Newtonian Dynamics

Scope of Book......Page 7
Major Sources......Page 8
Newtonian Dynamics......Page 9
Newton's First Law of Motion......Page 10
Newton's Second Law of Motion......Page 13
Newton's Third Law of Motion......Page 15
Non-Isolated Systems......Page 18
Exercises......Page 19
Motion in a General One-Dimensional Potential......Page 21
Velocity Dependent Forces......Page 24
Simple Harmonic Motion......Page 26
Damped Oscillatory Motion......Page 28
Quality Factor......Page 31
Resonance......Page 32
Periodic Driving Forces......Page 34
Transients......Page 37
Simple Pendulum......Page 38
Exercises......Page 41
Motion in a Two-Dimensional Harmonic Potential......Page 45
Projectile Motion with Air Resistance......Page 47
Charged Particle Motion in Electric and Magnetic Fields......Page 51
Exercises......Page 53
Newtonian Gravity......Page 55
Conservation Laws......Page 56
Polar Coordinates......Page 57
Conic Sections......Page 59
Kepler's Second Law......Page 62
Kepler's First Law......Page 63
Kepler's Third Law......Page 64
Orbital Energies......Page 65
Kepler Problem......Page 67
Motion in a Nearly Circular Orbit......Page 70
Exercises......Page 73
Reduced Mass......Page 75
Binary Star Systems......Page 76
Scattering in the Center of Mass Frame......Page 78
Scattering in the Laboratory Frame......Page 83
Exercises......Page 88
Rotating Reference Frames......Page 91
Centrifugal Acceleration......Page 92
Coriolis Force......Page 95
Foucault Pendulum......Page 97
Exercises......Page 100
Fundamental Equations......Page 103
Moment of Inertia Tensor......Page 104
Rotational Kinetic Energy......Page 105
Matrix Eigenvalue Theory......Page 106
Principal Axes of Rotation......Page 108
Euler's Equations......Page 110
Eulerian Angles......Page 113
Gyroscopic Precession......Page 118
Rotational Stability......Page 121
Exercises......Page 123
Generalized Coordinates......Page 125
Lagrange's Equation......Page 126
Motion in a Central Potential......Page 128
Atwood Machines......Page 129
Sliding down a Sliding Plane......Page 132
Generalized Momenta......Page 133
Spherical Pendulum......Page 134
Exercises......Page 136
Calculus of Variations......Page 139
Conditional Variation......Page 141
Hamilton's Principle......Page 144
Constrained Lagrangian Dynamics......Page 145
Hamilton's Equations......Page 149
Exercises......Page 151
Equilibrium State......Page 153
Stability Equations......Page 154
More Matrix Eigenvalue Theory......Page 155
Normal Modes......Page 157
Normal Coordinates......Page 158
Spring-Coupled Masses......Page 160
Triatomic Molecule......Page 162
Exercises......Page 164
Gravitational Potential......Page 167
Axially Symmetric Mass Distributions......Page 168
Potential Due to a Uniform Sphere......Page 171
Potential Outside a Uniform Spheroid......Page 172
Rotational Flattening......Page 174
McCullough's Formula......Page 176
Tidal Elongation......Page 177
Roche Radius......Page 181
Precession and Forced Nutation of the Earth......Page 183
Potential Due to a Uniform Ring......Page 191
Perihelion Precession of the Planets......Page 192
Perihelion Precession of Mercury......Page 195
Exercises......Page 196
Circular Restricted Three-Body Problem......Page 199
Jacobi Integral......Page 200
Tisserand Criterion......Page 201
Co-Rotating Frame......Page 203
Lagrange Points......Page 205
Zero-Velocity Surfaces......Page 208
Stability of Lagrange Points......Page 211
Historical Background......Page 217
Preliminary Analysis......Page 218
Lunar Equations of Motion......Page 219
Unperturbed Lunar Motion......Page 222
Perturbed Lunar Motion......Page 223
Description of Lunar Motion......Page 228
Basic Problem......Page 233
Analytic Solution......Page 235
Poincaré Section......Page 239
Spatial Symmetry Breaking......Page 241
Basins of Attraction......Page 245
Period-Doubling Bifurcations......Page 250
Route to Chaos......Page 253
Sensitivity to Initial Conditions......Page 258
Periodic Windows......Page 264
Further Investigation......Page 268
Scalars and Vectors......Page 273
Vector Algebra......Page 274
Cartesian Components of a Vector......Page 275
Coordinate Transformations......Page 276
Scalar Product......Page 278
Vector Product......Page 280
Rotation......Page 282
Scalar Triple Product......Page 284
Vector Triple Product......Page 285
Line Integrals......Page 286
Vector Line Integrals......Page 289
Volume Integrals......Page 290
Gradient......Page 291
Grad Operator......Page 294
Curvilinear Coordinates......Page 295
Exercises......Page 296