Engineering Dynamics

N. Jeremy Kasdin is professor of mechanical and aerospace engineering and lead investigator for the Terrestrial Planet Finder project at Princeton University. Derek A. Paley is assistant professor of aerospace engineering and director of the Collective Dynamics and Control Laboratory at the University of Maryland.

• Preface xi Chapter 1. Introduction 1 1.1 What Is Dynamics? 1 1.2 Organization of the Book 6 1.3 Key Ideas 8 1.4 Notes and Further Reading 9 1.5 Problems 10 Chapter 2. Newtonian Mechanics 11 2.1 Newton's Laws 11 2.2 A Deeper Look at Newton's Second Law 15 2.3 Building Models and the Free-Body Diagram 19 2.4 Constraints and Degrees of Freedom 21 2.5 A Discussion of Units 24 2.6 Tutorials 25 2.7 Key Ideas 37 2.8 Notes and Further Reading 38 2.9 Problems 38 PART ONE. PARTICLE DYNAMICS IN THE PLANE Chapter 3. Planar Kinematics and Kinetics of a Particle 45 3.1 The Simple Pendulum 45 3.2 More on Vectors and Reference Frames 47 3.3 Velocity and Acceleration in the Inertial Frame 56 3.4 Inertial Velocity and Acceleration in a Rotating Frame 66 3.5 The Polar Frame and Fictional Forces 79 3.6 An Introduction to Relative Motion 83 3.7 How to Solve a Dynamics Problem 87 3.8 Derivations--Properties of the Vector Derivative 88 3.9 Tutorials 93 3.10 Key Ideas 100 3.11 Notes and Further Reading 101 3.12 Problems 102 Chapter 4. Linear and Angular Momentum of a Particle 113 4.1 Linear Momentum and Linear Impulse 113 4.2 Angular Momentum and Angular Impulse 117 4.3 Tutorials 131 4.4 Key Ideas 141 4.5 Notes and Further Reading 142 4.6 Problems 143 Chapter 5. Energy of a Particle 148 5.1 Work and Power 148 5.2 Total Work and Kinetic Energy 153 5.3 Work Due to an Impulse 158 5.4 Conservative Forces and Potential Energy 159 5.5 Total Energy 169 5.6 Derivations--Conservative Forces and Potential Energy 172 5.7 Tutorials 173 5.8 Key Ideas 179 5.9 Notes and Further Reading 180 5.10 Problems 181 PART TWO. PLANAR MOTION OF A MULTIPARTICLE SYSTEM Chapter 6. Linear Momentum of a Multiparticle System 189 6.1 Linear Momentum of a System of Particles 189 6.2 Impacts and Collisions 205 6.3 Mass Flow 220 6.4 Tutorials 228 6.5 Key Ideas 235 6.6 Notes and Further Reading 237 6.7 Problems 237 Chapter 7. Angular Momentum and Energy of a Multiparticle System 245 7.1 Angular Momentum of a System of Particles 245 7.2 Angular Momentum Separation 252 7.3 Total Angular Momentum Relative to an Arbitrary Point 259 7.4 Work and Energy of a Multiparticle System 263 7.5 Tutorials 274 7.6 Key Ideas 285 7.7 Notes and Further Reading 287 7.8 Problems 288 PART THREE. RELATIVE MOTION AND RIGID-BODY DYNAMICS IN TWO DIMENSIONS Chapter 8. Relative Motion in a Rotating Frame 295 8.1 Rotational Motion of a Planar Rigid Body 295 8.2 Relative Motion in a Rotating Frame 302 8.3 Planar Kinetics in a Rotating Frame 311 8.4 Tutorials 318 8.5 Key Ideas 328 8.6 Notes and Further Reading 329 8.7 Problems 330 Chapter 9. Dynamics of a Planar Rigid Body 337 9.1 A Rigid Body Is a Multiparticle System 337 9.2 Translation of the Center of Mass--Euler's First Law 340 9.3 Rotation about the Center of Mass-- Euler's Second Law 343 9.4 Rotation about an Arbitrary Body Point 360 9.5 Work and Energy of a Rigid Body 368 9.6 A Collection of Rigid Bodies and Particles 376 9.7 Tutorials 385 9.8 Key Ideas 394 9.9 Notes and Further Reading 397 9.10 Problems 398 PART FOUR. DYNAMICS IN THREE DIMENSIONS Chapter 10. Particle Kinematics and Kinetics in Three Dimensions 