Über die Autorin bzw. den Autor

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.

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"There are few courses in the engineering curriculum that cause students more difficulty than rigid-body dynamics. By laying out the foundations of the subject with precision and clarity through unambiguous notation and rigorous definitions, Engineering Dynamics goes a long way toward remedying this situation. Numerous examples with motivating applications demonstrate the underlying ideas and solution techniques. This landmark text stands apart in the field, and will be welcomed by students and instructors alike."--Dennis S. Bernstein, University of Michigan

"Kasdin and Paley provide a thorough and rigorous introduction to engineering dynamics. They hit all the required topics, and also present material not normally addressed by an introductory text. This is an ambitious book and the authors carry it out well. It is in many ways better than almost all other comparable texts."--Geoffrey Shiflett, University of Southern California

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"There are few courses in the engineering curriculum that cause students more difficulty than rigid-body dynamics. By laying out the foundations of the subject with precision and clarity through unambiguous notation and rigorous definitions, Engineering Dynamics goes a long way toward remedying this situation. Numerous examples with motivating applications demonstrate the underlying ideas and solution techniques. This landmark text stands apart in the field, and will be welcomed by students and instructors alike."--Dennis S. Bernstein, University of Michigan

"Kasdin and Paley provide a thorough and rigorous introduction to engineering dynamics. They hit all the required topics, and also present material not normally addressed by an introductory text. This is an ambitious book and the authors carry it out well. It is in many ways better than almost all other comparable texts."--Geoffrey Shiflett, University of Southern California

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ENGINEERING DYNAMICS

PRINCETON UNIVERSITY PRESS

Contents

Preface...................................................................................xiChapter 1. Introduction...................................................................1Chapter 2. Newtonian Mechanics............................................................11Chapter 3. Planar Kinematics and Kinetics of a Particle...................................45Chapter 4. Linear and Angular Momentum of a Particle......................................113Chapter 5. Energy of a Particle...........................................................148Chapter 6. Linear Momentum of a Multiparticle System......................................189Chapter 7. Angular Momentum and Energy of a Multiparticle System..........................245Chapter 8. Relative Motion in a Rotating Frame............................................295Chapter 9. Dynamics of a Planar Rigid Body................................................337Chapter 10. Particle Kinematics and Kinetics in Three Dimensions..........................409Chapter 11. Multiparticle and Rigid-Body Dynamics in Three Dimensions.....................465Chapter 12. Some Important Examples.......................................................537Chapter 13. An Introduction to Analytical Mechanics.......................................580Appendix A. A Brief Review of Calculus....................................................623Appendix B. Vector Algebra and Useful Identities..........................................635Appendix C. Differential Equations........................................................645Appendix D. Moments of Inertia of Selected Bodies.........................................660Bibliography..............................................................................663Index.....................................................................................667

Chapter One

1.1 What Is Dynamics?

Dynamics is the science that describes the motion of bodies. Also called mechanics (we use the terms interchangeably throughout the book), its development was the first great success of modern physics. Much notation has changed, and physics has grown more sophisticated, but we still use the same fundamental ideas that Isaac Newton developed more than 300 years ago (using the formulation provided by Leonhard Euler and Joseph Louis Lagrange). The basic mathematical formulation and physical principles have stood the test of time and are indispensable tools of the practicing engineer.

Let's be more precise in our definition. Dynamics is the discipline that determines the position and velocity of an object under the action of forces. Specifically, it is about finding a set of differential equations that can be solved (either exactly or numerically on a computer) to determine the trajectory of a body.

In only the second paragraph of the book we have already introduced a great number of terms that require careful, mathematical definitions to proceed with the physics and eventually solve problems (and, perhaps, understand our admittedly very qualitative definition): position, velocity, orientation, force, object, body, differential equation, and trajectory. Although you may have an intuitive idea of what some of these terms represent, all have rigorous meanings in the context of dynamics. This rigor—and careful notation—is an essential part of the way we approach the subject of dynamics in this book. If you find some of the notation to be rather burdensome and superfluous early on, trust us! By the time you reach Part Two, you will find it indispensable.

We begin in this chapter and the next by providing qualitative definitions of the important concepts that introduce you to our notation, using only relatively simple ideas from geometry and calculus. In Chapter 3, we are much more careful and present the precise mathematical definitions as well as the full vector formulation of dynamics.

1.1.1 Vectors

We live in a three-dimensional Euclidean universe; we can completely locate the position of a point P relative to a reference point O in space by its relative distance in three perpendicular directions. (In Part One we talk about points rather than extended bodies and, consequently, don't have to keep track of the orientation of a body, as is necessary when discussing rigid bodies in Parts Three and Four.) We often call the reference point O the origin. An abstract quantity, the vector, is defined to represent the position of P relative to O, both in distance and direction.

Qualitative Definition 1.1 A vector is a geometric entity that has both magnitude and direction in space.

A position vector is denoted by a boldface, roman-type letter with subscripts that indicate its head and tail. For example, the position r_P/O of point P relative to the origin O is a vector (Figure 1.1). An important geometric property of vectors is that they can be added to get a new vector, called the resultant vector. Figure 1.1b illustrates how two vectors are added to obtain a new vector of different magnitude and direction by placing the summed vectors "head to tail."

When the position of point P changes with time, the position at time t is denoted by r_P/O(t). In this case, the velocity of point P with respect to O is also a vector. However, to define the velocity correctly, we need to introduce the concept of a reference frame.

1.1.2 Reference Frames, Coordinates, and Velocity

We have all heard about reference frames since high school, and you may already have an idea of what one is. For example, on a moving train, objects that are stationary on the train—and thus with respect to a reference frame fixed to the train—move with respect to a reference frame fixed to the ground (as in Figure 1.2). To successfully use dynamics, such an intuitive understanding is essential. Later chapters discuss how reference frames fit into the physics and how to use them mathematically; for that reason, we revisit the topic again in Chapter 3. For now, we summarize our intuition in the following qualitative definition of a reference frame.

Qualitative Definition 1.2 A reference frame is a point of view from which observations and measurements are made regarding the motion of a system.

It is impossible to overemphasize the importance of this concept. Solving a problem in dynamics always starts with defining the necessary reference frames.

From basic geometry, you may be used to seeing a reference frame written as three perpendicular axes meeting at an origin O, as illustrated in Figure 1.3. This representation is standard, as it highlights the three orthogonal Euclidean directions. However, this recollection should not be confused with a coordinate system. The reference frame and the coordinate system are not the same concept, but rather complement one another. It is necessary to introduce the reference frame to define a coordinate system, which we do next.

Definition 1.3 A coordinate system is the set of scalars that locate the position of a point relative to another point in a reference frame.

In our three-dimensional Euclidean...