## Table of contents for Vector mechanics for engineers. Statics and dynamics / Ferdinand P. Beer ... [et al.].

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```Contents
Preface xviii
Acknowledgments xxvi
List of Symbols xxix
INTRODUCTION 1
1.1 What Is Mechanics? 2
1.2 Fundamental Concepts and Principles 2
1.3 Systems of Units 5
1.4 Conversion from One System of Units to Another 10
1.5 Method of Problem Solution 11
1.6 Numerical Accuracy 13
STATICS OF PARTICLES 15
2.1 Introduction 16
Forces in a Plane 16
2.2 Force on a Particle---Resultant of Two Forces 16
2.3 Vectors 17
2.5 Resultant of Several Concurrent Forces 20
2.6 Resolution of a Force into Components 21
2.7 Rectangular Components of a Force. Unit Vectors 27
2.8 Addition of Forces by Summing x and y Components 30
2.9 Equilibrium of a Particle 35
2.10 Newton's First Law of Motion 36
2.11 Problems Involving the Equilibrium of a Particle----Free-Body Diagrams 36
Forces in Space 45
2.12 Rectangular Components of a Force in Space 45
2.13 Force Defined by Its Magnitude and Two Points on Its Line of Action 48
2.14 Addition of Concurrent Forces in Space 49
2.15 Equilibrium of a Particle in Space 57
Review and Summary for Chapter 2 64
Review Problems 67
Computer Problems 69
RIGID BODIES: EQUIVALENT SYSTEMS OF FORCES 73
3.1 Introduction 74
3.2 External and Internal Forces 74
3.3 Principle of Transmissibility. Equivalent Forces 75
3.4 Vector Product of Two Vectors 77
3.5 Vector Products Expressed in Terms of Rectangular Components 79
3.6 Moment of a Force about a Point 81
3.7 Varignon's Theorem 83
3.8 Rectangular Components of the Moment of a Force 83
3.9 Scalar Product of Two Vectors 93
3.10 Mixed Triple Product of Three Vectors 95
3.11 Moment of a Force about a Given Axis 97
3.12 Moment of a Couple 107
3.13 Equivalent Couples 108
3.15 Couples Can Be Represented by Vectors 110
3.16 Resolution of a Given Force Into a Force at One and a Couple 111
3.17 Reduction of a System of Forces to One Force and One Couple 122
3.18 Equivalent Systems of Forces 123
3.19 Equipollent Systems of Vectors 124
3.20 Further Reduction of a System of Forces 124
3.21 Reduction of a System of Forces to a Wrench 127
Review and Summary for Chapter 3 146
Review Problems 151
Computer Problems 153
EQUILIBRIUM OF RIGID BODIES 157
4.1 Introduction 158
4.2 Free-Body Diagram 159
Equilibrium in Two Dimensions 160
4.3 Reactions at Supports and Connections for a Two-Dimensional Structure 160
4.4 Equilibrium of a Rigid Body in Two Dimensions 162
4.5 Statically Indeterminate Reactions. Partial Constraints 164
4.6 Equilibrium of a Two-Force Body 183
4.7 Equilibrium of a Three-Force Body 184
Equilibrium in Three Dimensions 191
4.8 Equilibrium of a Rigid Body in Three Dimensions 191
4.9 Reactions at Supports and Connections for a Three-Dimensional Structure 191
Review and Summary for Chapter 4 211
Review Problems 213
Computer Problems 215
DISTRIBUTED FORCES: CENTROIDS AND CENTERS OF GRAVITY 219
5.1 Introduction 220
Areas and Lines 220
5.2 Center of Gravity of a Two-Dimensional Body 220
5.3 Centroids of Areas and Lines 222
5.4 First Moments of Areas and Lines 223
5.5 Composite Plates and Wires 226
5.6 Determination of Centroids by Integration 236
5.7 Theorems of Pappus-Guldinus 238
5.8 Distributed Loads on Beams 248
