Classical Mechanics

Contents......Page v
Preface to 3rd Edition......Page ix
1.1 Mechanics of a Particle......Page p1
1.2 Mechanics of a System of Particles......Page p5
1.3 Constraints......Page p12
1.4 D\'Alembert\'s Pr. & Lagrange\'s Eqns......Page p16
1.5 V-Dependent Potentials & Dissipation Function......Page p22
1.6 Simple Applications of the Lagrangian Formulation......Page p24
2.1 Hamilton\'s Principle......Page p34
2.2 Techniques of the Calculus of Variations......Page p36
2.3 Lagrange\'s Eqns from Hamilton\'s Principle......Page p44
2.4 Ext. of Hamilton\'s Pr. to Nonholonomic Systems......Page p45
2.5 Advantages of a Variational Principle Formulation......Page p51
2.6 Conservation Thms & Symmetry Properties......Page p54
2.7 Energy Function & Conservation of Energy......Page p60
3.1 Reduction to the Equivalent One-Body Problem......Page p70
3.2 Equations of Motion & First Integrals......Page p72
3.3 The 1-Dimensional Problem, & Classification of Orbits......Page p76
3.4 The Virial Theorem......Page p83
3.5 Diff. Eqn for the Orbit, & Integrable Power-Law Potentials......Page p86
3.6 Conditions for Closed Orbits (Bertrand\'s Theorem)......Page p89
3.7 The Kepler Problem: Inverse-Square Law of Force......Page p92
3.8 The Motion in Time in the Kepler Problem......Page p98
3.9 The Laplace-Runge-Lenz Vector......Page p102
3.10 Scattering in a Central Force Field......Page p106
3.11 Transf. of the Scattering Problem to Lab. Coordinates......Page p114
3.12 The Three-Body Problem......Page p121
4.1 The Independent Coordinates of a Rigid Body......Page p134
4.2 Orthogonal Transformations......Page p139
4.3 Formal Properties of the Transformation Matrix......Page p144
4.4 The Euler Angles......Page p150
4.5 Cayley-Klein Parameters & Related Quantities......Page p154
4.6 Euler\'s Theorem on the Motion of a Rigid Body......Page p155
4.7 Finite Rotations......Page p161
4.8 Infinitesimal Rotations......Page p163
4.9 Rate of Change of a Vector......Page p171
4.10 The Coriolis Effect......Page p174
5.1 Angular Mo & Kinetic E of Motion about a Point......Page p184
5.2 Tensors......Page p188
5.3 Inertia Tensor & Moment of Inertia......Page p191
5.4 Eigenvalues of the I.T. & Prin. Axis Transformation......Page p195
5.5 Rigid Body Probs & Euler Equations of Motion......Page p198
5.6 Torque-free Motion of a Rigid Body......Page p200
5.7 Heavy Symmetrical Top w. 1 Point Fixed......Page p208
5.8 Precession of Equinoxes & Satellite Orbits......Page p223
5.9 Prec. of Systems of Charges in a Magnetic Field......Page p230
6.1 Formulation of the Problem......Page p238
6.2 The Eigenvalue Eqn & Principal Axis Transformation......Page p241
6.3 Frequencies of Free Vibration, & Normal Coordinates......Page p250
6.4 Free Vibrations of a Linear Triatomic Molecule......Page p253
6.5 Forced Vibrations and the Effect of Dissipative Forces......Page p259
6.6 Beyond Small Oscillations: Damped Driven Pendulum, & Josephson Junction......Page p265
7 ■ The Classical Mechanics of Special Relativity......Page p276
7.1 Basic Postulates of the Special Theory......Page p277
7.2 Lorentz Transformations......Page p280
7.3 Velocity Addition and Thomas Precession......Page p282
7.4 Vectors and the Metric Tensor......Page p286
7.5 1-Forms and Tensors......Page p289
7.6 Forces in the Special Theory: Electromagnetism......Page p297
7.7 Relativistic Kinematics of Collisions & Many-Particle Systems......Page p300
7.8 Relativistic Angular Momentum......Page p309
7.9 Lagrangian Formulation of Relativistic Mechanics......Page p312
7.10 Covariant Lagrangian Formulations......Page p318
7.11 Intro. to the General Theory of Relativity......Page p324
8.1 Legendre Transf. &  Hamilton Eqns of Motion......Page p334
8.2 Cyclic Coordinates & Conservation Theorems......Page p343
8.3 Routh\'s Procedure......Page p347
8.4 Hamiltonian Formulation of Relativistic Mechanics......Page p349
8.5 Hamilton\'s Equations from a Variational Principle......Page p353
8.6 The Principle of Least Action......Page p356
9.1 The Equations of Canonical Transformation......Page p368
9.2 Examples of Canonical Transformations......Page p375
9.3 The Harmonic Oscillator......Page p377
9.4 Symplectic Approach to Canonical Transformations......Page p381
9.5 Poisson Brackets & Other Canonical Invariants......Page p388
.. and Conservation Theorems in Poisson Bracket Formulation......Page p396
9.7 The Angular Momentum Poisson Bracket Relations......Page p408
9.8 Symmetry Groups of Mechanical Systems......Page p412
9.9 Liouville\'s Theorem......Page p419
10.1 Hamilton-Jacobi Eqn for Hamilton\'s Principal Function......Page p430
10.2 Harmonic Oscillator as Ex. of Hamilton-Jacobi Method......Page p434
10.3 Hamilton-Jacobi Eqn for Hamilton\'s Characteristic Function......Page p440
10.4 Separation of Variables in the H-J Equation......Page p444
10.5 Ignorable Coordinates & the Kepler Problem......Page p445
10.6 Action-angle Variables for 1 Degree of Freedom......Page p452
10.7 Action-Angle Vars. for Completely Separable Systems......Page p457
10.8 The Kepler Problem in Action-angle Variables......Page p466
11 ■ Classical Chaos......Page p483
11.1 Periodic Motion......Page p484
11.2 Perturbations & Kolmogorov-Arnold-Moser Theorem......Page p487
11.3 Attractors......Page p489
11.4 Chaotic Trajectories & Liapunov Exponents......Page p491
11.5 Poincare Maps......Page p494
11.6 Henon-Heiles Hamiltonian......Page p496
... and Parametric Resonance......Page p505
11.8 The Logistic Equation......Page p509
11.9 Fractals and Dimensionality......Page p516
12.1 Introduction......Page p526
12.2 Time-dependent Perturbation Theory......Page p527
12.3 Illustrations of Time-dependent Perturbation Theory......Page p533
12.4 Time-independent Perturbation Theory......Page p541
12.5 Adiabatic Invariants......Page p549
13.1 Transition from Discrete to Continuous......Page p558
13.2 Lagrangian Formulation for Continuous Systems......Page p561
13.3 Stress-energy Tensor & Conservation Theorems......Page p566
13.4 Hamiltonian Formulation......Page p572
13.5 Relativistic Field Theory......Page p577
13.6 Ex. of Relativistic Field Theories......Page p583
13.7 Noethers Theorem......Page p589
Appendixes......Page 
......   and Cayley-Klein Parameters......Page p601
Appx В ■ Groups and Algebras......Page p605
Selected Bibliography......Page p617
Author Index......Page p623
Subject Index......Page p625