Part I Dynamics of Particles 1

1 Introduction to Dynamics 3

1/1 History and Modern Applications 3

1/2 Basic Concepts 4

1/3 Newton’s Laws 5

1/4 Units 6

1/5 Gravitation 7

1/6 Dimensions 10

1/7 Solving Problems in Dynamics 11

1/8 Chapter Review 13

2 Kinematics of Particles 16

2/1 Introduction 16

2/2 Rectilinear Motion 17

2/3 Plane Curvilinear Motion 25

2/4 Rectangular Coordinates (x-y) 27

2/5 Normal and Tangential Coordinates (n-t) 32

2/6 Polar Coordinates (r-𝜽) 37

2/7 Space Curvilinear Motion 42

2/8 Relative Motion (Translating Axes) 47

2/9 Constrained Motion of Connected Particles 51

2/10 Chapter Review 54

3 Kinetics of Particles 56

3/1 Introduction 56

Section A Force, Mass, and Acceleration 57

3/2 Newton’s Second Law 57

3/3 Equation of Motion and Solution of Problems 60

3/4 Rectilinear Motion 62

3/5 Curvilinear Motion 67

Section B Work and Energy 71

3/6 Work and Kinetic Energy 71

3/7 Potential Energy 81

Section C Impulse and Momentum 87

3/8 Introduction 87

3/9 Linear Impulse and Linear Momentum 87

3/10 Angular Impulse and Angular Momentum 93

Section D Special Applications 99

3/11 Introduction 99

3/12 Impact 99

3/13 Central-Force Motion 105

3/14 Relative Motion 112

3/15 Chapter Review 118

4 Kinetics of Systems of Particles 119

4/1 Introduction 119

4/2 Generalized Newton’s Second Law 120

4/3 Work-Energy 121

4/4 Impulse-Momentum 122

4/5 Conservation of Energy and Momentum 126

4/6 Steady Mass Flow 132

4/7 Variable Mass 138

4/8 Chapter Review 144

Part II Dynamics of Rigid Bodies 145

5 Plane Kinematics of Rigid Bodies 147

5/1 Introduction 147

5/2 Rotation 149

5/3 Absolute Motion 154

5/4 Relative Velocity 158

5/5 Instantaneous Center of Zero Velocity 165

5/6 Relative Acceleration 168

5/7 Motion Relative to Rotating Axes 173

5/8 Chapter Review 183

6 Plane Kinetics of Rigid Bodies 184

6/1 Introduction 184

Section A Force, Mass, and Acceleration 186

6/2 General Equations of Motion 186

6/3 Translation 192

6/4 Fixed-Axis Rotation 196

6/5 General Plane Motion 199

Section B Work and Energy 205

6/6 Work-Energy Relations 205

6/7 Acceleration from Work-Energy; Virtual Work 213

Section C Impulse and Momentum 217

6/8 Impulse-Momentum Equations 217

6/9 Chapter Review 225

7 Introduction to Three-Dimensional Dynamics of Rigid Bodies 226

7/1 Introduction 226

Section A Kinematics 227

7/2 Translation 227

7/3 Fixed-Axis Rotation 227

7/4 Parallel-Plane Motion 228

7/5 Rotation about a Fixed Point 228

7/6 General Motion 234

Section B Kinetics 240

7/7 Angular Momentum 240

7/8 Kinetic Energy 243

7/9 Momentum and Energy Equations of Motion 246

7/10 Parallel-Plane Motion 248

7/11 Gyroscopic Motion: Steady Precession 250

7/12 Chapter Review 259

8 Vibration and Time Response 260

8/1 Introduction 260

8/2 Free Vibration of Particles 261

8/3 Forced Vibration of Particles 270

8/4 Vibration of Rigid Bodies 278

8/5 Energy Methods 282

8/6 Chapter Review 286

Appendix A Area Moments of Inertia 287

Appendix B Mass Moments of Inertia 288

B/1 Mass Moments of Inertia about an Axis 288

B/2 Products of Inertia 296

Appendix C Selected Topics of Mathematics 302

C/1 Introduction 302

C/2 Plane Geometry 302

C/3 Solid Geometry 303

C/4 Algebra 303

C/5 Analytic Geometry 304

C/6 Trigonometry 304

C/7 Vector Operations 305

C/8 Series 308

C/9 Derivatives 308

C/10 Integrals 309

C/11 Newton’s Method for Solving Intractable Equations 312

C/12 Selected Techniques for Numerical Integration 314