5.9 Forces on Submerged Surfaces 249
Volumes 259
5.10 Center of Gravity of a Three-Dimensional Body---Centroid of a Volume 259
5.11 Composite Bodies 262
5.12 Determination of Centroids of Volumes by Integration 262
Review and Summary for Chapter 5 274
Review Problems 278
Computer Problems 281
ANALYSIS OF STRUCTURES 284
6.1 Introduction 285
Trusses 286
6.2 Definition of a Truss 286
6.3 Simple Trusses 288
6.4 Analysis of Trusses by the Method of Joints 289
6.6 Space Trusses 293
6.7 Analysis of Trusses by the Method of Sections 303
6.8 Trusses Made of Several Simple Trusses 304
Frames and Machines 315
6.9 Structures Containing Multiforce Members 315
6.10 Analysis of a Frame 315
6.11 Frames Which Cease to Be Rigid When Detached from Their Supports 316
6.12 Machines 331
Review and Summary for Chapter 6 343
Review Problems 346
Computer Problems 349
FORCES IN BEAMS AND CABLES 353
7.1 Introduction 354
7.2 Internal Forces in Members 354
Beams 361
7.4 Shear and Bending Moment in a Beam 362
7.5 Shear and Bending-Moment Diagrams 364
7.6 Relations among Load, Shear, and Bending Moment 372
Cables 383
7.7 Cables with Concentrated Loads 383
7.8 Cables with Distributed Loads 384
7.9 Parabolic Cable 385
7.10 Catenary 394
Review and Summary for Chapter 7 402
Review Problems 405
Computer Problems 408
FRICTION 411
8.1 Introduction 412
8.2 The Laws of Dry Friction. Coefficients of Friction 412
8.3 Angles of Friction 415
8.4 Problems Involving Dry Friction 416
8.5 Wedges 431
8.7 Journal Bearings--Axle Friction 440
8.8 Thrust Bearings--Disk Friction 442
8.9 Wheel Friction--Rolling Resistance 443
8.10 Belt Friction 450
Review and Summary for Chapter 8 461
Review Problems 464
Computer Problems 467
DISTRIBUTED FORCES: MOMENTS OF INERTIA 471
9.1 Introduction 472
Moments of Inertia of Areas 473
9.2 Second Moment, or Moment of Inertia, of an Area 473
9.3 Determination of the Moment of Inertia of an Area by Integration 474
9.4 Polar Moment of Inertia 475
9.5 Radius of Gyration of an Area 476
9.6 Parallel-Axis Theorem 483
9.7 Moments of Inertia of Composite Areas 484
9.8 Product of Inertia 497
9.9 Principal Axes and Principal Moments of Inertia 498
9.10 Mohr's Circle for Moments and Products of Inertia 506
Moments of Inertia of Masses 512
9.11 Moment of Inertia of a Mass 512
9.12 Parallel-Axis Theorem 514
9.13 Moments of Inertia of Thin Plates 515
9.14 Determination of the Moment of Inertia of a Three-Dimensional
Body by Integration 516
9.15 Moments of Inertia of Composite Bodies 516
9.16 Moment of Inertia of a Body with Respect to an Arbitrary Axis through O--
Mass Products of Inertia 531
9.17 Ellipsoid of Inertia. Principal Axes of Inertia 532
9.18 Determination of the Principal Axes and Principal Moments of Inertia of a
Body of Arbitrary Shape 534
Review and Summary for Chapter 9 545
Review Problems 551
Computer Problems 554
METHOD OF VIRTUAL WORK 557
10.1 Introduction 558
10.2 Work of a Force 558
10.3 Principle of Virtual Work 561
10.4 Applications of the Principle of Virtual Work 562
10.5 Real Machines. Mechanical Efficiency 564
10.6 Work of a Force during a Finite Displacement 578
10.7 Potential Energy 580
10.8 Potential Energy and Equilibrium 581
*10.9 Stability of Equilibrium 582
Review and Summary for Chapter 10 592
Review Problems 595
Computer Problems 597
KINEMATICS OF PARTICLES 601
