Mechanics and Strength of Materials

PrefaceIntroductionChapter 1. Kinematics 1.1. Motion of a Single Particle 1.2. Description of the Motion of a Rigid Body 1.3. Relative Motion 1.4. Plane Motion of a Rigid Body 1.5. Examples of the Determination of Velocities and Accelerations in the Motion of Plane MechanismsChapter 2. The Dynamics of a Particle 2.1. Fundamental Definitions and Theorems 2.2. Motion of a Particle 2.3. Center of Mass and Center of Gravity of a Particle System 2.4. Law of Variation of Momentum 2.5. Law of Variation of angular MomentumChapter 3. Statics 3.1. Equations of Equilibrium 3.2. Couple 3.3. Spatial System of Forces. Wrench 3.4. Analytical and graphical Methods in the Statics of Plane Systems Analytical Methods Graphical Methods (Funicular Polygon) 3.5. Examples Triple-Jointed System Free-Ends Beam Plane Trusses 3.6. The Distributive Character of Transverse Loads in Simple Rods 3.7. The Equilibrium of Rods Loaded with Transverse Forces 3.8. Friction Friction on an Inclined Plane Bearing Friction Friction of Rope against Wheel Problem of Friction in the Case of a Cylinder Rolling on Plane SurfaceChapter 4. The Statics of Elastic Systems 4.1. Hooke's Law 4.2. Safety Factor 4.3. Statically Indeterminate Systems 4.4. Problems of Simple Beam-Bending 4.5. Geometric Moments of Inertia 4.6. Strength Calculations of Beams 4.7. The Equation for the axis of a Deflected Beam 4.8. Graphical Methods of Determining Deflections of Simple Beams (Mohr's Analogy) 4.9. Oblique Bending 4.10. Some Special Problems of Bending Theory 4.11. Clapeyron's Systems 4.12. Buckling Problems of axially Compressed Rods 4.13. Highly Curved Rods 4.14. Torsion of Rods with Circular Cross-Section 4.15. Springs 4.16. Simultaneous Bending and Torsion of Rods with Circular Cross-SectionChapter 5. The Dynamics of Rigid Bodies 5.1. Moments of Inertia of Rigid Bodies 5.2. The Angular Momentum of a Rigid Body in General Motion 5.3. Angular Momentum in Circular Motion 5.4. Euler's Equations 5.5. The Kinetic Energy of Rigid Bodies in General MotionChapter 6. Dynamics in Relative Motion 6.1. Differential Equation of the Motion of a Particle in a Non-Inertial System 6.2. The Dynamics of Rigid Bodies in Relative MotionChapter 7. Fundamentals of Analytical Mechanics 7.1. Generalized Coordinates and Degrees of Freedom of a Mechanical System 7.2. D'Alembert's Principle 7.3. Hamilton's Principle 7.4. Lagrange Equations of the First Order 7.5. Lagrange Equations of the Second Order 7.6. Kinetic Energy of a System 7.7. Impulsive Motion 7.8. Gyroscopic and Dissipative Forces 7.9. The Lagrange Equations for Electromechanical Systems 7.10. Hamilton's Canonical Equations 7.11. The Total Energy of a Mechanical System 7.12. Configurational Space 7.13. The Stability of Mechanical SystemsChapter 8. Vibrations of Systems with One Degree of Freedom 8.1. Preliminary Discussion 8.2. Free Vibrations of Harmonic Oscillators 8.3. The Influence of Dissipative Forces in the Free Vibrations of Harmonic Oscillators 8.4. Forced Vibrations of Harmonic Oscillators 8.5. Vibrations of Harmonic Oscillators with Kinematical Input 8.6. Vibrations of Harmonic Oscillators under Periodic Input Forces 8.7. Vibrations of Non-Linear SystemsChapter 9. Vibrations Of Systems with Many Degrees of Freedom 9.1. Preliminary Discussion 9.2. Problems of Linearization of the Equations 9.3. Free Vibrations of Conservative Systems 9.4. Normal Coordinates 9.5. Forced Vibrations of a System 9.6. Free Vibrations of Dissipative Systems 9.7. Forced Vibrations in Dissipative Systems 9.8. Vibrations of Clapeyron's SystemsChapter 10. Some Methods of Describing Random Phenomena in Mechanics 10.1. Basic Concepts 10.2. Methods of Describing Stochastic Processes 10.3. Stochastic Linearization 10.4. Random Vibrations of Linear Systems with One Degree of Freedom 10.5. Random Vibrations of Systems with Many Degrees of Freedom 10.6. The Problem of Departures 10.7. Fokker—Planck—Kolmogorov Equations 10.8. Proposal for a Method of Direct Determination of Probability DensityBibliographySubject Index