Vector Mechanics for Engineers : Dynamics

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Preface

Acknowledgments

List of Symbols

**Chapter 11 Kinematics of Particles**

**11.1** Introduction to Dynamics Rectilinear Motion of
Particles

**11.2** Position, Velocity, and Acceleration

**11.3** Determination of the Motion of a Particle

**11.4** Uniform Rectilinear Motion

**11.5** Uniformly Accelerated Rectilinear Motion

**11.6** Motion of Several Particles

***11.7** Graphical Solution of Rectilinear-Motion Problems

***11.8** Other Graphical Methods Curvilinear Motion of
Particles

**11.9** Position Vector, Velocity, and Acceleration

**11.10** Derivatives of Vector Functions

**11.11** Rectangular Components of Velocity and
Acceleration

**11.12** Motion Relative to a Frame in Translation

**11.13** Tangential and Normal Components

**11.14** Radial and Transverse Components

Review and Summary

Review Problems

Computer Problems

**Chapter 12 Kinetics of Particles: Newton’s Second Law**

**12.1** Introduction

**12.2** Newton’s Second Law of Motion

**12.3** Linear Momentum of a Particle. Rate of Change of Linear
Momentum

**12.4** Systems of Units

**12.5** Equations of Motion

**12.6** Dynamic Equilibrium

**12.7** Angular Momentum of a Particle. Rate of Change of
Angular Momentum

**12.8** Equations of Motion in Terms of Radial and Transverse
Components

**12.9** Motion under a Central Force. Conservation of Angular
Momentum

**12.10** Newton’s Law of Gravitation

***12.11** Trajectory of a Particle under a Central Force

***12.12** Application to Space Mechanics

***12.13** Kepler’s Laws of Planetary Motion

Review and Summary

Review Problems

Computer Problems

**Chapter 13 Kinetics of Particles: Energy and Momentum
Methods**

**13.1** Introduction

**13.2** Work of a Force

**13.3** Kinetic Energy of a Particle. Principle of Work and
Energy

**13.4** Applications of the Principle of Work and Energy

**13.5** Power and Efficiency

**13.6** Potential Energy

***13.7** Conservative Forces

**13.8** Conservation of Energy

**13.9** Motion under a Conservative Central Force. Application
to Space Mechanics

**13.10** Principle of Impulse and Momentum 806

**13.11** Impulsive Motion

**13.12** Impact

**13.13** Direct Central Impact

**13.14** Oblique Central Impact

**13.15** Problems Involving Energy and Momentum

Review and Summary

Review Problems

Computer Problems 852

**Chapter 14 Systems of Particles** **14.1**
Introduction

**14.2** Application of Newton’s Laws to the Motion of a System
of Particles. Effective Forces

**14.3** Linear and Angular Momentum of a System of
Particles

**14.4** Motion of the Mass Center of a System of Particles

**14.5** Angular Momentum of a System of Particles about Its
Mass Center

**14.6** Conservation of Momentum for a System of Particles

**14.7** Kinetic Energy of a System of Particles

**14.8** Work-Energy Principle. Conservation of Energy for a
System of Particles

**14.9** Principle of Impulse and Momentum for a System of
Particles

***14.10** Variable Systems of Particles

***14.11** Steady Stream of Particles

***14.12** Systems Gaining or Losing Mass

Review and Summary

Review Problems

Computer Problems

**Chapter 15 Kinematics of Rigid Bodies**

**15.1** Introduction

**15.2** Translation

**15.3** Rotation about a Fixed Axis

**15.4** Equations Defining the Rotation of a Rigid Body about a
Fixed Axis

**15.5** General Plane Motion

**15.6** Absolute and Relative Velocity in Plane Motion

**15.7** Instantaneous Center of Rotation in Plane Motion

**15.8** Absolute and Relative Acceleration in Plane Motion

***15.9** Analysis of Plane Motion in Terms of a Parameter

**15.10** Rate of Change of a Vector with Respect to a Rotating
Frame

**15.11** Plane Motion of a Particle Relative to a Rotating
Frame. Coriolis Acceleration

***15.12** Motion about a Fixed Point 984

***15.13** General Motion 987

***15.14** Three-Dimensional Motion of a Particle Relative to a
Rotating Frame. Coriolis Acceleration

***15.15** Frame of Reference in General Motion

Review and Summary

Review Problems

Computer Problems

**Chapter 16 Plane Motion of Rigid Bodies: Forces and
Accelerations**

**16.1** Introduction

**16.2** Equations of Motion for a Rigid Body

**16.3** Angular Momentum of a Rigid Body in Plane Motion

**16.4** Plane Motion of a Rigid Body. D’Alembert’s
Principle

***16.5** A Remark on the Axioms of the Mechanics of Rigid
Bodies

**16.6** Solution of Problems Involving the Motion of a Rigid
Body

