Engineering dynamics : a comprehensive introduction

This textbook introduces undergraduate students to engineering dynamics using an innovative approach that is at once accessible and comprehensive. Combining the strengths of both beginner and advanced dynamics texts, this book has students solving dynamics problems from the very start and gradually guides them from the basics to increasingly more challenging topics without ever sacrificing rigor. __Engineering Dynamics__ spans the full range of mechanics problems, from one-dimensional particle kinematics to three-dimensional rigid-body dynamics, including an introduction to Lagrange's and Kane's methods. It skillfully blends an easy-to-read, conversational style with careful attention to the physics and mathematics of engineering dynamics, and emphasizes the formal systematic notation students need to solve problems correctly and succeed in more advanced courses. This richly illustrated textbook features numerous real-world examples and problems, incorporating a wide range of difficulty; ample use of MATLAB for solving problems; helpful tutorials; suggestions for further reading; and detailed appendixes. * Provides an accessible yet rigorous introduction to engineering dynamics * Uses an explicit vector-based notation to facilitate understanding Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class\_use/solutions.html Cover 1 Title 4 Copyright 5 Contents 8 Preface 12 Chapter 1. Introduction 18 1.1 What Is Dynamics? 18 1.2 Organization of the Book 23 1.3 Key Ideas 25 1.4 Notes and Further Reading 26 1.5 Problems 27 Chapter 2. Newtonian Mechanics 28 2.1 Newton’s Laws 28 2.2 A Deeper Look at Newton’s Second Law 32 2.3 Building Models and the Free-Body Diagram 36 2.4 Constraints and Degrees of Freedom 38 2.5 A Discussion of Units 41 2.6 Tutorials 42 2.7 Key Ideas 54 2.8 Notes and Further Reading 55 2.9 Problems 55 PART ONE. PARTICLE DYNAMICS IN THE PLANE 60 Chapter 3. Planar Kinematics and Kinetics of a Particle 62 3.1 The Simple Pendulum 62 3.2 More on Vectors and Reference Frames 64 3.3 Velocity and Acceleration in the Inertial Frame 73 3.4 Inertial Velocity and Acceleration in a Rotating Frame 83 3.5 The Polar Frame and Fictional Forces 96 3.6 An Introduction to Relative Motion 100 3.7 How to Solve a Dynamics Problem 104 3.8 Derivations—Properties of the Vector Derivative 105 3.9 Tutorials 110 3.10 Key Ideas 117 3.11 Notes and Further Reading 118 3.12 Problems 119 Chapter 4. Linear and Angular Momentum of a Particle 130 4.1 Linear Momentum and Linear Impulse 130 4.2 Angular Momentum and Angular Impulse 134 4.3 Tutorials 148 4.4 Key Ideas 158 4.5 Notes and Further Reading 159 4.6 Problems 160 Chapter 5. Energy of a Particle 165 5.1 Work and Power 165 5.2 Total Work and Kinetic Energy 170 5.3 Work Due to an Impulse 175 5.4 Conservative Forces and Potential Energy 176 5.5 Total Energy 186 5.6 Derivations—Conservative Forces and Potential Energy 189 5.7 Tutorials 190 5.8 Key Ideas 196 5.9 Notes and Further Reading 197 5.10 Problems 198 PART TWO. PLANAR MOTION OF A MULTIPARTICLE SYSTEM 204 Chapter 6. Linear Momentum of a Multiparticle System 206 6.1 Linear Momentum of a System of Particles 206 6.2 Impacts and Collisions 222 6.3 Mass Flow 237 6.4 Tutorials 245 6.5 Key Ideas 252 6.6 Notes and Further Reading 254 6.7 Problems 254 Chapter 7. Angular Momentum and Energy of a Multiparticle System 262 7.1 Angular Momentum of a System of Particles 262 7.2 Angular Momentum Separation 269 7.3 Total Angular Momentum Relative to an Arbitrary Point 276 7.4 Work and Energy of a Multiparticle System 280 7.5 Tutorials 291 7.6 Key Ideas 302 7.7 Notes and Further Reading 304 7.8 Problems 305 PART THREE. RELATIVE MOTION AND RIGID-BODY DYNAMICS IN TWO DIMENSIONS 310 Chapter 8. Relative Motion in a Rotating Frame 312 8.1 Rotational Motion of a Planar Rigid Body 312 8.2 Relative Motion in a Rotating Frame 319 8.3 Planar Kinetics in a Rotating Frame 328 8.4 Tutorials 335 8.5 Key Ideas 345 8.6 Notes and Further Reading 346 8.7 Problems 347 Chapter 9. Dynamics of a Planar Rigid Body 354 9.1 A Rigid Body Is a Multiparticle System 354 9.2 Translation of the Center of Mass—Euler’s First Law 357 9.3 Rotation about the