MIT OpenCourseWare http://ocw.mit.edu Electromechanical Dynamics For any use or distribution of this textbook, please cite as follows: Woodson, Herbert H., and James R. Melcher. Electromechanical Dynamics. 3 vols. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-NonCommercial-Share Alike For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/termsELECTROMECHANICAL DYNAMICSPart I: Discrete Systems__ ELECTROMECHANICALDYNAMICSPart I: Discrete SystemsHERBERT H. WOODSONPhilip Sporn Professor of Energy ProcessingDepartments of Electrical and Mechanical EngineeringJAMES R. MELCHERAssociate Professor of Electrical EngineeringDepartment of Electrical Engineeringboth of Massachusetts Institute of TechnologyJOHN WILEY & SONS, INC., NEW YORK -LONDON .SYDNEY~__To our parentsI___ ___PREFACEPart I: Discrete SystemsIn the early 1950's the option structure was abandoned and a common corecurriculum was instituted for all electrical engineering students at M.I.T.The objective of the core curriculum was then, and is now, to provide afoundation in mathematics and science on which a student can build in hisprofessional growth, regardless of the many opportunities in electricalengineering from which he may choose. In meeting this objective, corecurriculum subjects cannot serve the needs of any professional area withrespect to nomenclature, techniques, and problems unique to that area.Specialization comes in elective subjects, graduate study, and professionalactivities.To be effective a core curriculum subject must be broad enough to begermane to the many directions an electrical engineer may go professionally,yet it must have adequate depth to be of lasting value. At the same time, thesubject must be related to the real world by examples of application. Thisis true because students learn by seeing material in a familiar context, andengineering students are motivated largely by the relevance of the materialto the realities of the world around them.In the organization of the core curriculum in electrical engineering atM.I.T. electromechanics is one major component. As our core curriculumhas evolved, there have been changes in emphasis and a broadening of thetopic. The basic text in electromechanics until 1954, when a new departurewas made, was Electric Machinery by Fitzgerald and Kingsley. This changeproduced ElectromechanicalEnergy Conversion by White and Woodson,which was used until 1961. At that time we started the revision that resultedin the present book. During this period we went through many versions ofnotes while teaching the material three semesters a year.Our objective has always been to teach a subject that combines classicalmechanics with the fundamentals of electricity and magnetism. Thus thesubject offers the opportunity to teach both mechanics and electromagnetictheory in a context vital to much of the electrical engineering community.Our choice of material was to some extent determined by a desire to givethe student a breadth of background sufficient for further study of almostany type of electromechanical interaction, whether in rotating machinery,Prefaceplasma dynamics, the electromechanics of biological systems, or magneto-elasticity. It was also chosen to achieve adequate depth while maintainingsuitable unity, but, most important, examples were chosen that could beenlivened for the engineering student interested in the interplay of physicalreality and the analytical model. There were many examples from which tochoose, but only a few satisfied the requirement of being both mathe-matically lucid and physically demonstrable, so that the student could "pushit or see it" and directly associate his observations with symbolic models.Among the areas of electrical engineering, electromechanics excels in offeringthe opportunity to establish that all-important "feel" for a physical phe-nomenon. Properly selected electromechanical examples can be the basis fordiscerning phenomena that are remote from human abilities to observe.Before discussing how the material can be used to achieve these ends, areview of the contents is in order. The student who uses this book is assumedto have a background in electrostatics and magnetostatics. Consequently,Chapter 1 and Appendix B are essentially a review to define our startingpoint.Chapter 2 is a generalization of the concepts of inductance and capacitancethat are necessary to the treatment of electromechanical systems; it alsoprovides a brief introduction to rigid-body mechanics. This treatment isincluded because many curricula no longer cover mechanics, other thanparticle mechanics in freshman physics. The basic ideas of Chapter 2 arerepeated in Chapter 3 to establish some properties of electromechanicalcoupling in lumped-parameter systems and to obtain differential equationsthat describe the dynamics of lumped-parameter systems.Next, the techniques of Chapters 2 and 3 are used to study rotatingmachines in Chapter 4. Physical models are defined, differential equationsare written, machine types are classified, and steady-state characteristics areobtained and discussed. A separate chapter on rotating machines has beenincluded not only because of the technological importance of machines butalso because rotating machines are rich in examples of the kinds of phe-nomena that can be found in lumped-parameter electromechanical systems.Chapter 5 is devoted to the study, with examples, of the dynamic behaviorof lumped-parameter systems. Virtually all electromechanical systems aremathematically nonlinear; nonetheless, linear incremental models are usefulfor studying the stability of equilibria and the nature of the dynamicalbehavior in the vicinity of an equilibrium. The second half of this chapterdevelops the classic potential-well motions and loss-dominated dynamics inthe context of electromechanics. These studies of nonlinear dynamics affordan opportunity to place linear models in perspective while forming furtherinsights on the physical significance of, for example, flux conservation andstate functions.PrefaceChapter 6 represents our first departure from lumped-parameter systemsinto continuum systems with a discussion of how observers in relative motionwill define and measure field quantities and the related effects of materialmotion on electromagnetic fields. It is our belief that de rotating
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