Lagrangian and Hamiltonian Mechanics

Preface v CHAPTER I NEWTON'S LAWS 1(27) Newton's laws 1(2) Free fall 3(1) Simple harmonic oscillator 4(2) Central force 6(3) Gravitational force: qualitative 9(2) Gravitational force: quantitative 11(5) Parameters of earth's orbit 16(3) Scattering 19(2) Coulomb scattering 21(1) Exercises 22(6) CHAPTER II THE PRINCIPLE OF VIRTUAL WORK AND D'ALEMBERT'S PRINCIPLE 28(12) Constraints 28(1) Principle of virtual work 29(3) D'Alembert's principle and generalized coordinates 32(1) Lever 33(1) Inclined plane 34(1) Plane pendulum 34(3) Exercises 37(3) CHAPTER III LAGRANGE'S EQUATIONS 40(19) Lagrange's equations 40(4) Plane pendulum 44(1) Spherical pendulum 45(1) Electromagnetic interaction 46(3) Interaction of an electric charge and a magnet 49(5) Exercises 54(5) CHAPTER IV THE PRINCIPLE OF STATIONARY ACTION OR HAMILTON'S PRINCIPLE 59(21) Principle of stationary action 59(3) Calculus of variations 62(2) Geodesics 64(7) Examples 67(4) Path integral formulation of quantum mechanics 71(4) Exercises 75(5) CHAPTER V INVARIANCE TRANSFORMATIONS AND CONSTANTS OF THE MOTION 80(18) Invariance transformations 80(1) Free particle (a) 81(1) Infinitesimal transformations 82(1) Free particle (b) 83(1) Space time transformations 84(6) Spatial displacement 85(1) Spatial rotation 85(2) Galilean transformation 87(1) Time displacement 88(2) Covariance, invariance, and the action 90(6) Exercises 96(2) CHAPTER VI HAMILTON'S EQUATIONS 98(17) Hamilton's equations 98(3) Plane pendulum 101(2) Spherical pendulum 103(1) Rotating pendulum 104(3) Electromagnetic interaction 107(1) Poisson brackets 107(3) Exercises 110(5) CHAPTER VII CANONICAL TRANSFORMATIONS 115(28) One degree of freedom 115(4) Generating functions 119(4) Identity and point transformations 123(2) Infinitesimal canonical transformations 125(1) Invariance transformations 126(2) Lagrange and Poisson brackets 128(4) Time dependence 132(2) Integral invariants 134(6) Exercises 140(3) CHAPTER VIII HAMILTON-JACOBI THEORY 143(28) Hamilton's principal function 143(4) Jacobi's complete integral 147(4) Time-independent Hamilton-Jacobi equation 151(4) Separation of variables 155(1) Free particle, in cartesian coordinates 155(2) Central force, in spherical polar coordinates 157(5) Hamilton-Jacobi mechanics, geometric optics, and wave mechanics 162(5) Exercises 167(4) CHAPTER IX ACTION-ANGLE VARIABLES 171(20) Action-angle variables 171(5) Example: simple harmonic oscillator 176(2) Example: central force 178(3) Adiabatic change 181(6) Exercises 187(4) CHAPTER X NON-INTEGRABLE SYSTEMS 191(19) Surface of section 191(5) Integrable and non-integrable systems 196(3) Perturbation theory 199(2) Irrational tori 201(2) Rational tori 203(4) Exercises 207(3) INDEX 210