Dynamics of Physical Systems

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ISBN: 9780486428659 | 0486428656
Cover: Paperback
Copyright: 9/16/2003

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Comprehensive text and reference covers modeling of physical systems in several media, derivation of differential equations of motion and related physical behavior, dynamic stability and natural behavior, response to continuing and abrupt forcing inputs, and analysis and synthesis of feedback control systems. 334 figures. 12 tables. 1967 edition.

Dynamic Investigation

(30)

The scope of dynamic investigation

(1)

The stages of a dynamic investigation

(4)

The block diagram: a conceptual tool

(2)

Stage I. Physical modeling: from actual system to physical model

(9)

Dimensions and units

(12)

PART A: EQUATIONS OF MOTION FOR PHYSICAL SYSTEMS

Equations of Motion for Simple Physical Systems: Mechanical, Electrical, and Electromechanical

(63)

Stage II. Equations of motion: from physical model to mathematical model

(2)

One-dimensional mechanical systems

(19)

Mechanical energy and power

(1)

Gear trains and levers

(3)

Motion in two and three dimensions

(1)

Simple electrical systems

(17)

A recapitulation of Procedure A

(1)

Amplifiers and transformers

(4)

Simple electromechanical systems

(6)

Electromechanical elements: an empirical sampling

(9)

Equations of Motion for Simple Heat-Conduction and Fluid Systems

(27)

Simple heat conduction

(8)

Simple fluid systems

102

(19)

Analogies

121

(22)

Analogies between physical media

121

(4)

The electrical analog of mechanical systems

125

(7)

Classification of dynamic system elements

132

(1)

The benefits and limitations of analysis by analog

133

(4)

The network approach to analysis

137

(6)

Equations of Motion for Mechanical Systems in Two and Three Dimensions

143

(39)

Geometry of motion in two and three dimensions

143

(6)

Rotating reference frames

149

(3)

Dynamic equilibrium for rigid body in general motion

152

(4)

Equations of motion for systems of rigid bodies: examples

156

(3)

Advantages of the D'Alembert method. The gyro

159

(4)

Energy methods

163

(4)

Lagrange's method

167

(2)

Lagrange's method for conservative systems

169

(4)

Lagrange's method for nonconservative systems

173

(5)

The relative advantages of Lagrange's method

178

(2)

PART B: DYNAMIC RESPONSE OF ELEMENTARY SYSTEMS

Introduction

180

(2)

First-Order Systems

182

(43)

First-order systems

183

(3)

Natural (unforced) motion

186

(7)

Forced motion

193

(4)

Linearity and superposition

197

(3)

Initial conditions

200

(4)

Special case: the pure integrator

204

(3)

Special case: resonance

207

(3)

Response to a very short impulse

210

(8)

Initial conditions involving sudden change

218

(2)

Generalization to an arbitrary input: convolution

220

(5)

Undamped Second-Order Systems: Free Vibrations

225

(19)

Physical vibrations

226

(10)

Complex numbers

236

(2)

Mathematical operations with complex numbers

238

(4)

Complex-vector (phasor) representation of a sine wave

242

(2)

Damped Second-Order Systems

244

(65)

Second-order systems

245

(1)

Natural motion

246

(2)

Dynamic characteristics and the s plane

248

(7)

Initial conditions: 1 < ζ

255

(2)

Initial conditions: ζ < 1

257

(2)

Sketching time response when ζ < 1

259

(4)

Initial conditions: ζ = 1

263

(3)

Forced motion alone

266

(7)

Transfer functions and pole-zero diagrams

273

(7)

Impedance and admittance

280

(2)

Total response to abrupt disturbances

282

(8)

Transient and steady state

290

(1)

Impulse response of certain second-order systems

291

(7)

Response of a second-order system by convolution

298

(1)

Simulation: the analog computer

299

(10)

Forced Oscillations of Elementary Systems

309

(46)

The nature of sinusoidal response

311

(2)

Operation at a single frequency: the impedance viewpoint

313

(1)

Frequency response

314

(7)

Computing frequency response

321

(1)

Logarithmic scales for plotting frequency response

322

(2)

Forced oscillation of first-order systems: the plotting techniques of Bode

324

(6)

Forced oscillation of undamped second-order systems: resonance

330

(5)

Forced oscillation of damped second-order systems

335

(2)

Techniques for plotting second-order frequency response

337

(5)

Obtaining frequency response from the s plane

342

(3)

Seismic instruments

345

(7)

Frequency response of RLC circuits

352

(3)

Natural Motions of Nonlinear Systems and Time-Varying Systems

355

(21)

Methods of linear approximation

356

(4)

State-space analysis

360

(7)

Large motions of pendulum with damping

367

(2)

Piecewise-linear elements

369

(1)

Linear equations with time-varying coefficients

370

(4)

PART C: NATURAL BEHAVIOR OF COMPOUND SYSTEMS

Introduction

374

(2)

Dynamic Stability

376

(43)

The concept of stability

377

(2)

The elementary second-order system

379

(5)

Locus of roots by graphical construction

384

(2)

Damping as a variable

386

(6)

Coupled pairs of first-order systems

392

(1)

Feedback systems

393

(3)

Third-order systems

396

(5)

The root-locus method of Evans

401

(3)

An introduction to root-locus sketching

404

(2)

