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What's the Origin of the First Edition of Dynamics?...
This book has been developed from the author's lecture notes used in presenting dynamics courses at the University of Southern California. The material presented is appropriate for a one-term undergraduate course aimed at adding the power of vector calculus to students' skills in solving problems of mechanics based on Newton's Second Law of Motion. Successful study of this material requires an understanding of basic calculus and elementary mechanics. Many introductory dynamics texts have been written during the past five decades, and most have a common denominator of minimal mathematical complexity, which is done primarily to emphasize the physics of dynamics without losing the student in the equations. This text is no exception on that count.
An Antidote for Modern Dynamics Textbooks...
One of the primary differences between this book and virtually all modern dynamics books is the style in which problems are presented and solved. All examples and problems are cast in terms of algebraic quantities. This stands in distinct contrast to common practice of going straight to a calculator and bypassing the logical development of an answer in a form that can be checked for dimensional consistency, and that might be used in a design study and/or incorporated in a computer program.
A second key difference is a unified treatment both of rigid-body kinematics and of rigid-body kinetics. Many of the current dynamics books treat rigid-body kinematics in a disjointed manner, first focusing on two-dimensional motion before turning to three dimensions. No such artificial separation has been made in this book. Virtually all modern dynamics books include separate chapters on two-dimensional and three-dimensional rigid-body kinetics, which obscures the connection between angular momentum and the inertia tensor. In a single chapter on kinetics, this manuscript first develops the full inertia tensor, and then demonstrates how it simplifies in the limiting case of two-dimensional motion.
The primary goal of this book is to provide a rigorous and understandable introduction to the fascinating field of dynamics with a classical point of view. While maintaining a commitment to mathematical rigor throughout, the text continually emphasizes the underlying physics, i.e., Newton's Second Law of Motion. Mathematical results are repeatedly reinforced and verified by appealing to physical arguments. To avoid making derivations for simplified (non-general) geometries, the text makes extensive use of basic vector calculus. The text accommodates the reader who needs a review of vector calculus by providing all that is needed to follow the text in Section 1.5.
To assist the reader in developing the ability to apply the concepts, many of the most complex homework problems at the end of each chapter have multiple parts that lead the reader through a logical sequence of steps to develop the solution. In this sense, some of the homework problems can be viewed as pseudo-examples. Numerous homework problems require only an algebraic result. More often than not, the answers are even rigged to involve only rational numbers to help simplify the algebra. This is a reflection of a desire to stress the importance of understanding the physics, rather than improving the student's ability to use a calculator. It also permits emphasizing the importance of good engineering practices such as checking mathematical results for dimensional consistency and examining limiting cases for which properties of the solution are evident. Of course, some feel for the magnitudes of quantities of interest in practical dynamics applications is needed, and problems have been included throughout the text that require a numerical answer.
What's in Dynamics?...
The book has undergone extensive review by peers and students. Review copies are available on request for universities interested in considering the book for adoption. The book has 9 chapters as follows (Click here to view the Table of Contents).):
- Introduction: Historical overview of how the field evolved; dimensions and units; review of vectors; cylindrical coordinates; conic sections.
- Particle Kinematics: Rectilinear and dependent motion; motion relative to a translating frame; curvilinear motion.
- Force and Acceleration: Inertial and noninertial frames; Newton's Second Law of Motion; typical forces in dynamics applications; linear and angular momentum; central forces, Newton's Law of Universal Gravitation; space mechanics.
- Work and Energy: Principle of Work and Energy; work, power, efficiency and potential energy; conservation of energy; space mechanics rtevisited.
- Impulse and Momentum: Principle of Impulse and Momentum; impulsive motion; direct and oblique central impacts; constrained motion.
- Systems of Particles: Internal and external forces; center of mass; linear and angular momentum; Principles of Work and Energy and of Impulse and Momentum for a finite system; fluid mechanics.
- Rigid-Body Kinematics: Pure translation; pure rotation about a fixed axis; general plane motion and Chaslee's Theorem; motion about a fixed point and the Coriolis Theorem.
- Rigid-Body Kinetics: Center of mass; angular-momentum and the inertia tensor; two-dimensional rigid-body motion; three-dimensional rigid-body motion; Principles of Work and Energy and of Impulse and Momentum for a rigid body.
- Mechanical Vibrations: Undamped free vibrations; undamped forced vibrations; damped free vibrations; damped forced vibrations; electrical analogues and dynamic similitude.
The companion CD includes a 71-page study guide. It is entirely typeset in LaTex and has been carefully proofread to insure accuracy. The study guide contains worked examples based on exam problems used by Dr. Wilcox. The solutions are presented with complete details that augment the worked examples in the text. The study guide is sufficiently comprehensive to be used by students in preparing for exams.
Solution Manual and Lecture Notes: The 830-page solution manual is provided on a CD for professors who adopt the book for course use. It is entirely typeset in LaTex and has been carefully proofread to insure accuracy. Some of the solutions are 3 or more pages long and have been prepared by Dr. Wilcox with enough detail that they can serve as an additional teaching aid.
The CD also includes a complete set of Dr. Wilcox's lecture notes that have been developed at USC over the past decade. They have been prepared as a Power Point Presentation. There are 338 slides that address all major topics covered in the text. They should be especially helpful to a professor who is teaching the course for the first time who needs to develop a set of lecture notes. The CD includes the Power Point source files so that they can be modified for personal taste and need. The veteran teacher with an established set of lecture notes can make use of some of the figures, graphs and tables to further enhance his or her existing presentation.