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Contents Preface xii Acknowledgments xix List of Symbols xxii KINEMATICS OF PARTICLES 601 11.1 Introduction to Dynamics 602 Rectilinear Motion of Particles 603 11.2 Position, Velocity, and Acceleration 603 11.3 Determination of the Motion of a Particle 607 11.4 Uniform Rectilinear Motion 616 11.5 Uniformly Accelerated Rectilinear Motion 617 11.6 Motion of Several Particles 618 11.7 Graphical Solution of Rectilinear-Motion Problems 630 11.8 Other Graphical Methods 631 Curvilinear Motion of Particles 641 11.9 Position Vector, Velocity, and Acceleration 641 11.10 Derivatives of Vector Functions 643 11.11 Rectangular Components of Velocity and Acceleration 645 11.12 Motion Relative to a Frame in Translation 646 11.13 Tangential and Normal Components 663 11.14 Radial and Transverse Components 666 Review and Summary for Chapter 11 680 Review Problems 684 Computer Problems 687 KINETICS OF PARTICLES: NEWTON'S SECOND LAW 691 12.1 Introduction 692 12.2 Newton's Second Law of Motion 693 12.3 Linear Momentum of a Particle. Rate of Change of Linear Momentum 694 vii 12.4 Systems of Units 695 12.5 Equations of Motion 697 12.6 Dynamic Equilibrium 699 12.7 Angular Momentum of a Particle. Rate of Change of Angular Momentum 718 12.8 Equations of Motion in Terms of Radial and Transverse Components 719 12.9 Motion under a Central Force. Conservation of Angular Momentum 720 12.10 Newton's Law of Gravitation 721 12.11 Trajectory of a Particle under a Central Force 731 12.12 Application to Space Mechanics 732 12.13 Kepler's Laws of Planetary Motion 735 Review and Summary for Chapter 12 744 Review Problems 748 Computer Problems 751 KINETICS OF PARTICLES: ENERGY AND MOMENTUM METHODS 755 13.1 Introduction 756 13.2 Work of a Force 756 13.3 Kinetic Energy of a Particle. Principle of Work and Energy 760 13.4 Applications of the Principle of Work and Energy 762 13.5 Power and Efficiency 763 13.6 Potential Energy 781 13.7 Conservative Forces 783 13.8 Conservation of Energy 784 13.9 Motion under a Conservative Central Force. Application to Space Mechanics 786 13.10 Principle of Impulse and Momentum 805 13.11 Impulsive Motion 808 13.12 Impact 820 13.13 Direct Central Impact 820 13.14 Oblique Central Impact 823 13.15 Problems Involving Energy and Momentum 826 Review and Summary for Chapter 13 842 Review Problems 848 Computer Problems 851 SYSTEMS OF PARTICLES 855 14.1 Introduction 856 14.2 Application of Newton's Laws to the Motion of a System of Particles. Effective Forces 856 14.3 Linear and Angular Momentum of a System of Particles 859 14.4 Motion of the Mass Center of a System of Particles 860 14.5 Angular Momentum of a System of Particles about Its Mass Center 862 14.6 Conservation of Momentum for a System of Particles 864 14.7 Kinetic Energy of a System of Particles 873 14.8 Work-Energy Principle. Conservation of Energy for a System of Particles 875 14.9 Principle of Impulse and Momentum for a System of Particles 875 14.10 Variable Systems of Particles 886 14.11 Steady Stream of Particles 886 14.12 Systems Gaining or Losing Mass 889 Review and Summary for Chapter 14 904 Review Problems 908 Computer Problems 911 KINEMATICS OF RIGID BODIES 915 15.1 Introduction 916 15.2 Translation 918 15.3 Rotation about a Fixed Axis 919 15.4 Equations Defining the Rotation of a Rigid Body about a Fixed Axis 922 15.5 General Plane Motion 932 15.6 