Dynamics: A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities (Cambridge Library Collection - Mathematics)

A. S. Ramsey (1867-1954) was a distinguished Cambridge mathematician and President of Magdalene College. He wrote several textbooks 'for the use of higher divisions in schools and for first year students at university'. This book on dynamics, published in 1929, was based upon his lectures to students of the mathematical tripos, and reflects the way in which this branch of mathematics had expanded in the first three decades of the twentieth century. It assumes some knowledge of elementary dynamics, and contains an extensive collection of examples for solution, taken from scholarship and examination papers of the period. The subjects covered include vectors, rectilinear motion, harmonic motion, motion under constraint, impulsive motion, moments of inertia and motion of a rigid body. Ramsey published a companion volume, Statics, in 1934. 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 A textbook on dynamics first published in 1929, based upon lectures by the distinguished twentieth-century Cambridge mathematician, and containing an extensive collection of examples for solution. Subjects covered include vectors, rectilinear motion, harmonic motion, motion under constraint, impulsive motion, moments of inertia and motion of a rigid body.