11.1 Introduction to Dynamics 602
Rectilinear Motion of Particles 603
11.2 Position, Velocity, and Acceleration 603
11.3 Determination of the Motion of a Particle 607
11.4 Uniform Rectilinear Motion 616
11.5 Uniformly Accelerated Rectilinear Motion 617
11.6 Motion of Several Particles 618
11.7 Graphical Solution of Rectilinear-Motion Problems 630
11.8 Other Graphical Methods 631
Curvilinear Motion of Particles 641
11.9 Position Vector, Velocity, and Acceleration 641
11.10 Derivatives of Vector Functions 643
11.11 Rectangular Components of Velocity and Acceleration 645
11.12 Motion Relative to a Frame in Translation 646
11.13 Tangential and Normal Components 663
11.14 Radial and Transverse Components 666
Review and Summary for Chapter 11 680
Review Problems 684
Computer Problems 687
KINETICS OF PARTICLES: NEWTON'S SECOND LAW 691
12.1 Introduction 692
12.2 Newton's Second Law of Motion 693
12.3 Linear Momentum of a Particle---Rate of Change of Linear Momentum 694
12.4 Systems of Units 695
12.5 Equations of Motion 697
12.6 Dynamic Equilibrium 699
12.7 Angular Momentum of a Particle---Rate of Change of Angular Momentum 718
12.8 Equations of Motion in Terms of Radial and Transverse Components 719
12.9 Motion under a Central Force--Conservation of Angular Momentum 720
12.10 Newton's Law of Gravitation 721
12.11 Trajectory of a Particle under a Central Force 731
12.12 Application to Space Mechanics 732
12.13 Kepler's Laws of Planetary Motion 735
Review and Summary for Chapter 12 744
Review Problems 748
Computer Problems 751
KINETICS OF PARTICLES: ENERGY AND MOMENTUM METHODS 755
13.1 Introduction 756
13.2 Work of a Force 756
13.3 Kinetic Energy of a Particle. Principle of Work and Energy 760
13.4 Applications of the Principle of Work and Energy 762
13.5 Power and Efficiency 763
13.6 Potential Energy 781
13.7 Conservative Forces 783
13.8 Conservation of Energy 784
13.9 Motion under a Conservative Central Force?Application to Space Mechanics
786
13.10 Principle of Impulse and Momentum 805
13.11 Impulsive Motion 808
13.12 Impact 820
13.13 Direct Central Impact 820
13.14 Oblique Central Impact 823
13.15 Problems Involving Energy and Momentum 826
Review and Summary for Chapter 13 842
Review Problems 848
Computer Problems 851
SYSTEMS OF PARTICLES 855
14.1 Introduction 856
14.2 Application of Newton's Laws to the Motion of a System of Particles--
Effective Forces 856
14.3 Linear and Angular Momentum of a System of Particles 859
14.4 Motion of the Mass Center of a System of Particles 860
14.5 Angular Momentum of a System of Particles about Its Mass Center 862
14.6 Conservation of Momentum for a System of Particles 864
14.7 Kinetic Energy of a System of Particles 873
14.8 Work-Energy Principle. Conservation of Energy for a System of Particles 875
14.9 Principle of Impulse and Momentum for a System of Particles 875
14.10 Variable Systems of Particles 886
14.11 Steady Stream of Particles 886
14.12 Systems Gaining or Losing Mass 889
Review and Summary for Chapter 14 904
Review Problems 908
Computer Problems 911
KINEMATICS OF RIGID BODIES 915
15.1 Introduction 916
15.2 Translation 918
15.3 Rotation about a Fixed Axis 919
15.4 Equations Defining the Rotation of a Rigid Body about a Fixed Axis 922
15.5 General Plane Motion 932
15.6 Absolute and Relative Velocity in Plane Motion 934
