Engineering Mechanics: Dynamics, 1st Edition [Rental Edition]

Benson H. Tongue, Ph.D. is a Professor of Mechanical Engineering at University of California-Berkeley. He received his Ph.D. from Princeton University in 1988, and Currently teaches graduate and undergraduate courses in dynamics vibrations, and control theory. His research concentrates on the modeling and analysis of nonlinear dynamical systems and the control of both structural and acoustic systems. This work involves experimental, theoretical, and numerical analysis and has been directed toward helicopters, computer disk drives, robotic manipulators, and general structural systems. Most recently, he has been involved in a multidisciplinary stud of automated highways and has directed research aimed at understanding the nonlinear behavior of vehicles traveling in platoons and in devising controllers that optimize the platoon's behavior in the face of non-nominal operating conditions. His most recent research has involved in the active control of loudspeakers and biomechanical analysis of human fall dynamics.
Dr. Tongue is the author of Principles of Vibration, a senior/first-year graduate-level textbook. He has served as Associate Technical Editor of the ASME Journal of Vibration and Acoustics and is currently a member of the ASME Committee on Dynamics of Structures and Systems. He is the recipient of the NSF Presidential Young Investigator Award, the Sigma Xi Junior Faculty award, and the Pi Tau Sigma Excellence in Teaching award. He serves as a reviewer for numerous journals and funding agencies and is the author of more than sixty publications.

Daniel T. Kawano, is an Assistant Professor of Mechanical Engineering at Rose-Hulman Institute of Technology in Terre Haute, Indiana. He received his B.S. degree in Mechanical Engineering from California Polytechnic State University, San Luis Obispo in 2006. He obtained his M.S. (2008) and Ph.D. (2011) degrees in Mechanical Engineering, with a focus in dynamical systems, from the University of California, Berkeley. Daniel currently teaches primarily undergraduate courses in vibration, programming, dynamics, and system dynamics. His research and academic interests include modeling, analysis, simulation, and testing of dynamical systems; design of dynamic structures; linear vibratory theory and its applications; numerical solution of differential and differential-algebraic equations; and pedagogy in engineering education. Daniel serves as the faculty advisor for Rose-Hulman's Formula SAE competition team, Rose Grand Prix Engineering. In his spare time, Daniel enjoys reading, listening to music, shooting sports, and spending time outdoors.

