Mechanics and Relativity

Cover Idema E-Book front......Page 2
Cover page......Page 3
Contents......Page 7
Preface......Page 11
I Classical mechanics......Page 15
Dimensions and units......Page 17
Worked example: Dimensional analysis of the harmonic oscillator......Page 18
Problems......Page 20
Newton's laws of motion......Page 23
Springs: Hooke's law......Page 24
Gravity: Newton's law of gravity......Page 25
Friction and drag......Page 26
Equations of motion......Page 27
Worked example: falling stone with drag......Page 28
Multiple forces......Page 29
Statics......Page 30
Worked example: Suspended sign......Page 31
Case 2: F = F(x)......Page 32
Worked example: velocity of the harmonic oscillator......Page 33
Problems......Page 34
Work......Page 39
Kinetic energy......Page 40
Gravitational potential energy......Page 42
General conservative forces......Page 43
Energy landscapes......Page 44
Worked example: The Lennard-Jones potential......Page 45
Problems......Page 47
Center of mass of an object......Page 53
Conservation of momentum......Page 54
Kinetic energy of a collection of particles......Page 55
Rocket equation......Page 56
Impulse......Page 57
Worked example: bike crash......Page 59
Elastic collisions in the COM frame......Page 60
Problems......Page 62
Rotation basics......Page 65
Torque......Page 66
Moment of inertia......Page 67
Angular momentum......Page 68
Rolling and slipping motion......Page 69
Worked example: A cylinder rolling down a slope......Page 71
Precession and nutation......Page 72
Problems......Page 74
General planar motion in polar coordinates......Page 81
Motion under the action of a central force......Page 82
Kepler's laws......Page 84
Problems......Page 86
Rotating reference frames......Page 87
Moment of inertia tensor......Page 89
Euler's equations......Page 90
Problems......Page 93
Pendulum......Page 97
Damped harmonic oscillator......Page 98
Driven harmonic oscillator......Page 99
Coupled oscillators......Page 100
Two coupled pendulums......Page 101
Normal modes......Page 102
Problems......Page 104
Sinusoidal waves......Page 107
The wave equation......Page 108
Wave superposition......Page 110
Sound waves......Page 112
The Doppler effect......Page 113
Problems......Page 116
II Special relativity......Page 119
An old and a new axiom......Page 121
Loss of simultaneity......Page 122
Time dilation......Page 123
Lorentz contraction......Page 125
Problems......Page 127
Derivation of the Lorentz transformations......Page 129
Loss of simultaneity......Page 132
Rapdity and repeated Lorentz transformations*......Page 133
Problems......Page 136
Time dilation and space contraction revisited......Page 139
An invariant measure of length......Page 141
Worked example: Causal connections......Page 142
The invariant interval and the ordering of events......Page 143
Worldlines and proper time......Page 144
Problems......Page 146
The position four-vector......Page 149
Lorentz transformation matrix and metric tensor*......Page 150
Relativistic energy......Page 151
Conservation of energy and momentum......Page 152
Problems......Page 153
Totally inelastic collision......Page 155
Radioactive decay and the center-of-momentum frame......Page 157
Totally elastic collision: Compton scattering......Page 158
Problems......Page 160
The force four-vector......Page 163
The four-acceleration......Page 164
Relativistic waves......Page 165
Problems......Page 168
Appendices......Page 169
Vector basics......Page 171
Polar coordinates......Page 173
First-order linear ordinary differential equations......Page 174
Second-order linear ordinary differential equations with constant coefficients......Page 176
Second-order linear ordinary differential equations of Euler type......Page 177
Power series solutions......Page 178
Problems......Page 181
Moments of inertia......Page 183
Solar system objects......Page 184
Special relativity......Page 185
Images......Page 187
Problems......Page 188
About the author......Page 189
Index......Page 191
Cover Idema E-Book back......Page 0