Absolute and Relative Velocity in Plane Motion 934 15.7 Instantaneous Center of Rotation in Plane Motion 945 15.8 Absolute and Relative Acceleration in Plane Motion 956 15.9 Analysis of Plane Motion in Terms of a Parameter 958 15.10 Rate of Change of a Vector with Respect to a Rotating Frame 971 15.11 Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration 973 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 998 15.15 Frame of Reference in General Motion 999 Review and Summary for Chapter 15 1011 Review Problems 1018 Computer Problems 1021 PLANE MOTION OF RIGID BODIES: FORCES AND ACCELERATIONS 1025 16.1 Introduction 1026 16.2 Equations of Motion for a Rigid Body 1027 16.3 Angular Momentum of a Rigid Body in Plane Motion 1028 16.4 Plane Motion of a Rigid Body. d'Alembert's Principle 1029 16.5 A Remark on the Axioms of the Mechanics of Rigid Bodies 1030 16.6 Solution of Problems Involving the Motion of a Rigid Body 1031 16.7 Systems of Rigid Bodies 1032 16.8 Constrained Plane Motion 1051 Review and Summary for Chapter 16 1073 Review Problems 1075 Computer Problems 1078 PLANE MOTION OF RIGID BODIES: ENERGY AND MOMENTUM METHODS 1081 17.1 Introduction 1082 17.2 Principle of Work and Energy for a Rigid Body 1082 17.3 Work of Forces Acting on a Rigid Body 1083 17.4 Kinetic Energy of a Rigid Body in Plane Motion 1084 17.5 Systems of Rigid Bodies 1085 17.6 Conservation of Energy 1086 17.7 Power 1087 17.8 Principle of Impulse and Momentum for the Plane Motion of a Rigid Body 1104 17.9 Systems of Rigid Bodies 1107 17.10 Conservation of Angular Momentum 1107 17.11 Impulsive Motion 1120 17.12 Eccentric Impact 1120 Review and Summary for Chapter 17 1134 Review Problems 1138 Computer Problems 1141 KINETICS OF RIGID BODIES IN THREE DIMENSIONS 1145 18.1 Introduction 1146 18.2 Angular Momentum of a Rigid Body in Three Dimensions 1147 18.3 Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body 1151 18.4 Kinetic Energy of a Rigid Body in Three Dimensions 1152 18.5 Motion of a Rigid Body in Three Dimensions 1165 18.6 Euler's Equations of Motion. Extension of d'Alembert's Principle to the Motion of a Rigid Body in Three Dimensions 1166 18.7 Motion of a Rigid Body about a Fixed Point 1167 18.8 Rotation of a Rigid Body about a Fixed Axis 1168 18.9 Motion of a Gyroscope. Eulerian Angles 1183 18.10 Steady Precession of a Gyroscope 1185 18.11 Motion of an Axisymmetrical Body under No Force 1186 Review and Summary for Chapter 18 1199 Review Problems 1204 Computer Problems 1208 MECHANICAL VIBRATIONS 1213 19.1 Introduction 1214 Vibrations without Damping 1214 19.2 Free Vibrations of Particles. Simple Harmonic Motion 1214 19.3 Simple Pendulum (Approximate Solution) 1218 19.4 Simple Pendulum (Exact Solution) 1219 19.5 Free Vibrations of Rigid Bodies 1228 19.6 Application of the Principle of Conservation of Energy 1240 19.7 Forced Vibrations 1251 Damped Vibrations 1261 19.8 Damped Free Vibrations 1261 19.9 Damped Forced Vibrations 1264 19.10 Electrical Analogues 1265 Review and Summary for Chapter 19 1277 Review Problems 1282 Computer Problems 1285 Appendix A SOME USEFUL DEFINITIONS AND PROPERTIES OF VECTOR ALGEBRA 1289 Appendix B MOMENTS OF INERTIA OF MASSES 1295 Appendix C FUNDAMENTALS OF ENGINEERING EXAMINATION 1333 Photo Credits 1335 Index 1337 Answers to Problems 1345
Library of Congress Subject Headings for this publication:
Dynamics.
Vector analysis.
Mechanics, Applied.