Dynamics

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.

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

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