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Third Edition

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Andrew Pytel The Pennsylvania State University

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7??e Pennsylvania State University

SI Edition prepared by Ishan Sharma Indian Institute of Technology, Kanpur

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Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

Contents

Preface to the SI Edition xi

Preface xiii

Chapter 11 Introduction to Dynamics 1 11.1 Introduction 1 11.2 Derivatives of Vector Functions 3 11.3 Position, Velocity, and Acceleration of a Particle 4 11.4 Newtonian Mechanics 5

Chapter 12 Dynamics of a Particle: Rectangular Coordinates 15

12.1 Introduction 15 12.2 Kinematics 16 12.3 Kinetics: Force-Mass-Acceleration Method 27 12.4 Dynamics of Rectilinear Motion 29 12.5 Curvilinear Motion 44

* 12.6 Analysis of Motion by the Area Method 56

Chapter 13 Dynamics of a Particle: Curvilinear Coordinates 69

13.1 Introduction 69 13.2 Kinematics—Path (Normal-Tangential) Coordinates 70 13.3 Kinematics—Polar and Cylindrical Coordinates 82 13.4 Kinetics: Force-Mass-Acceleration Method 95

Chapter 14 Work-Energy and Impulse-Momentum Principles for a Particle 117

14.1 Introduction 117 14.2 Work of a Force 118 14.3 Principle of Work and Kinetic Energy 122 14.4 Conservative Forces and the Conservation of Mechanical

Energy 133

* Indicates optional articles

VÜi Contents

14.5 Power and Efficiency 144 14.6 Principle of Impulse and Momentum 150 14.7 Principle of Angular Impulse and Momentum 158

* 14.8 Space Motion under a Gravitational Force 168

Chapter 15 Dynamics of Particle Systems 185 15.1 Introduction 185 15.2 Kinematics of Relative Motion 186 15.3 Kinematics of Constrained Motion 192 15.4 Kinetics: Force-Mass-Acceleration Method 198 15.5 Work-Energy Principles 214 15.6 Principle of Impulse and Momentum 217 15.7 Principle of Angular Impulse and Momentum 218 15.8 Plastic Impact 234 15.9 Impulsive Motion 236

15.10 Elastic Impact 248 *15.11 Mass Flow 257

Chapter 16 Planar Kinematics of Rigid Bodies 273 16.1 Introduction 273 16.2 Plane Angular Motion 275 16.3 Rotation about a Fixed Axis 278 16.4 Relative Motion of Two Points in a Rigid Body 287 16.5 Method of Relative Velocity 288 16.6 Instant Center for Velocities 301 16.7 Method of Relative Acceleration 312 16.8 Absolute and Relative Derivatives of Vectors 326 16.9 Motion Relative to a Rotating Reference Frame 329

*16.10 Method of Constraints 344

Chapter 17 Planar Kinetics of Rigid Bodies: Force-Mass-Acceleration Method 357

17.1 Introduction 357 17.2 Mass Moment of Inertia; Composite Bodies 358 17.3 Angular Momentum of a Rigid Body 368 17.4 Equations of Motion 371 17.5 Force-Mass-Acceleration Method: Plane Motion 373

*17.6 Differential Equations of Motion 398

Chapter 18 Planar Kinetics of Rigid Bodies: Work-Energy and Impulse-Momentum Methods 415

18.1 Introduction 415 Part A: Work-Energy Method 416 18.2 Work and Power of a Couple 416 18.3 Kinetic Energy of a Rigid В ody 418 18.4 Work-Energy Principle and Conservation of Mechanical

Energy 429

Part B: Impulse-Momentum Method 442 18.5 Momentum Diagrams 442 18.6 Impulse-Momentum Principles 444 18.7 Rigid-Body Impact 459

Chapter 19 Rigid-Body Dynamics in Three Dimensions 475

*19.1 Introduction 475 *19.2 Kinematics 476 *19.3 Impulse-Momentum Method 491 *19.4 Work-Energy Method 497 * 19.5 Force-Mass-Acceleration Method 511 *19.6 Motion of an Axisymmetric Body 527

Chapter 20 Vibrations 547 20.1 Introduction 547 20.2 Free Vibrations of Particles 548 20.3 Forced Vibrations of Particles 565 20.4 Rigid-Body Vibrations 578

*20.5 Methods Based on Conservation of Energy 587

Appendix D Proof of the Relative Velocity Equation for Rigid-Body Motion 599

Appendix E Numerical Solution of Differential Equations 601

E.l Introduction 601 E.2 Numerical Methods 601 E.3 Application of MATLAB 602 E.4 Linear Interpolation 605

Appendix F Mass Moments and Products of Inertia 607 F. 1 Introduction 607 F.2 Review of Mass Moment of Inertia 607 F.3 Moments of Inertia of Thin Plates 608 F.4 Mass Moment of Inertia by Integration 609 F.5 Mass Products of Inertia; Parallel-Axis Theorems 616 F.6 Products of Inertia by Integration; Thin Plates 617 F.7 Inertia Tensor; Moment of Inertia about an Arbitrary

Axis 618 F.8 Principal Moments and Principal Axes of Inertia 619

Answers to Even-Numbered Problems 633

Index 641