Table of Contents:
| Preface | i | |||
| I | Statics | 1 | ||
| 1 | Forces Acting on a Point Mass | 3 | ||
| 1.1 | Kinematics | 4 | ||
| 1.2 | Dynamics | 6 | ||
| 1.2.1 | Examples of Forces | 10 | ||
| 1.2.1 | Superposition of Forces | 16 | ||
| 2 | Statics of Rigid Bodies | 17 | ||
| 2.1 | Kinematics | 17 | ||
| 2.1.1 | Geometry of Rigid Bodies | 17 | ||
| 2.2 | Forces and Torques | 19 | ||
| 2.2.1 | Principle of Equivalence | 22 | ||
| 2.2.2 | Reduction of Systems of Forces | 25 | ||
| 2.3 | Bearings and Trusses | 28 | ||
| 2.3.1 | Bearings | 28 | ||
| 2.3.2 | Trusses | 30 | ||
| 2.4 | Frictional Forces | 34 | ||
| 3 | Elastostatics | 39 | ||
| 3.1 | Stresses | 34 | ||
| 3.1.1 | On the Derivation of the Stress Tensor | 41 | ||
| 3.1.2 | Planar Stress | 43 | ||
| 3.1.3 | The Stress Ellipsoid | 45 | ||
| 3.1.4 | Forces and Moments in the 3-dimensional Case | 47 | ||
| 3.2 | Strains | 48 | ||
| 3.3 | On Hooke’s Law | 52 | ||
| 3.3.1 | Torsion of Cylindrical Rod | 57 | ||
| 3.3.2 | Bending of Beams | 58 | ||
| 3.4 | Hydrostatics | 65 | ||
| 3.5 | Aerostatics | 68 | ||
| II | Dynamics | 71 | ||
| 4 | Point Mass Kinetics | 73 | ||
| 4.1 | Energy Theorem of Point Mechanics | 73 | ||
| 4.2 | Angular Momentum | 75 | ||
| 4.3 | Kepler Motion | 78 | ||
| 4.3.1 | Bounded and Unbounded Motion | 83 | ||
| 4.4 | Scattering off a Central Potential | 87 | ||
| 4.4.1 | The Effective Cross Section | 95 | ||
| 5 | Dynamics of Rigid Bodies | 97 | ||
| 5.1 | The Tensor of Inertia | 97 | ||
| 5.2 | Euler’s Equations | 102 | ||
| 5.2.1 | Euler Angles | 106 | ||
| 5.3 | Gyroscope, Nutation, Precession | 110 | ||
| 5.3.1 | Moving Frames of Reference | 121 | ||
| 6 | Systems of Point Masses | 127 | ||
| 6.1 | Momentum Theorem | 127 | ||
| 6.2 | Auxilliary Conditions and Constraint Forces | 129 | ||
| 6.2.1 | D’Alembert Principle - Virtual Work | 130 | ||
| 6.3 | Lagrange Equations | 132 | ||
| 6.3.1 | Lagrange Equations of the First Kind | 132 | ||
| 6.3.2 | Lagrange Equations of the Second Kind | 137 | ||
| 6.3.3 | Non-holonomic Systems | 152 | ||
| 6.4 | Small Oscillations | 158 | ||
| 7 | Continuum Mechanics | 173 | ||
| 7.1 | Elastodynamics | 173 | ||
| 7.1.1 | Elastic Waves | 176 | ||
| 7.2 | Hydrodynamics | 178 | ||
| 7.2.1 | Equation of Continuity | 179 | ||
| 7.2.2 | Streamlines and Stream Function | 181 | ||
| 7.2.3 | Momentum Balance | 185 | ||
| 7.2.4 | Bernoulli Equation | 188 | ||
| 7.2.5 | Energy Balance | 191 | ||
| 7.2.6 | Circulation | 198 | ||
| 7.2.7 | Helmholtz Vortex Theorems | 202 | ||
| 7.2.8 | Sound Waves | 211 | ||
| 7.2.9 | Viscous Liquids | 214 | ||
| 7.2.10 | Potential Flow | 220 | ||
| Appendix | 237 | |||