Engineering mechanics: an introduction to dynamics /

646 Pages·2003·126.855 MB·English

by  David J. McGill , Wilton W. King.

• ENGINEERING MECHANICS
AN INTRODUCTION TO
• DYNAMICS

• ENGINEERING MECHANICS
Fourth Edition • AN INTRODUCTION TO
• DYNAMICS
DAVID J. MCGILL AND WILTON W. KING
Professors Emeritus, Georgia Institute of Technology
Copyright © 2003 by David J. McGill and Wilton W. King
All rights reserved. No part of this book may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means —electronic, mechanical,
photocopying, recording, or otherwise—without prior written permission of the
authors.
For more information, contact:
Tichenor
Publishing Tichenor Publishing
5005 North State Road 37 Business
Bloomington, IN 47404-1626
Division of T.I.S., Inc.
To OUR WIVES, CAROLYN AND KAY

CONTENTS
PREFACE xi
1 KINEMATICS OF MATERIAL POINTS OR PARTICLES 1
1.1 Introduction, 2
1.2 Reference Frames and Vector Derivatives, 3
Position, Velocity, and Acceleration, 6
1.4 Kinematics of a Point in Rectilinear Motion, 8
1.5 Rectangular Cartesian Coordinates, 24
1.6 Cylindrical Coordinates, 31
1.7 Tangential and Normal Components, 43
Summary, 53
Review Questions, 54
2 KINETICS OF PARTICLES AND OF MASS CENTERS
OF BODIES 55
2.1 Introduction, 56
2.2 Newton's Laws and Euler's First Law, 56
2.3 Motions of Particles and of Mass Centers of Bodies, 62
2.4 Work and Kinetic Energy for Particles, 87
2.5 Momentum Form of Euler's First Law, 101
2.6 Euler's Second Law (The Moment Equation), 117
Summary, 125
Review Questions, 128
3 KINEMATICS OF PLANE MOTION OF A RIGID BODY 129
3.1 Introduction, 130
3.2 Velocity and Angular Velocity Relationship for Two Points of the Same
Rigid Body, 134
3.3 Translation, 147
3.4 Instantaneous Center of Zero Velocity, 149
3.5 Acceleration and Angular Acceleration Relationship for Two Points of
the Same Rigid Body, 163
vii
Page viii
3.6 Rolling, 170
3.7 Relationship Between the Velocities of a Point with Respect to Two
Different Frames of Reference, 198
3.8 Relationship Between the Accelerations of a Point with Respect to
Two Different Frames of Reference, 207
Summary, 215
Review Questions, 216
KINETICS OF A RIGID BODY IN PLANE MOTION/
DEVELOPMENT AND SOLUTION OF THE DIFFERENTIAL
EQUATIONS GOVERNING THE MOTION 217
4.1 Introduction, 218
4.2 Rigid Bodies in Translation, 219
Moment of Momentum (Angular Momentum), 227
Moments and Products of Inertia/The Parallel-Axis Theorems, 229
4.5 The Mass-Center Form of the Moment Equation of Motion, 246
4.6 Other Useful Forms of the Moment Equation, 272
4.7 Rotation of Unbalanced Bodies, 291
Summary, 301
Review Questions, 303
5 SPECIAL INTEGRALS OF THE EQUATIONS OF PLANE
MOTION OF RIGID BODIES: WORK-ENERGY AND
IMPULSE-MOMENTUM METHODS 304
5.1 Introduction, 305
5.2 The Principle(s) of Work and Kinetic Energy, 305
5.3 The Principles of Impulse and Momentum, 343
Summary, 375
Review Questions, 377
6 KINEMATICS OF A RIGID BODY IN
THREE-DIMENSIONAL MOTION 379
Introduction, 380
Relation Between Derivatives/The Angular Velocity Vector, 380
6.3 Properties of Angular Velocity, 384
6.4 The Angular Acceleration Vector, 398
6.5 Velocity and Acceleration in Moving Frames of Reference, 401
The Earth as a Moving Frame, 410
Velocity and Acceleration Equations for Two Points of the Same Rigid
Body, 414
6.8 Describing the Orientation of a Rigid Body, 428
6.9 Rotation Matrices, 434
Summary, 441
Review Questions, 442
iPage x
7 KINETICS OF A RIGID BODY IN GENERAL MOTION 444
7.1 Introduction, 445
7.2 Moment of Momentum {Angular Momentum) in Three Dimensions, 446
7.3 Transformations of Inertia Properties, 448
7.4 Principal Axes and Principal Moments of Inertia, 455
7.5 The Moment Equation Governing Rotational Motion, 472
7.6 Gyroscopes, 492
7.7 Impulse and Momentum, 499
7.8 Work and Kinetic Energy, 504
Summary, 513
Review Questions, 514
8 SPECIAL TOPICS 516
8.1 Introduction, 517
8.2 Introduction to Vibrations, 517
8.3 Euler's Law for a Control Volume, 535
8.4 Central Force Motion, 543
Review Questions, 554
APPENDICES CONTENTS 557
Appendix A UNITS, 558
Appendix B EXAMPLES OF NUMERICAL ANALYSIS/THE NEWTON-
RAPHSON METHOD, 564
Appendix C MOMENTS OF INERTIA OF MASSES, 567
Appendix D ANSWERS TO ODD-NUMBERED PROBLEMS, 573
INDEX, 583
SUPPLEMENTARY PROBLEMS 589