Elements of Hamiltonian mechanics

Elements of Hamiltonian Mechanics ......Page 3
Copyright ......Page 4
Preface ......Page 5
Contents ......Page 7
1. Newton's Laws ......Page 9
2. Central Fields of Force ......Page 13
3. Systems of Particles ......Page 29
1. Constraints ......Page 33
2. D'Alembert's Principle ......Page 37
3. Lagrange's Equations of Motion ......Page 43
4. Cyclic Coordinates ......Page 49
5. Non-Holonomic Constraints; Velocity-Dependent Potentials ......Page 53
6. Conservation Laws ......Page 55
1. The Theory of Small Vibrations. ......Page 58
2. The Double Pendulum ......Page 65
3. Molecular Vibrations ......Page 70
4. The Normal Vibrations of a One-Dimensional Crystal ......Page 77
5. Oscillations Around an Equilibrium Motion ......Page 81
1. Introduction ......Page 83
2. The Euler Equations ......Page 89
3. Rotating Frames of Reference; The Coriolis Force ......Page 99
1. The Hamiltonian Equations of Motion ......Page 103
2. Canonical Transformations ......Page 106
3. Poisson and Lagrangian Brackets; Infinitesimal Transformations ......Page 111
4. Variational Principles; Time and Energy as Canonically Conjugate Variables ......Page 122
1. The Hamilton-Jacobi Equation ......Page 129
2. Action and Angle Variables ......Page 140
3. Adiabatic Invariants ......Page 147
1. The Anharmonic Oscillator ......Page 154
2. Canonical Perturbation Theory ......Page 161
3. Zeeman and Stark Effect of the Hydrogen Atom ......Page 170
1. The Lagrangian and Hamiltonian Formalism for Continua ......Page 175
2. Sound Waves; The Maxwell Equations ......Page 183
BIBLIOGRAPHY ......Page 189
PROBLEMS ......Page 191
INDEX ......Page 205
GLOSSARY OF SYMBOLS ......Page 208