409 10.1 Two New Coordinate Systems 409 10.2 The Cylindrical and Spherical Reference Frames 413 10.3 Linear Momentum, Angular Momentum, and Energy 422 10.4 Relative Motion in Three Dimensions 426 10.5 Derivations--Euler's Theorem and the Angular Velocity 445 10.6 Tutorials 450 10.7 Key Ideas 458 10.8 Notes and Further Reading 459 10.9 Problems 460 Chapter 11. Multiparticle and Rigid-Body Dynamics in Three Dimensions 465 11.1 Euler's Laws in Three Dimensions 465 11.2 Three-Dimensional Rotational Equations of Motion of a Rigid Body 472 11.3 The Moment Transport Theorem and the Parallel Axis Theorem in Three Dimensions 495 11.4 Dynamics of Multibody Systems in Three Dimensions 502 11.5 Rotating the Moment of Inertia Tensor 504 11.6 Angular Impulse in Three Dimensions 509 11.7 Work and Energy of a Rigid Body in Three Dimensions 510 11.8 Tutorials 515 11.9 Key Ideas 523 11.10 Notes and Further Reading 526 11.11 Problems 527 PART FIVE. ADVANCED TOPICS Chapter 12. Some Important Examples 537 12.1 An Introduction to Vibrations and Linear Systems 537 12.2 Linearization and the Linearized Dynamics of an Airplane 551 12.3 Impacts of Finite-Sized Particles 568 12.4 Key Ideas 578 12.5 Notes and Further Reading 579 Chapter 13. An Introduction to Analytical Mechanics 580 13.1 Generalized Coordinates 580 13.2 Degrees of Freedom and Constraints 583 13.3 Lagrange's Method 589 13.4 Kane's Method 605 13.5 Key Ideas 618 13.6 Notes and Further Reading 619 APPENDICES Appendix A. A Brief Review of Calculus 623 A.1 Continuous Functions 623 A.2 Differentiation 624 A.3 Integration 626 A.4 Higher Derivatives and the Taylor Series 627 A.5 Multivariable Functions and the Gradient 629 A.6 The Directional Derivative 632 A.7 Differential Volumes and Multiple Integration 633 Appendix B. Vector Algebra and Useful Identities 635 B.1 The Vector 635 B.2 Vector Magnitude 637 B.3 Vector Components 637 B.4 Vector Multiplication 638 Appendix C. Differential Equations 645 C.1 What Is a Differential Equation? 645 C.2 Some Common ODEs and Their Solutions 647 C.3 First-Order Form 650 C.4 Numerical Integration of an Initial Value Problem 651 C.5 Using matlab to Solve ODEs 657 Appendix D. Moments of Inertia of Selected Bodies 660 Bibliography 663 Index 667

"Engineering Dynamics: A Comprehensive Introduction targets students who are taking an introductory course in dynamics. The authors' stated intent is to provide a clear, rigorous, and complete view of the fundamentals of Newtonian dynamics, emphasizing a deep understanding of the concepts and the mathematics behind them. The result is a book that covers ample topics of engineering dynamics in a structured, detailed, and systematic manner... [The] appendices provide a quick and easy way to review the main concepts and mathematical tools used in solving dynamics problems... Adding to the nice reading, the notation used throughout the book is clearly described. It is consistent and easy to understand; it also promotes a clear identification of the system of reference used... Kasdin and Paley provide a sound mathematical approach in a modern and systematic manner. Engineering Dynamics is an outstanding book that presents an invigorating perspective on one of the most important topics in engineering, proving that, although 'dynamics is difficult,' it is nevertheless extremely important, and, with the right support, one can see that it is also beautiful."--Corina Sandu, Journal of Guidance, Control, and Dynamics