《理论力学纳要 英文版》

CONTENTS1

Part Ⅰ．Statics1

Chapter 1．Fundamental Concepts and Principles of Statics1

§1-1 Rigid Body1

§1-2 Force2

§1-3 Principles of Statics3

§1-4 Free-Body Diagram4

§1-5 Types of Force Systems5

Chapter 2．Concurrent Forces6

§2-1 Composition of Concurrent Forces6

§2-2 Method of Projections7

§2-3 Equilibrium of Concurrent Forces8

§2-4 Equilibrium of Three Forces9

§3-2 Characteristics of a Couple10

§3-1 Definitions10

Chapter 3．Couples10

§3-3 Composition and Equilibrium of Couples12

Chapter 4．Moment of a Force12

§4-1 Moment of a Force with Respect toan Axis12

§4-2 Moment of a Force with Respect to a Point13

§4-3 Varignon's Theorem14

Chapter 5．General Case of Forces in a Plane15

§5-1 Resolution of a Given Force into a Force15

and a Couple15

§5-2 Reduction of a System of Coplanar Forces16

§5-3 Equilibrium of Coplanar Forces17

§5-4 Plane Truss19

Chapter 6．Friction21

§6-1 Friction Defined21

§6-2 Coefficient of Friction and Angle of Friction22

§6-3 Angle of Repose23

§6-4 Types of Problems Involving Frictional Forces24

Chapter 7．General Case of Forces in Space25

§7-1 Reduction of a System of Forces in Space25

§7-2 Equilibrium of Forces in Space27

Chapter 8．Center of Gravity28

§8-1 Center of Parallel Forces28

§8-2 Center of Gravity and Centroid29

Part Ⅱ．Kinematics32

Chapter 9．Kinematics of a Point32

§9-1 Types of Motion of a Point32

§9-2 Rectilinear Motion of a Point33

§9-3 Curvilinear Motion of a Point36

§9-4 Tangential and Normal Components of Acceleration39

§10-3 Rotation of a Rigid Body about a Fixed Axis41

§10-2 Translation of a Rigid Body41

§10-1 Types of Motion of Rigid Bodies41

Chapter 10．Translation and Rotation41

§10-4 Relations between Linear and Angular Velocities，Linear and Angular Accelera-tions in Rotation43

Chapter 11．Relative Motion44

§11-1 Introduction44

§11-2 Relation between Relative and Absolute Velocities45

§11-3 Relation between Relative and Absolute Accelerations46

Chapter 12．Plane Motion47

§12-1 Introduction47

§12-2 Resolution of a Plane Motion48

§12-3 Relation of Velocities in Plane Motion49

§12-4 Instantaneous Center of Rotation50

§12-5 Relation of Accelerations in Plane Motion52

Chapter 13．Rotation of a Rigid Body about a Fixed Point53

§13-1 Introduction53

§13-2 The Eulerian Angles54

§13-3 Angular Velocity and Angular Acceleration of a Rotating Body55

Chapter 14．Principles of Kinetics57

§14-1 Introduction57

Part Ⅲ．Kinetics57

§14-2 Newton's Laws58

§14-3 Noninertial Reference System and Inertia Forces61

Chapter 15．Differential Equations of Motion of a Particle62

§15-1 Differential Equations of Motion of a Particle62

§15-2 Motion of a Projectile63

Chapter 16．Mechanical Vibrations66

§16-1 Introduction66

§16-2 Free Vibrations68

§16-3 Free Vibrations with Viscous Damping70

§16-4 Forced Vibrations73

§16-5 Vibration Reduction77

§17-1 Principle of Momentum of a Particle79

Chapter 17．Principle of Momentum79

§17-2 Principle of Momentum of a System of Particles80

§17-3 Motion of the Mass Center of a System of Particles81

Chapter 18．Principle of Moment of Momentum83

§18-1 Principle of Moment of Momentum of a Particle83

§18-2 Principle of Moment of Momentum of a System of Particles85

§18-3 Equation of Motion for a Rigid Body86

Rotating about a Fixed Axis86

§18-4 Principle of Moment of Momentum of a System about Its Center of Mass87

§18-5 Equations of Motion for a Rigid Body in Plane Motion88

Chapter 19．Principle of Work and Energy89

§19-1 Work Defined89

§19-2 Force Field and Conservative Force90

§19-3 Potential and Potential Energy92

§19-4 Kinetic Energy95

§19-6 Principle of Work and Energy for a System of Particles98

§19-5 Principle of Work and Energy for a Particle98

§19-7 Forces which Do No Work99

§19-8 Law of Conservation of Mechanical Energy101

Chapter 20．Moment of Inertia103

§20-1 Definitions103

§20-2 Parallel Axis Theorem104

§20-3 Moment of Inertia about an Arbitrary Axis and Ellipsoid of Inertia104

Chapter 21．Impact109

§21-1 Introduction109

§21-2 Direct Central Impact111

§21-3 Center of Percussion115

Chapter 22．D'Alembert's Principle117

§22-1 D'A1embert's Principle and Inertia-Force Method117

§22-2 Inertia Forces of a Rigid Body in Translation118

§22-3 Inertia Forces of a Rigid Body in Centroidal Rotation119

§22-4 Inertia Forces of a Rigid Body in Plane Motion120

§22-5 Dynamical Pressures on the Bearings121

Part Ⅳ．Elements of Analytical Mechanics122

Chapter 23．Principle of Virtual Work122

§23-1 Introduction122

§23-2 Constraints and Degrees of Freedom123

§23-3 Generalized Coordinates126

§23-4 Virtual Displacements128

§23-5 Virtual Work129

§23-6 Principle of Virtual Work131

§23-7 Equations of Equilibrium in Generalized Coordinates133

§23-8 Stability of Equilibrium of Systems with One Degree of Freedom137

Chapter 24．Lagrange's Equations139

§24-1 Introduction139

§24-2 Generalized Principle of D'Alembert140

§24-3 Derivation of Lagrange's Equations142

§24-4 Conservation Theorems147