**16.7** Systems of Rigid Bodies

**16.8** Constrained Plane Motion

Review and Summary

Review Problems

Computer Problems 1079

**Chapter 17 Plane Motion of Rigid Bodies: Energy and Momentum
Methods**

**17.1** Introduction

**17.2** Principle of Work and Energy for a Rigid Body

**17.3** Work of Forces Acting on a Rigid Body

**17.4** Kinetic Energy of a Rigid Body in Plane Motion

**17.5** Systems of Rigid Bodies

**17.6** Conservation of Energy

**17.7** Power

**17.8** Principle of Impulse and Momentum for the Plane Motion
of a Rigid Body

**17.9** Systems of Rigid Bodies

**17.10** Conservation of Angular Momentum

**17.11** Impulsive Motion

**17.12** Eccentric Impact

Review and Summary

Review Problems

Computer Problems

**Chapter 18 Kinetics of Rigid Bodies in Three
Dimensions**

***18.1** Introduction

***18.2** Angular Momentum of a Rigid Body in Three
Dimensions

***18.3** Application of the Principle of Impulse and Momentum
to the Three-Dimensional Motion of a Rigid Body

***18.4** Kinetic Energy of a Rigid Body in Three Dimensions

***18.5** Motion of a Rigid Body in Three Dimensions

***18.6** Euler’s Equations of Motion. Extension of D’Alembert’s
Principle to the Motion of a Rigid Body in Three Dimensions

***18.7** Motion of a Rigid Body about a Fixed Point

***18.8** Rotation of a Rigid Body about a Fixed Axis

***18.9** Motion of a Gyroscope. Eulerian Angles

***18.10** Steady Precession of a Gyroscope

***18.11** Motion of an Axisymmetrical Body under No Force

Review and Summary

Review Problems

Computer Problems

**Chapter 19 Mechanical Vibrations**

**19.1** Introduction Vibrations without Damping

**19.2** Free Vibrations of Particles. Simple Harmonic
Motion

**19.3** Simple Pendulum (Approximate Solution)

***19.4** Simple Pendulum (Exact Solution)

**19.5** Free Vibrations of Rigid Bodies

**19.6** Application of the Principle of Conservation of
Energy

**19.7** Forced Vibrations Damped Vibrations

***19.8** Damped Free Vibrations

***19.9** Damped Forced Vibrations

***19.10** Electrical Analogues

Review and Summary

Review Problems

Computer Problems

Appendix A Some Useful Definitions and Properties of Vector
Algebra

Appendix B Moments of Inertia of Masses

Appendix C Fundamentals of Engineering Examination

Photo Credits

Index

Answers to Problems

Born in France and educated in France and Switzerland, Ferdinand Beer held an M.S. degree from the Sorbonne and an Sc.D. degree in theoretical mechanics from the University of Geneva. He came to the United States after serving in the French army during the early part of World War II and taught for four years at Williams College in the Williams-MIT joint arts and engineering program. Following his service at Williams College, Beer joined the faculty of Lehigh University, where he taught for thirty-seven years. He held several positions, including the University Distinguished Professors Chair and Chairman of the Mechanical Engineering and Mechanics Department. In 1995, Beer was awarded an honorary Doctor of Engineering degree by Lehigh University. Born in Philadelphia, Russ holds a B.S. degree in civil engineering from the University of Delaware and an Sc.D. degree in the field of structural engineering from The Massachusetts Institute of Technology (MIT). He taught at Lehigh University and Worchester Polytechnic Institute (WPI) before joining the faculty of the University of Connecticut where he held the position of Chairman of the Civil Engineering Department and taught for twenty-six years. In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engineers. Phillip J. Cornwell holds a B.S. degree in mechanical engineering from Texas Tech University and M.A. and Ph.D. degrees in mechanical and aerospace engineering from Princeton University. He is currently a professor of mechanical engineering at Rose-Hulman Institute of Technology, where he has taught since 1989. His present interests include structural dynamics, structural health monitoring, and undergraduate engineering education. Cornwell spends his summers working at Los Alamos National Laboratory, where he is a mentor in the Los Alamos Dynamics Summer School and does research in the area of structural health monitoring. He received an SAE Ralph R. Teetor Educational Award in 1992, the Dean's Outstanding Scholar Award at Rose-Hulman in 2000, and the Board of Trustees Outstanding Scholar Award at Rose-Hulman in 2001.

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