Center of Mass—Euler’s Second Law 360 9.4 Rotation about an Arbitrary Body Point 377 9.5 Work and Energy of a Rigid Body 385 9.6 A Collection of Rigid Bodies and Particles 393 9.7 Tutorials 402 9.8 Key Ideas 411 9.9 Notes and Further Reading 414 9.10 Problems 415 PART FOUR. DYNAMICS IN THREE DIMENSIONS 424 Chapter 10. Particle Kinematics and Kinetics in Three Dimensions 426 10.1 Two New Coordinate Systems 426 10.2 The Cylindrical and Spherical Reference Frames 430 10.3 Linear Momentum, Angular Momentum, and Energy 439 10.4 Relative Motion in Three Dimensions 443 10.5 Derivations—Euler’s Theorem and the Angular Velocity 462 10.6 Tutorials 467 10.7 Key Ideas 475 10.8 Notes and Further Reading 476 10.9 Problems 477 Chapter 11. Multiparticle and Rigid-Body Dynamics in Three Dimensions 482 11.1 Euler’s Laws in Three Dimensions 482 11.2 Three-Dimensional Rotational Equations of Motion of a Rigid Body 489 11.3 The Moment Transport Theorem and the Parallel Axis Theorem in Three Dimensions 512 11.4 Dynamics of Multibody Systems in Three Dimensions 519 11.5 Rotating the Moment of Inertia Tensor 521 11.6 Angular Impulse in Three Dimensions 526 11.7 Work and Energy of a Rigid Body in Three Dimensions 527 11.8 Tutorials 532 11.9 Key Ideas 540 11.10 Notes and Further Reading 543 11.11 Problems 544 PART FIVE. ADVANCED TOPICS 552 Chapter 12. Some Important Examples 554 12.1 An Introduction to Vibrations and Linear Systems 554 12.2 Linearization and the Linearized Dynamics of an Airplane 568 12.3 Impacts of Finite-Sized Particles 585 12.4 Key Ideas 595 12.5 Notes and Further Reading 596 Chapter 13. An Introduction to Analytical Mechanics 597 13.1 Generalized Coordinates 597 13.2 Degrees of Freedom and Constraints 600 13.3 Lagrange’s Method 606 13.4 Kane’s Method 623 13.5 Key Ideas 635 13.6 Notes and Further Reading 636 APPENDICES 638 Appendix A. A Brief Review of Calculus 640 A.1 Continuous Functions 640 A.2 Differentiation 641 A.3 Integration 643 A.4 Higher Derivatives and the Taylor Series 644 A.5 Multivariable Functions and the Gradient 646 A.6 The Directional Derivative 649 A.7 Differential Volumes and Multiple Integration 650 Appendix B. Vector Algebra and Useful Identities 652 B.1 The Vector 652 B.2 Vector Magnitude 654 B.3 Vector Components 654 B.4 Vector Multiplication 655 Appendix C. Differential Equations 662 C.1 What Is a Differential Equation? 662 C.2 Some Common ODEs and Their Solutions 664 C.3 First-Order Form 667 C.4 Numerical Integration of an Initial Value Problem 668 C.5 Using MATLAB to Solve ODEs 674 Appendix D. Moments of Inertia of Selected Bodies 677 Bibliography 680 Index 684 A 684 B 684 C 684 D 685 E 685 F 685 G 685 H 685 I 686 J 686 K 686 L 686 M 686 N 686 O 687 P 687 Q 687 R 687 S 688 T 688 U 688 V 688 W 689 Y 689 Z 689 An accessible yet rigorous introduction to engineering dynamicsThis textbook introduces undergraduate students to engineering dynamics using an innovative approach that is at once accessible and comprehensive. Combining the strengths of both beginner and advanced dynamics texts, this book has students solving dynamics problems from the very start and gradually guides them from the basics to increasingly more challenging topics without ever sacrificing rigor.Engineering Dynamics spans the full range of mechanics problems, from one-dimensional particle kinematics to three-dimensional rigid-body dynamics, including an introduction to Lagrange's and Kane's methods. It skillfully blends an easy-to-read, conversational style with careful attention to the physics and mathematics of engineering dynamics, and emphasizes the formal systematic notation students need to solve problems correctly and succeed in more advanced courses. This richly illustrated textbook features numerous real-world examples and problems, incorporating a wide range of difficulty; ample use of MATLAB for solving problems; helpful tutorials; suggestions for further reading; and detailed appendixes.Provides an accessible yet rigorous introduction to engineering dynamicsUses an explicit vector-based notation to facilitate understandingProfessors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: https://press.princeton.edu/class_use/solutions.html

