Dynamics of Physical Systems

Robert H., Jr. Cannon

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486428659
• eBook ISBN: 9780486139692
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

A comprehensive text and reference for a first study of system dynamics and control, this volume emphasizes engineering concepts — modeling, dynamics feedback, and stability, for example — rather than mechanistic analysis procedures designed to yield routine answers to programmable problems. Its focus on physical modeling cultivates an appreciation for the breadth of dynamic systems without resorting to analogous electric-circuit formulation and analysis.
After a careful treatment of the modeling of physical systems in several media and the derivation of the differential equations of motion, the text determines the physical behavior those equations connote: the free and forced motions of elementary systems and compound "systems of systems." Dynamic stability and natural behavior receive comprehensive linear treatment, and concluding chapters examine response to continuing and abrupt forcing inputs and present a fundamental treatment of analysis and synthesis of feedback control systems. This text's breadth is further realized through a series of examples and problems that develop physical insight in the best traditions of modern engineering and lead students into richer technical ground.
As presented in this book, the concept of dynamics forms the basis for understanding not only physical devices, but also systems in such fields as management and transportation. Indeed, the fundamentals developed here constitute the common language of engineering, making this text applicable to a wide variety of undergraduate and graduate courses. 334 figures. 12 tables.

Chapter 1

DYNAMIC INVESTIGATION

It is, at last, the day and the hour for launch. The forty-story gantry yawns slowly open and rolls back, leaving its sometime tenant to stand alone, tall, white, cloaked now only in a veil of liquid-oxygen vapor.

Minutes hence the huge vehicle will thunder skyward on a white-hot cone of fire, and in an hour its forebody will be pursuing an unerring path to a distant planet. But at this moment it stands silent in the spotlight of a hundred arc lamps, mixed with the early rays of dawn, while a thousand test signals are checked and rechecked by the men and machines who attend it.

The loudspeaker intones: “All systems are go.” It is a commonplace phrase by now, but its connotation is almost unbelievable! Twenty months ago this vehicle—this collection of hundreds of intricate systems and subsystems—was no more than a concept, a bundle of specifications. Today every system will work, and in perfectly matched, intimate harmony with all the others.

When the start button is pushed, high-capacity pumps will pour fuel into the ravenous rocket chambers. The enormous fuel tanks will be emptied in one minute flat; but flow will be precisely uniform, and the last drop will be delivered exactly on schedule.

Quick, sure hydraulic pistons will swivel and aim the huge rocket engines, as the automatic pilot solves the problem of balancing a long, limber reed on one end.

Precise inertial instruments—each an intricate dynamic system in its own right—will sense the vehicle’s path; and a miniature, high-capacity computer will solve the trajectory equations and generate continuous path-correction signals. Two dozen radio and television channels will handle instantly the voluminous communication between the vehicle and its ground base, and a world-wide radar tracking network will monitor its path through the sky.

In the vehicle’s nose a myriad of delicate instrument systems are ready to measure, to observe, to photograph, to record and report their findings. Additional systems provide the essential environment for these instruments. A sophisticated air-conditioning system controls temperature and humidity. Carefully designed shock-mounting systems will isolate the delicate instruments from the tremendous vibration of the rocket engines. If there are human passengers, an elaborate complex of life-support systems will operate as well.

Few of the hundreds of systems in this vehicle existed until this decade. Some are based on technology that did not exist four years ago. Many will be making their first flight today. All have been developed specifically for this vehicle, and matched meticulously to one another.

How could so many interrelated systems be developed so rapidly at the same time? How can we be sure each will respond and perform as it must through the abruptly changing sequence of thunderous launch, searing air, and cold, empty space?

There are several underlying answers to these questions. The first is that we have come to understand some of nature’s laws, and to know that they are perfectly dependable. This we call science.

Another answer is that we have learned how to use nature’s laws to build systems of our own to perform tasks we wish done. This we call engineering.

A third answer is part of the second: We have learned to predict the dynamic behavior of systems not yet built. This is called dynamic analysis. When used in careful support of design and testing programs, dynamic analysis is the key to telescoping the development time of new systems, the key to confidence that they will work properly together in a strange new environment.

A fourth answer is in turn part of the third: Nature is orderly and systematic, and the dynamic behavior of large, intricate compound systems is found to be made up of elementary behavior patterns which can be discerned and studied one by one. The process of discernment is sometimes an involved one; but it is straightforward and it can be accomplished by repeated (and astute) application of relatively elementary analytical techniques ; and thereon hangs our ability to contemplate very involved systems of systems, and to predict their behavior with confidence.

