Dynamics

by Goodman, Lawrence E.; Warner, William H.

• ISBN13: 9780486420066
• ISBN10: 048642006X
• Format: Paperback
• Copyright: 2001-10-08
• Publisher: Dover Publications

Summary

Carefully written text, of great value to beginning engineering students, presents complete theoretical treatment of mechanical model systems before dealing with their technological applications. Topics include an introduction to the calculus of vectors, particle motion, dynamics of particle systems and plane rigid bodies, technical applications in plane motions, the theory of mechanical vibrations, and more. Exercises and answers appear at end of each chapter.

Table of Contents

Introduction to the Calculus of Vectors	9	(68)
Fundamental Ideas	9	(3)
Vectors	12	(2)
Summary of Vector Algebra	14	(6)
Velocity and Acceleration	20	(5)
Integration of Vector Functions	25	(3)
Vector Fields	28	(1)
Elements of Particle Kinematics	28	(1)
Rectangular Cartesian Coordinates	29	(12)
Normal and Tangential Coordinates	41	(9)
Plane and Cylindrical Polar Coordinates	50	(7)
Spherical Polar Coordinates	57	(11)
Theory of Particle Motion	68	(60)
Introduction	68	(1)
Newton's Laws of Motion; Mass and Force	69	(12)
Units	81	(7)
Impulse and Momentum	88	(5)
Impulsive Forces	93	(2)
Power, Work, and Kinetic Energy	95	(9)
Force Fields and Potential Energy	104	(14)
Mechanical Energy and Conservation of Energy	118	(10)
Applications in Particle Motion	128	(56)
Introduction	128	(1)
The Uniform Force Field	129	(7)
Simple Harmonic Motion	136	(11)
Effect of a Periodic Disturbing Force	147	(6)
Central Force Motion	153	(11)
Central Repulsive Force	164	(2)
Dissipative Forces	166	(18)
Dynamics of Particle Systems and Plane Rigid Bodies	184	(97)
Introduction	184	(1)
Relative Motion of Two Particles	185	(10)
Dynamics of Multiparticle Systems	195	(15)
Kinematics of Plane Rigid Bodies	210	(20)
Dynamics of Plane Systems	230	(9)
Impulse-Momentum Principles for Systems	239	(6)
The Work-Energy Principle for Particle Systems and Plane Rigid Bodies	245	(12)
Work and Energy for General Plane Systems; Real and Ideal Constraints	257	(24)
Technical Applications in Plane Motion	281	(56)
Introduction	281	(1)
Elementary Analysis; Force and Acceleration at Particular Instants	282	(14)
Impact and Impulsive Motion	296	(17)
Variable Mass	313	(5)
Conservative Systems	318	(19)
Rigid Body Dynamics in Three Dimensions	337	(63)
Introduction to Rigid-Body Kinematics in Space	337	(2)
General Displacement of a Rigid Body; Finite Rotations and Euler's Theorem	339	(5)
Small Rotations of a Rigid Body; Angular Velocity	344	(6)
Rotating Coordinates; General Relative Motion Equations	350	(17)
The Angular Momentum of a Rigid Body; Moments and Products of Inertia	367	(14)
The Kinetic Energy of a Rigid Body; The Work-Energy Principle	381	(5)
Special Forms of the Dynamical Equations; Euler's Equations	386	(3)
Equilibrium of a Rigid Body	389	(11)
Three-Dimensional Applications of the Principles of Dynamics	400	(66)
Introduction	401	(1)
Effects of the Earth's Rotation on Particle Motion near the Surface	402	(11)
Fixed-Axis Rotation	413	(15)
Application of d'Alembert's Principle	428	(5)
Gyroscopic Effects	433	(15)
Intrinsic Equations of the Gyroscope	448	(3)
Description of Spatial Position: Euler's Angular Coordinates	451	(15)
The Principle of virtual Work	466	(46)
Work, Energy, and Equilibrium	466	(2)
Equilibrium of a Particle	468	(5)
Equilibrium of Systems; The Rigid Body	473	(11)
Real Systems; Potential Energy	484	(9)
Stability of Equilibrium	493	(7)
Summary	500	(12)
Elements of the Theory of Mechanical Vibrations	512	(48)
Introduction	512	(1)
Free Vibrations of a Simple Mechanical System	513	(10)
Effect of a Disturbing Force	523	(3)
Effect of a Harmonic Disturbing Force	526	(7)
Multiple-Degree-of Freedom Mechanical Systems	533	(14)
The Analogies between Electrical and Mechanical Vibrations	547	(13)
Appendix I vector Algebra	560	(9)
AI.1 Scalar and Vector Quantities	560	(1)
AI.2 Vector Addition	561	(1)
AI.3 Unit Vectors	562	(1)
AI.4 The Scalar Product	563	(1)
AI.5 The Vector Product	564	(1)
AI.6 Triple Products	565	(4)
Appendix II Properties of the Inertia Matrix	569	(40)
AII.1 The Definition of the Inertia Matrix	569	(3)
AII.2 The Parallel-Axis Transfer Theorems	572	(2)
AII.3 The Rotation-of Axes Transfer Theorems	574	(9)
AII.4 Further Comments on the Determination of the Inertia Matrix	583	(2)
AII.5 Summary	585	(1)
AII.6 Inertia Properties of Uniform Bodies	586	(23)
Index	609