Dynamics: A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities

Cover......Page 1
Dynamics......Page 6
PREFACE......Page 10
Contents......Page 12
1·4. Rates of Change......Page 18
1·6. Equations of the First Order......Page 19
1·7. Equations of the Second Order......Page 20
2·1. Vectors and Scalars......Page 23
2·4. Analytical Method of Composition......Page 24
2·6. Centroids or Mean Centres......Page 25
2·7--2.9. Centroid Method of Compounding Vectors......Page 26
Examples......Page 27
3·2. Acceleration. Velocity-time curve......Page 28
3·3. Acceleration represented as a space rate of change......Page 29
3·4. Units......Page 30
3·5. Uniformly Accelerated Motion......Page 31
3·6. Applications......Page 33
3·7. Graphical Methods......Page 35
3·8. Worked Examples......Page 36
Examples......Page 38
4·1. Newtonian Mechanics......Page 41
4·2. Impulse......Page 45
4·3. Work......Page 46
4·4. Energy, Kinetic and Potential......Page 48
4·5. Locomotive Engines and Motor Cars......Page 51
4·6. Resistance Depending on Velocity......Page 55
4·7. Motion of a Chain......Page 58
4·8. Units and Dimensions......Page 59
Examples......Page 60
5·1. Velocity......Page 69
5·2. Relative Velocity......Page 72
5·3. Angular Velocity......Page 73
5·4. Centre of Rotation......Page 75
5·5. Angular Velocity of a Body......Page 79
Examples......Page 83
6·2. Motion of Projectiles......Page 86
6·3. Resisting Media......Page 91
6·4. Principle of Work......Page 94
Examples......Page 95
7·l. Simple Harmonic Motion......Page 100
7·2. Geometrical Representation......Page 102
7·3. Elastic Strings. Hooke\'s Law......Page 103
7·4. Heavy Particle suspended by an Elastic String......Page 105
7·5. Applications......Page 107
7·6. Simple Pendulum......Page 110
7·7. Disturbed Simple Harmonic Motion......Page 113
7·8. Damped Harmonic Oscillations......Page 115
7·9. Damped Forced Oscillations......Page 116
Examples......Page 117
8·2. Motion on a Smooth Curve......Page 122
8·3. Motion on a Smooth Circle......Page 123
8·4. Cycloidal Motion......Page 125
Examples......Page 127
9·2. Motion of a System of Particles. Conservation of Momentum......Page 131
9·3. Motion of the Centre of Gravity. Independence of Translation and Rotation......Page 133
9·5. Kinetic Energy in reference to Centre of Gravity......Page 135
9·8. Applications. Car rounding a Curve......Page 136
Examples......Page 138
10·2. Relative Motion......Page 140
10·3. Motion on a Wedge......Page 141
10·4. Examples of Conservation of Momentum and Energy......Page 142
10·5. Conical Pendulum......Page 143
10·6. Transmission of Energy by a Belt......Page 144
10·7. Further Problems on Strings and Chains......Page 145
10·8. Problems on Changing Mass......Page 147
Examples......Page 149
11·2. Equations of Motion for Impulsive Forces......Page 155
11·3. Impact of Smooth Spheres......Page 157
11·4. Examples of Impulsive Motion......Page 161
11·5. Kinetic Energy created by Impulses......Page 163
11·6. Elasticity and Impulses......Page 164
Examples......Page 165
12·1. Velocity and Acceleration in Polar Coordinates......Page 172
12·2. Central Orbits......Page 173
12·3. Circular Orbits......Page 175
12·4. Elliptic Orbit. Force directed to the Centre......Page 176
12·5. Elliptic Orbit. Force directed to Focus......Page 178
12·6. Kepler\'s Laws of Planetary Motion......Page 184
12·7. Use of u, [GREEK SMALL LETTER THETA] Formulae......Page 188
12·8. Repulsive Forces......Page 195
12·9. Motion of Two Particles......Page 196
Examples......Page 198
13·2. Theorem of Parallel Axes......Page 205
13·4. Reference Table. Routh\'s Rule......Page 206
13·5. Momental Ellipse......Page 209
Examples......Page 211
14·1. Rigid Body. Fundamental Principles......Page 214
14·2. Kinetic Energy of a Rigid Body......Page 216
14·3. Momentum of a Rigid Body......Page 218
14·4. Examples of Conservation of Energy and Momentum......Page 221
Examples......Page 223
15·2. Applications of the Equations of Motion......Page 225
15·3. Equations of Impulsive Motion......Page 230
15·4. Examples of Impulses......Page 231
15·5. Motion about a Fixed Axis......Page 233
15·6. Examples of Motion about an Axis......Page 238
15·7. Moment of Momentum......Page 239
15·8. Moments about a Moving Axis......Page 240
Examples......Page 241
16·1. Rolling and Sliding......Page 248
16·2. Two Spheres in Contact......Page 250
16·3. Initial Motions and Stresses......Page 252
16·4. Bending Moments in Bodies in Motion......Page 253
16·5. Steady Motion in Three Dimensions......Page 255
16·6. Use of the Instantaneous Centre of Rotation......Page 256
Examples......Page 259
17·2. Application of the Principle of Energy......Page 264
17·3. Examples......Page 265
17·4. Use of the Instantaneous Centre of Rotation......Page 267
17·5. Oscillations of a Particle Constrained to move on a Revolving Curve......Page 268
17·6. Stability of Steady Motion......Page 270
17·8. Example......Page 271
17·9. Steady Motion of a Particle on a Sphere......Page 273
Examples......Page 274