This textbook introduces undergraduate students to engineering dynamics using an innovative approach that is at once accessible and comprehensive. Combining the strengths of both beginner and advanced dynamics texts, this book has students solving dynamics problems from the very start and gradually guides them from the basics to increasingly more challenging topics without ever sacrificing rigor.

Engineering Dynamics spans the full range of mechanics problems, from one-dimensional particle kinematics to three-dimensional rigid-body dynamics, including an introduction to Lagrange's and Kane's methods. It skillfully blends an easy-to-read, conversational style with careful attention to the physics and mathematics of engineering dynamics, and emphasizes the formal systematic notation students need to solve problems correctly and succeed in more advanced courses. This richly illustrated textbook features numerous real-world examples and problems, incorporating a wide range of difficulty; ample use of MATLAB for solving problems; helpful tutorials; suggestions for further reading; and detailed appendixes.

• Provides an accessible yet rigorous introduction to engineering dynamics
• Uses an explicit vector-based notation to facilitate understanding

Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

An accessible yet rigorous introduction to engineering dynamics This textbook introduces undergraduate students to engineering dynamics using an innovative approach that is at once accessible and comprehensive. Combining the strengths of both beginner and advanced dynamics texts, this book has students solving dynamics problems from the very start and gradually guides them from the basics to increasingly more challenging topics without ever sacrificing rigor. Engineering Dynamics spans the full range of mechanics problems, from one-dimensional particle kinematics to three-dimensional rigid-body dynamics, including an introduction to Lagrange's and Kane's methods. It skillfully blends an easy-to-read, conversational style with careful attention to the physics and mathematics of engineering dynamics, and emphasizes the formal systematic notation students need to solve problems correctly and succeed in more advanced courses. This richly illustrated textbook features numerous real-world examples and problems, incorporating a wide range of difficulty; ample use of MATLAB for solving problems; helpful tutorials; suggestions for further reading; and detailed appendixes. A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer Content: Introduction -- Newtonian mechanics -- Planar Kinematics and kinetics of a particle -- Linear and angular momentum of a particle -- Energy of a particle -- Linear momentum of a multiparticle system -- Angular momentum and energy of a multiparticle system -- Relative motion in a rotating frame -- Dynamics of a planar rigid body -- Particle kinematics and kinetics in there dimensions -- Multiparticle and rigid-body dynamics in three dimensions -- Some important examples -- An introduction to analytical mechanics -- Appendix A.A brief review of calculus -- Appendix B. Vector algebra and useful identities -- Appendix C. Differential equations -- Appendix D. Moments of intertia of selected bodies.