Elements of Hamiltonian Mechanics

Blank......Page 1
Elements of Hamiltonian Mechanics......Page 4
Copyright......Page 5
Preface......Page 6
Contents......Page 8
1. Newton's Laws......Page 10
2. Central Fields of Force......Page 14
3. Systems of Particles......Page 30
1. Constraints......Page 34
2. D'Alembert's Principle......Page 38
3. Lagrange's Equations of Motion......Page 44
4. Cyclic Coordinates......Page 50
5. Non-Holonomic Constraints; Velocity-Dependent Potentials......Page 54
6. Conservation Laws......Page 56
1. The Theory of Small Vibrations.......Page 59
2. The Double Pendulum......Page 66
3. Molecular Vibrations......Page 71
4. The Normal Vibrations of a One-Dimensional Crystal......Page 78
5. Oscillations Around an Equilibrium Motion......Page 82
1. Introduction......Page 84
2. The Euler Equations......Page 90
3. Rotating Frames of Reference; The Coriolis Force......Page 100
1. The Hamiltonian Equations of Motion......Page 104
2. Canonical Transformations......Page 107
3. Poisson and Lagrangian Brackets; Infinitesimal Transformations......Page 112
4. Variational Principles; Time and Energy as Canonically Conjugate Variables......Page 123
1. The Hamilton-Jacobi Equation......Page 130
2. Action and Angle Variables......Page 141
3. Adiabatic Invariants......Page 148
1. The Anharmonic Oscillator......Page 155
2. Canonical Perturbation Theory......Page 162
3. Zeeman and Stark Effect of the Hydrogen Atom......Page 171
1. The Lagrangian and Hamiltonian Formalism for Continua......Page 176
2. Sound Waves; The Maxwell Equations......Page 184
BIBLIOGRAPHY......Page 190
PROBLEMS......Page 192
INDEX......Page 206
GLOSSARY OF SYMBOLS......Page 209