and Lagrange's Equations
16(6)
Velocity-Dependent Potentials and the Dissipation Function
22(2)
Simple Applications of the Lagrangian Formulation
24(10)
Variational Principles and Lagrange's Equations
34(36)
Hamilton's Principle
34(2)
Some Techniques of the Calculus of Variations
36(8)
Derivation of Lagrange's Equations from Hamilton's Principle
44(1)
Extension of Hamilton's Principle to Nonholonomic Systems
45(6)
Advantages of a Variational Principle Formulation
51(3)
Conservation Theorems and Symmetry Properties
54(6)
Energy Function and the Conservation of Energy
60(10)
The Central Force Problem
70(64)
Reduction to the Equivalent One-Body Problem
70(2)
The Equations of Motion and First Integrals
72(4)
The Equivalent One-Dimensional Problem, and Classification of Orbits
76(7)
The Virial Theorem
83(3)
The Differential Equation for the Orbit, and Integrable Power-Law Potentials
86(3)
Conditions for Closed Orbits (Bertrant's Theorem)
89(3)
The Kepler Problem: Inverse-Square Law of Force
92(4)
The Motion in Time in the Kepler Problem
96(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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