15.7 Instantaneous Center of Rotation in Plane Motion 945
15.8 Absolute and Relative Acceleration in Plane Motion 956
*15.9 Analysis of Plane Motion in Terms of a Parameter 958
15.10 Rate of Change of a Vector with Respect to a Rotating Frame 971
15.11 Plane Motion of a Particle Relative to a Rotating Frame?Coriolis
Acceleration 973
15.12 Motion about a Fixed Point 984
15.13 General Motion 987
15.14 Three-Dimensional Motion of a Particle Relative to a Rotating Frame--
Coriolis Acceleration 998
15.15 Frame of Reference in General Motion 999
Review and Summary for Chapter 15 1011
Review Problems 1018
Computer Problems 1021
PLANE MOTION OF RIGID BODIES: FORCES AND ACCELERATIONS 1025
16.1 Introduction 1026
16.2 Equations of Motion for a Rigid Body 1027
16.3 Angular Momentum of a Rigid Body in Plane Motion 1028
16.4 Plane Motion of a Rigid Body. d'Alembert's Principle 1029
16.5 A Remark on the Axioms of the Mechanics of Rigid Bodies 1030
16.6 Solution of Problems Involving the Motion of a Rigid Body 1031
16.7 Systems of Rigid Bodies 1032
16.8 Constrained Plane Motion 1051
Review and Summary for Chapter 16 1073
Review Problems 1075
Computer Problems 1078
PLANE MOTION OF RIGID BODIES: ENERGY AND MOMENTUM METHODS 1081
17.1 Introduction 1082
17.2 Principle of Work and Energy for a Rigid Body 1082
17.3 Work of Forces Acting on a Rigid Body 1083
17.4 Kinetic Energy of a Rigid Body in Plane Motion 1084
17.5 Systems of Rigid Bodies 1085
17.6 Conservation of Energy 1086
17.7 Power 1087
17.8 Principle of Impulse and Momentum for the Plane Motion of a Rigid Body 1104
17.9 Systems of Rigid Bodies 1107
17.10 Conservation of Angular Momentum 1107
17.11 Impulsive Motion 1120
17.12 Eccentric Impact 1120
Review and Summary for Chapter 17 1134
Review Problems 1138
Computer Problems 1141
KINETICS OF RIGID BODIES IN THREE DIMENSIONS 1145
18.1 Introduction 1146
18.2 Angular Momentum of a Rigid Body in Three Dimensions 1147
18.3 Application of the Principle of Impulse and Momentum to the
Three-Dimensional Motion of a Rigid Body 1151
18.4 Kinetic Energy of a Rigid Body in Three Dimensions 1152
18.5 Motion of a Rigid Body in Three Dimensions 1165
18.6 Euler's Equations of Motion. Extension of d'Alembert's Principle to the
Motion of a Rigid Body in Three Dimensions 1166
18.7 Motion of a Rigid Body about a Fixed Point 1167
18.8 Rotation of a Rigid Body about a Fixed Axis 1168
18.9 Motion of a Gyroscope--Eulerian Angles 1183
18.10 Steady Precession of a Gyroscope 1185
18.11 Motion of an Axisymmetrical Body under No Force 1186
Review and Summary for Chapter 18 1199
Review Problems 1204
Computer Problems 1208
MECHANICAL VIBRATIONS 1213
19.1 Introduction 1214
Vibrations without Damping 1214
19.2 Free Vibrations of Particles--Simple Harmonic Motion 1214
19.3 Simple Pendulum (Approximate Solution) 1218
19.4 Simple Pendulum (Exact Solution) 1219
19.5 Free Vibrations of Rigid Bodies 1228
19.6 Application of the Principle of Conservation of Energy 1240
19.7 Forced Vibrations 1251
Damped Vibrations 1261
19.8 Damped Free Vibrations 1261
19.9 Damped Forced Vibrations 1264
19.10 Electrical Analogues 1265
Review and Summary for Chapter 19 1277
Review Problems 1282
Computer Problems 1285
Appendix
FUNDAMENTALS OF ENGINEERING EXAMINATION 1289
Photo Credits 1291
Index 1293