Chapter 1 Background and Roadmap 1

1.1 Newton’s Laws 2

1.2 How You’ll Be Approaching Dynamics 3

1.3 Units 5

1.4 Symbols, Notation, and Conventions 7

1.5 Gravitation 13

1.6 A Comprehensive Dynamics Application 14

Chapter 2 Motion of Translating Bodies 17

2.1 Straight-Line Motion 18

Example 2.1 Velocity Determination Via Integration 25

Example 2.2 Deceleration Limit Determination 26

Example 2.3 Constant Acceleration/Speed/Distance Relationship 27

Example 2.4 Position-Dependent Acceleration 28

Example 2.5 Velocity-Dependent Acceleration (A) 30

Example 2.6 Velocity-Dependent Acceleration (B) 31

2.2 Cartesian Coordinates 32

Example 2.7 Coordinate Transformation (A) 38

Example 2.8 Coordinate Transformation (B) 39

Example 2.9 Rectilinear Trajectory Determination (A) 40

Example 2.10 Rectilinear Trajectory Determination (B) 43

2.3 Polar and Cylindrical Coordinates 44

Example 2.11 Velocity—Polar Coordinates 50

Example 2.12 Acceleration—Polar Coordinates (A) 52

Example 2.13 Acceleration—Polar Coordinates (B) 53

Example 2.14 Velocity and Acceleration—Cylindrical Coordinates 54

2.4 Path Coordinates 55

Example 2.15 Analytical Determination of Radius of Curvature 59

Example 2.16 Acceleration—Path Coordinates 60

Example 2.17 Speed Along a Curve 62

2.5 Relative Motion and Constraints 64

Example 2.18 One Body Moving on Another 71

Example 2.19 Two Bodies Moving Independently (A) 72

Example 2.20 Two Bodies Moving Independently (B) 73

Example 2.21 Simple Pulley 74

Example 2.22 Double Pulley 75

2.6 Just the Facts 77

Chapter 3 Inertial Response of Translating Bodies 81

3.1 Cartesian Coordinates 82

Example 3.1 Analysis of a Spaceship 84

Example 3.2 Forces Acting on an Airplane 85

Example 3.3 Sliding Ming Bowl 86

Example 3.4 Response of an Underwater Probe 88

Example 3.5 Particle in an Enclosure 90

3.2 Polar Coordinates 92

Example 3.6 Ming Bowl on a Moving Slope 92

Example 3.7 Ming Bowl in Motion 94

Example 3.8 Ming Bowl on a Moving Slope with Friction 95

Example 3.9 No-Slip in a Rotating Arm 98

Example 3.10 Forces Acting on a Payload 100

3.3 Path Coordinates 102

Example 3.11 Forces Acting on My Car 102

Example 3.12 Finding a Rocket’s Radius of Curvature 104

Example 3.13 Force and Acceleration for a Sliding Pebble 105

Example 3.14 Determining Slip Point in a Turn 107

3.4 Linear Momentum and Linear Impulse 108

Example 3.15 Changing the Space Shuttle’s Orbit 110

Example 3.16 Block on a Sanding Belt 112

Example 3.17 Two-Car Collision 113

3.5 Angular Momentum and Angular Impulse 114

Example 3.18 Change in Speed of a Model Plane 116

Example 3.19 Angular Momentum of a Bumper 117

Example 3.20 Angular Momentum of a Tetherball 119

3.6 Orbital Mechanics 121

Example 3.21 Analysis of an Elliptical Orbit 133

Example 3.22 Determining Closest Approach Distance 134

3.7 Impact 135

Example 3.23 Dynamics of Two Pool Balls 139

Example 3.24 More Pool Ball Dynamics 141

3.8 Oblique Impact 141

Example 3.25 Oblique Billiard Ball Collision 144

Example 3.26 Another Oblique Collision 146

3.9 Just The Facts 149

Chapter 4 Energetics of Translating Bodies 151

4.1 Kinetic Energy 152

Example 4.1 Speed of an Arrow 154

Example 4.2 Change in Speed Due to an Applied Force 155

Example 4.3 Change in Speed Due to Slipping 156

4.2 Potential Energy 157

Example 4.4 Speed Due to a Drop 161

Example 4.5 Designing a Nutcracker 163

Example 4.6 Change in Speed Using Potential Energy 164

Example 4.7 Falling Enclosure 166

Example 4.8 Reexamination of an Orbital Problem 167

4.3 Power 168

Example 4.9 Time Needed to Increase Speed 171

Example 4.10 0 to 60 Time at Constant Power 172

Example 4.11 Determining a Cyclist’s Energy Efficiency 173

4.4 Just the Facts 173

Chapter 5 Multibody Systems 177

5.1 Force Balance and Linear Momentum 178

Example 5.1 Finding a Mass Center 182

Example 5.2 Finding a System’s Linear Momentum 183

Example 5.3 Motion of a Two-Particle System 184

Example 5.4 Finding Speed of a Bicyclist/Cart 185

Example 5.5 Momentum of a Three-Mass System 186

5.2 Angular Momentum 187

Example 5.6 Angular Momentum of Three Particles 190

Example 5.7 Angular Momentum About a System’s Mass Center 191

5.3 Work and Energy 192

Example 5.8 Kinetic Energy of a Modified Baton 194

Example 5.9 Kinetic Energy of a Translating Modified 196

Example 5.10 Spring-Mass System 197

5.4 Stationary Enclosures with Mass Inflow and Outflow 198

Example 5.11 Water Jet Impinging on Stationary Vane 201

Example 5.12 Force Due to a Stream of Mass Particles 202

5.5 Nonconstant Mass Systems 203

Example 5.13 Motion of a Toy Rocket 207

Example 5.14 Helicopter Response to a Stream of Bullets 208

5.6 Just the Facts 209

Chapter 6 Kinematics of Rigid Bodies Undergoing Planar Motion 213

6.1 Relative Velocities on a Rigid Body 214

Example 6.1 Velocity of a Pendulum 220

Example 6.2 Velocity of a Constrained Link 221

Example 6.3 Angular Speed of a Spinning Disk 222