The method of Routh: third-order example

406

(3)

Routh's method: general case

409

(6)

Special case of a zero term in the first column

415

(1)

Special case of a zero row

416

(3)

Coupled Modes of Natural Motion: Two Degrees of Freedom

419

(38)

Forms of physical coupling

420

(3)

Coupled equations of motion

423

(3)

A simple vibrating system of coupled members

426

(5)

The effect of coupling strength

431

(6)

Beat generation

437

(5)

Inertial coupling

442

(3)

Normal coordinates

445

(2)

General case, with damping: eigenvalues and eigenvectors

447

(10)

Coupled Modes of Natural Motion: Many Degrees of Freedom

457

(35)

Many degrees of freedom

458

(4)

Distributed-parameter systems: equations of motion

462

(5)

Natural motions of a class of one-dimensional distributed-parameter systems

467

(5)

Brief description of general distributed-parameter systems

472

(3)

Certain musical instruments

475

(5)

A note on the musical scale

480

(2)

Rayleigh's method

482

(8)

PART D: TOTAL RESPONSE OF COMPOUND SYSTEMS

Introduction

490

(2)

est and Transfer Functions

492

(18)

Review of the transfer-function concept

493

(2)

Transferred response of subsystems in cascade

495

(2)

Graphical evaluation of transfer functions from the system pole-zero diagram

497

(3)

Transferred response of systems with general coupling

500

(2)

Matrix representation and standard form

502

(7)

Matrix description of eigenvector calculation

509

(1)

Forced Oscillations of Compound Systems

510

(19)

Frequency response of subsystems in cascade

511

(3)

Frequency response of systems with two-way coupling

514

(4)

Resonance in coupled systems

518

(7)

Design for a single frequency: the vibration absorber

525

(4)

Response to Periodic Functions: Fourier Analysis

529

(6)

Real Fourier series

529

(4)

Complex Fourier series

533

(1)

Spectral representation

534

(1)

The Laplace Transform Method

535

(49)

Demonstration of the Laplace transform method

537

(7)

Evolution of the Laplace transform

544

(5)

Application of the Laplace transform: the one-sided Laplace transform

549

(5)

Summary of basic Laplace transform relations

554

(1)

Derivation of common Laplace transform pairs

555

(4)

Transfer functions from Laplace transformation

559

(3)

Total response by the Laplace transform method

562

(5)

The final-value theorem and the initial-value theorem

567

(5)

A system's response to an impulse and its L transform

572

(1)

Initial conditions and impulse response: a physical interpretation

572

(4)

Equations of motion in standard form: state variables

576

(4)

Convolution and the Laplace transform

580

(4)

From Laplace Transform to Time Response by Partial Fraction Expansion

584

(13)

Formulation of the task

584

(1)

Partial fraction expansion: case one

585

(3)

Special handling of complex conjugate poles

588

(1)

Use of the s-plane pole-zero array to compute response coefficients

589

(3)

The case of repeated poles: case two

592

(3)

Summary of Procedure D-2: partial fraction expansion

595

(2)

Complete System Analysis: Some Case Studies

597

(33)

A fluid clutch

600

(5)

An electromechanical shaker

605

(5)

A thermal quenching operation

610

(4)

An aircraft hydraulic servo

614

(3)

The two-axis gyroscope

617

(11)

PART E: FUNDAMENTALS OF CONTROL-SYSTEM ANALYSIS

Introduction

628

(2)

Feedback Control

630

(14)

The philosophy of feedback control

631

(4)

Performance objectives

635

(2)

The sequence of control-system analysis

637

(1)

Review of dynamic coupling

638

(1)

The algebra of loop closing

639

(5)

Evans' Root-Locus Method

644

(39)

The basic principle

645

(6)

Root-locus sketching procedure

651

(2)

Sketching rules for 180° loci

653

(2)

Rule 1: Real-axis segments

655

(2)

Rule 2: Asymptotes

657

(3)

Rule 3: Directions of departure and arrival

660

(4)

Rule 4: Breakaway from the real axis

664

(5)

Rule 4 (continued): The saddle-point concept

669

(4)

Rule 5: Routh and Evans

673

(4)

Rule 6: Fixed centroid

677

(1)

A typical construction of root loci

678

(4)

Summary

682

(1)

Some Case Studies in Automatic Control

683

(74)

Analysis of an electromechanical remote-indicator servo

683

(8)

Synthesis of indicator servo using network compensation to improve performance

691

(5)

Roll-control autopilot: a multiloop system

696

(7)

Control of an unstable mechanical system: the stick balancer

703

(8)

APPENDICES

A Physical conversion factors to eight significant figures

711

(1)

B Vector dot product and cross product

712

(2)

C Vector differentiation in a rotating reference frame

714

(2)

D Newton's laws of motion

716

(2)

E Angular momentum and its rate of change for a rigid body; moments of inertia

718

(3)

F Fluid friction for flow through long tubes and pipes

721

(2)

G Duals of electrical networks

723

(2)

H Determinants and Cramer's rule

725

(2)

I Computation with a Spirule

727

(4)

J Table of Laplace transform pairs

731

(26)

Problems

757

(108)

Answers to odd-numbered problems

865

(16)

Selected references

881

(4)

Index

885

(20)

About the Author

905

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Dynamics of Physical Systems

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