CONTENTS 1
Part Ⅰ．Statics 1
Chapter 1．Fundamental Concepts and Principles of Statics 1
§1-1 Rigid Body 1
§1-2 Force 2
§1-3 Principles of Statics 3
§1-4 Free-Body Diagram 4
§1-5 Types of Force Systems 5
Chapter 2．Concurrent Forces 6
§2-1 Composition of Concurrent Forces 6
§2-2 Method of Projections 7
§2-3 Equilibrium of Concurrent Forces 8
§2-4 Equilibrium of Three Forces 9
§3-2 Characteristics of a Couple 10
§3-1 Definitions 10
Chapter 3．Couples 10
§3-3 Composition and Equilibrium of Couples 12
Chapter 4．Moment of a Force 12
§4-1 Moment of a Force with Respect toan Axis 12
§4-2 Moment of a Force with Respect to a Point 13
§4-3 Varignon's Theorem 14
Chapter 5．General Case of Forces in a Plane 15
§5-1 Resolution of a Given Force into a Force 15
and a Couple 15
§5-2 Reduction of a System of Coplanar Forces 16
§5-3 Equilibrium of Coplanar Forces 17
§5-4 Plane Truss 19
Chapter 6．Friction 21
§6-1 Friction Defined 21
§6-2 Coefficient of Friction and Angle of Friction 22
§6-3 Angle of Repose 23
§6-4 Types of Problems Involving Frictional Forces 24
Chapter 7．General Case of Forces in Space 25
§7-1 Reduction of a System of Forces in Space 25
§7-2 Equilibrium of Forces in Space 27
Chapter 8．Center of Gravity 28
§8-1 Center of Parallel Forces 28
§8-2 Center of Gravity and Centroid 29
Part Ⅱ．Kinematics 32
Chapter 9．Kinematics of a Point 32
§9-1 Types of Motion of a Point 32
§9-2 Rectilinear Motion of a Point 33
§9-3 Curvilinear Motion of a Point 36
§9-4 Tangential and Normal Components of Acceleration 39
§10-3 Rotation of a Rigid Body about a Fixed Axis 41
§10-2 Translation of a Rigid Body 41
§10-1 Types of Motion of Rigid Bodies 41
Chapter 10．Translation and Rotation 41
§10-4 Relations between Linear and Angular Velocities，Linear and Angular Accelera-tions in Rotation 43
Chapter 11．Relative Motion 44
§11-1 Introduction 44
§11-2 Relation between Relative and Absolute Velocities 45
§11-3 Relation between Relative and Absolute Accelerations 46
Chapter 12．Plane Motion 47
§12-1 Introduction 47
§12-2 Resolution of a Plane Motion 48
§12-3 Relation of Velocities in Plane Motion 49
§12-4 Instantaneous Center of Rotation 50
§12-5 Relation of Accelerations in Plane Motion 52
Chapter 13．Rotation of a Rigid Body about a Fixed Point 53
§13-1 Introduction 53
§13-2 The Eulerian Angles 54
§13-3 Angular Velocity and Angular Acceleration of a Rotating Body 55
Chapter 14．Principles of Kinetics 57
§14-1 Introduction 57
Part Ⅲ．Kinetics 57
§14-2 Newton's Laws 58
§14-3 Noninertial Reference System and Inertia Forces 61
Chapter 15．Differential Equations of Motion of a Particle 62
§15-1 Differential Equations of Motion of a Particle 62
§15-2 Motion of a Projectile 63
Chapter 16．Mechanical Vibrations 66
§16-1 Introduction 66
§16-2 Free Vibrations 68
§16-3 Free Vibrations with Viscous Damping 70
§16-4 Forced Vibrations 73
§16-5 Vibration Reduction 77
§17-1 Principle of Momentum of a Particle 79
Chapter 17．Principle of Momentum 79
§17-2 Principle of Momentum of a System of Particles 80
§17-3 Motion of the Mass Center of a System of Particles 81
Chapter 18．Principle of Moment of Momentum 83
§18-1 Principle of Moment of Momentum of a Particle 83
§18-2 Principle of Moment of Momentum of a System of Particles 85
§18-3 Equation of Motion for a Rigid Body 86
Rotating about a Fixed Axis 86
§18-4 Principle of Moment of Momentum of a System about Its Center of Mass 87
§18-5 Equations of Motion for a Rigid Body in Plane Motion 88
Chapter 19．Principle of Work and Energy 89
§19-1 Work Defined 89
§19-2 Force Field and Conservative Force 90
§19-3 Potential and Potential Energy 92
§19-4 Kinetic Energy 95
§19-6 Principle of Work and Energy for a System of Particles 98
§19-5 Principle of Work and Energy for a Particle 98
§19-7 Forces which Do No Work 99
§19-8 Law of Conservation of Mechanical Energy 101
Chapter 20．Moment of Inertia 103
§20-1 Definitions 103
§20-2 Parallel Axis Theorem 104
§20-3 Moment of Inertia about an Arbitrary Axis and Ellipsoid of Inertia 104
Chapter 21．Impact 109
§21-1 Introduction 109
§21-2 Direct Central Impact 111
§21-3 Center of Percussion 115
Chapter 22．D'Alembert's Principle 117
§22-1 D'A1embert's Principle and Inertia-Force Method 117
§22-2 Inertia Forces of a Rigid Body in Translation 118
§22-3 Inertia Forces of a Rigid Body in Centroidal Rotation 119
§22-4 Inertia Forces of a Rigid Body in Plane Motion 120
§22-5 Dynamical Pressures on the Bearings 121
Part Ⅳ．Elements of Analytical Mechanics 122
Chapter 23．Principle of Virtual Work 122
§23-1 Introduction 122
§23-2 Constraints and Degrees of Freedom 123
§23-3 Generalized Coordinates 126
§23-4 Virtual Displacements 128
§23-5 Virtual Work 129
§23-6 Principle of Virtual Work 131
§23-7 Equations of Equilibrium in Generalized Coordinates 133
§23-8 Stability of Equilibrium of Systems with One Degree of Freedom 137
Chapter 24．Lagrange's Equations 139
§24-1 Introduction 139
§24-2 Generalized Principle of D'Alembert 140
§24-3 Derivation of Lagrange's Equations 142
§24-4 Conservation Theorems 147