Example 6.4 Velocity of Link-Constrained Body 223

Example 6.5 Relative Angular Velocity 224

6.2 Instantaneous Center of Rotation (ICR) 226

Example 6.6 Angular Speed Determination Via ICR 227

Example 6.7 Velocity on a Constrained Body Via ICR 228

Example 6.8 Velocity of the Contact Point During Roll without Slip 229

Example 6.9 Pedaling Cadence and Bicycle Speed 230

Example 6.10 Rotation Rate of an Unwinding Reel Via ICR 232

6.3 Rotating Reference Frames and Rigid-Body Accelerations 234

Example 6.11 Acceleration of a Pedal Spindle 237

Example 6.12 Acceleration During Roll without Slip 238

Example 6.13 Tip Acceleration of a Two-Link Manipulator 239

Example 6.14 Acceleration of a Point on a Cog of a Moving Bicycle 241

Example 6.15 Path of Point on Rolling Disk 242

6.4 Relative Motion on a Rigid Body 244

Example 6.16 Absolute Velocity of a Specimen in a Centrifuge 247

Example 6.17 Velocity Constraints—Closing Scissors 248

Example 6.18 Velocity and Acceleration in a Tube 249

Example 6.19 Angular Acceleration of a Constrained Body 251

Example 6.20 Angular Acceleration 253

6.5 Just the Facts 254

Chapter 7 Kinetics of Rigid Bodies Undergoing Two-Dimensional Motions 257

7.1 Curvilinear Translation 258

Example 7.1 Determining the Acceleration of a Translating Body 259

Example 7.2 Tension in Support Chains 260

Example 7.3 General Motion of a Swinging Sign 263

Example 7.4 Normal Forces on a Steep Hill 266

7.2 Rotation About a Fixed Point 268

Example 7.5 Mass Moment of Inertia of a Rectangular Plate 272

Example 7.6 Mass Moment of Inertia of a Circular Sector 274

Example 7.7 Mass Moment of Inertia of a Complex Disk 277

Example 7.8 Analysis of a Rotating Body 278

Example 7.9 Forces Acting at Pivot of Fireworks Display 281

Example 7.10 Determining a Wheel’s Imbalance Eccentricity 284

7.3 General Motion 285

Example 7.11 Acceleration Response of an Unrestrained Body 288

Example 7.12 Response of a Falling Rod 292

Example 7.13 More Response of a Falling Rod 294

Example 7.14 Acceleration Response of a Driven Wheel 296

Example 7.15 Acceleration Response of a Driven Wheel—Take Two 298

Example 7.16 Falling Spool 301

Example 7.17 Tipping of a Ming Vase 302

Example 7.18 Equations of Motion for a Simple Car Model 305

Example 7.19 Analysis of a Simple Transmission 307

7.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies 309

Example 7.20 Angular Impulse Applied to Space Station 310

Example 7.21 Impact Between a Pivoted Rod and a Moving Particle 312

7.5 Work/Energy of Two-Dimensional Rigid Bodies 313

Example 7.22 Angular Speed of a Hinged Two- Dimensional Body 315

Example 7.23 Response of a Falling Rod Via Energy 316

Example 7.24 Design of a Spring-Controlled Drawbridge 318

7.6 Just The Facts 320

Chapter 8 Kinematics and Kinetics of Rigid Bodies in Three-dimensional Motion 323

8.1 Spherical Coordinates 324

8.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion 326

Example 8.1 Angular Velocity of a Simplified Gyroscope 330

Example 8.2 Angular Velocity of a Hinged Plate 331

8.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion 332

Example 8.3 Angular Acceleration of a Simple Gyroscope 333

8.4 General Motion of and on Three-Dimensional Bodies 333

Example 8.4 Motion of a Disk Attached to a Bent Shaft 335

Example 8.5 Velocity and Acceleration of a Robotic Manipulator 338

8.5 Moments and Products of Inertia for a Three-Dimensional Body 340

8.6 Parallel Axis Expressions for Inertias 343

Example 8.6 Inertial Properties of a Flat Plate 345

8.7 Angular Momentum 346

Example 8.7 Angular Momentum of a Flat Plate 351

Example 8.8 Angular Momentum of a Simple Structure 351

8.8 Equations of Motion for a Three-Dimensional Body 353

Example 8.9 Reaction Forces of a Constrained, Rotating Body 355

8.9 Energy of Three-Dimensional Bodies 357

Example 8.10 Kinetic Energy of a Rotating Disk 359

8.10 Just The Facts 361

Chapter 9 Vibratory Motions 365

9.1 Undamped, Free Response for Single-Degree-of-Freedom Systems 366

Example 9.1 Natural Frequency of a Cantilevered Balcony 369

Example 9.2 Displacement Response of a Single-Story Building 372

9.2 Undamped, Sinusoidally Forced Response for Single-Degree-of-Freedom Systems 373

Example 9.3 Forced Response of a Spring-Mass System 376

Example 9.4 Time Response of an Undamped System 377

9.3 Damped, Free Response for Single-Degree-of-Freedom Systems 378

Example 9.5 Vibration Response of a Golf Club 381

9.4 Damped, Sinusoidally Forced Response for Single-Degree-of-Freedom Systems 382

Example 9.6 Response of a Simple Car Model on a Wavy Road 385

Example 9.7 Response of a Sinusoidally Forced, Spring-Mass Damper 387

9.5 Just The Facts 388

Appendix A Numerical Integration Light 391

Appendix B Properties of Plane and Solid Bodies 399

Appendix C Some Useful Mathematical Facts 403

Appendix D Material Densities 407

Biblography 409

Index 411