Thus, in the development of a space-vehicle system—or of a television network, a power complex, or any other compound dynamic system—a program of dynamic investigation is the central cord that threads together the myriad of physical systems at their inception. It writes the script from which specifications are established, preliminary designs are evolved, “breadboard” models are constructed, early tests are conceived, performed, and analyzed, and final design decisions are made. This is the script against which the final performance of each system will be measured, first alone and then in concert with its teammates. This is the script by which several hundred complex systems have been developed in months, have been tested and integrated together and tested again and again. And now this system of systems is ready to be launched.

This process of dynamic investigation—its fundamental concepts, its basic building blocks, and its applications—is the subject of this book.

1.1 THE SCOPE OF DYNAMIC INVESTIGATION

Dynamics is the study of how things change with time, and of the forces that cause them to do so. It is an intriguing discipline. Moreover, in this transilient era of space travel, instant communication, and pervasive automation, it is a pivotal discipline: Analysis of the dynamic behavior of physical systems has become a keystone to modern technology.

The motion of a space vehicle, for example, must be thoroughly understood, and its precision control correctly provided for early in the design of the vehicle, many months before it is actually launched. The design of an atomic power plant is predicated in part on the predicted dynamic response of the plant to sudden changes in load. The circuit design and component selection for a high-fidelity radio receiver system are based on calculations of how the electronic section will combine with the speakers, in their enclosures, to produce dynamic response that will match to the desired degree the original sound at the broadcasting station.

In these engineering problems and countless others the first requirement is to predict, before construction, the dynamic behavior a physical system will have—its natural motions when disturbed, and its response to commands and stimuli. More, perhaps, than any other field, the study of dynamic behavior links the engineering disciplines.

In a larger sense, the field of dynamics extends well beyond the realm of physical phenomena. In the field of biology, the response of the eye pupil to a sudden change in light intensity, or of the hand to motor commands from the brain, and the transient adjustment of the body’s energy balance to the trauma of major surgery are exciting subjects for dynamic analysis. In economics, the response of a banking system to fluctuations in market activity, of an industry to variations in consumer demand, and, more broadly, the dynamic behavior of the entire economy, have become the subject of dynamic analysis of increasing penetration and importance. Even the phenomena of “group dynamics”—the collective dynamic behavior of teams of individuals having specific tasks to perform—are being studied quantitatively with useful results.

The twofold objective of this book is to develop familiarity with the elementary concepts of dynamic behavior, and to develop proficiency with the techniques of linear dynamic analysis.

Consideration is confined to physical systems in the interest of efficient exposition, because physical phenomena are more familiar and because their behavior is more easily analyzed. Once a degree of proficiency and insight has been attained for one medium, the extension to others will be found to follow by analogy (and to be most intriguing).

Moreover, the similarity in dynamic behavior of different physical systems is accompanied by a striking consistency in the pattern of analytical investigation by which that behavior can most effectively be studied. There are certain broad stages through which an investigation nearly always pr...

Table of contents

• Title Page
• Dedication
• Copyright Page
• FOREWORD
• PREFACE
• METHODS AND RELATIONSHIPS
• Table of Contents
• Chapter 1 - DYNAMIC INVESTIGATION
• PART A - EQUATIONS OF MOTION FOR PHYSICAL SYSTEMS
• PART B - DYNAMIC RESPONSE OF ELEMENTARY SYSTEMS
• PART C - NATURAL BEHAVIOR OF COMPOUND SYSTEMS
• PART D - TOTAL RESPONSE OF COMPOUND SYSTEMS
• PART E - FUNDAMENTALS OF CONTROL-SYSTEM ANALYSIS
• Appendix A - PHYSICAL CONVERSION FACTORS TO EIGHT SIGNIFICANT FIGURES †
• Appendix B - VECTOR DOT PRODUCT AND CROSS PRODUCT
• Appendix C - VECTOR DIFFERENTIATION IN A ROTATING REFERENCE FRAME
• Appendix D - NEWTON’S LAWS OF MOTION
• Appendix E - ANGULAR MOMENTUM AND ITS RATE OF CHANGE FOR A RIGID BODY; MOMENTS OF INERTIA
• Appendix F - FLUID FRICTION FOR FLOW THROUGH LONG TUBES AND PIPES
• Appendix G - DUALS OF ELECTRICAL NETWORKS
• Appendix H - DETERMINANTS AND CRAMER’S RULE
• Appendix I - COMPUTATION WITH A SPIRULE
• Appendix J - TABLE OF LAPLACE TRANSFORM PAIRS
• PROBLEMS
• ANSWERS TO ODD-NUMBERED PROBLEMS
• SELECTED REFERENCES
• INDEX
• ROBERT H. CANNON, JR.