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/termsAppendix DGLOSSARY OFCOMMONLY USED SYMBOLSSection references indicate where symbols of a given significance areintroduced; grouped symbols are accompanied by their respective references.The absence of a section reference indicates that a symbol has been appliedfor a variety of purposes. Nomenclature used in examples is not included.SymbolMeaningSectionAAi(A+, A-)A,aa, (ae, as)ab(a, b, c)a,B, Br, B,B, Bi, BoBi(Br, Bra, Brb, Brm)[Bf, (Bf)av]bbCC, (C., Cb), CoCC(C",C-)cross-sectional areacoefficient in differential equationcomplex amplitudes of components of nthmodecross-sectional area of armature conductorspacing of pole faces in magnetic circuitphase velocity of acoustic related wavesAlfv6n velocityLagrangian coordinatesconstant coefficient in differential equationinstantaneous acceleration of point p fixedin materialdamping constant for linear, angular andsquare law dampersmagnetic flux densityinduced flux densityradial components of air-gap fluxdensitiesradial flux density due to field currentwidth of pole faces in magnetic circuithalf thickness of thin beamcontour of integrationcapacitancecoefficient in boundary conditionthe curl of the displacementdesignation of characteristic lines5.1.19.2.16.4.18.5.113.2.1, 11.4.112.2.311.15.1.12.2.1c2.2.1b, 4.1.1, 5.2.21.1.1a, 8.1, 6.4.27.04.1.46.4.18.511.4.2b1.1.2a2.1.2, 7.2.1a, 5.2.19.1.111.49.1.1Glossary of Commonly Used SymbolsMeaningCv,CvDddadf,dldT,dVEEE, EoE,EEie11, eijeijFFFFoffff'ffGGGGgg, g(H, H,, H,, Hz)hI, I, (I, 1,s), it(i, i1, i,2.... ik),(iar, ias, ibr, ibs),ia, (ia, ib, ic),(if, it), (ir, i)specific heat capacity at constant pressurespecific heat capacity at constant volumeelectric displacementlengthelemental areatotal elemental force on material in rigidbodyelemental line segmenttorque on elemental volume of materialelemental volumeconstant of motionYoung's modulus or the modulus ofelasticityelectric field intensitymagnitude of armature voltage generatedby field current in a synchronousmachineinduced electric field intensitystrain tensorstrain-rate tensormagnetomotive force (mmf)force densitycomplex amplitude off(t)amplitude of sinusoidal driving forceequilibrium tension of stringdriving functionforcearbitrary scalar functionscalar function in moving coordinatesystemthree-dimensional surfaceintegration constanta constantshear modulus of elasticityspeed coefficientconductanceair-gap lengthacceleration of gravitymagnetic field intensityspecific enthalpyelectrical currentelectrical current13.1.213.1.21.1.1a1.1.2a2.2.1c1.1.2a2.2.1c1.1.2b5.2.19.1l.1.la, 5.1.2d4.1.6a7.09.1, 11.214.1.1a13.2.21.1.1a5.1.19.1.39.25.1.12.2.1, 2.2.1c, 3.1,5.1.2a, 3.1.2b, 8.1,9.16.16.16.211.4.2a5.1.2c11.2.26.4.13.15.2.15.1.2c, 12.1.31.1.1a13.1.210.4.3, 12.2.1a, 4.1.2,6.4.12.1, 4.1.3, 6.4.1, 4.1.7,6.4.1, 4.1SymbolSection~__Appendix DSymbolis(i", ,,Pi,), (i1,i,1idJ,JfiJ, hrnKK,K1KKk, ke, (k,,kI)kk,k.(L, L1, L2), (La, L),L,, (Lo, L2),(L7,L,,La), L,5L11,1,1,,MMMMMM,M,MmNNnnnPPPPPPa,P,,PMPrQq, q,, q,Meaningunit vector perpendicular to area ofintegrationunit vector normal to surface ofintegrationunit vectors in coordinate directionscurrent densitymoment of inertiaproducts of inertiaV-1loading factorsurface current densitylinear or torsional spring constantinduced surface current densitywavenumbersummation indexmaximum coefficient of couplingnth eigenvalueinductancelength of incremental line segmentvalue of relative displacement for whichspring force is zerolengthHartmann numbermass of one mole of gas in kilogramsMach numbermassnumber of mechanical terminal pairsmutual inductancemagnetization densitymass/unit length of stringnumber of electrical terminal pairsnumber of turnsnumber density of ionsintegerunit normal vectorpolarization densitypowernumber of pole pairs in a machinepower per unit areapressurepowerelectric chargeelectric chargeradiusSection6.2.16.2.12.2.1c7.0, 1.1.1a5.1.2b, 4.1.1, 2.2.1c2.2.1ec4.1.6a13.2.27.0, 1.1.1a2.2.1a7.07.1.3, 10.1.3, 10.02.1.14.1.6b9.22.1.1, 6.4.1, 2.1.1,4.2.1, 4.1.1, 4.2.46.2.12.2.1a14.2.213.1.213.2.12.2.1c2.1.14.1.1, 4.2.41.l.la9.22.1.15.2.212.3.17.1.11.1.21.1.1a12.2.1a4.1.814.2.15.1.2d and 12.1.44.1.6a, 4.1.6b, 4.1.2,4.1.6b7.2.1a1.1.3 and 2.1.2, 8.1,2.1.2Glossary of Commonly Used SymbolsMeaningR, Ra, Rb, R1, Rr, R,(R, R,)R,RmrrrrmSSSSS,(s, SmTr)sTTTT, T, TP, Tem, Tm,To,T,TT•nTo,TTT,ttIUUuUUo(x -Zo)u_1(t)Vv, v 7,v,, V8resistancegas constantelectric Reynolds numbermagnetic Reynolds numberradial coordinateposition vector of materialposition vector in moving reference framecenter of mass of rigid bodyreciprocal modulus of elasticitysurface of integrationnormalized frequencymembrane tensiontransverse force/unit length acting on stringcomplex frequencyslipith root of characteristic equation, anatural frequencyperiod of oscillationtemperaturetorquesurface forcemechanical stress tensorthe component of the stress-tensor in themth-direction on a cartesian surface witha normal vector in the nth-directionconstant of coulomb dampinginitial stress distribution on thin rodlongitudinal stress on a thin rodtransverse force per unit area onmembranetransverse force per unit area acting onthin beamtimetime measured in moving reference framegravitational potentiallongitudinal steady velocity of string ormembraneinternal energy per unit masssurface coordinateunit impulse at x = xotransverse deflection of wire in x-directionunit step occurring at t = 0velocityvolumevoltagepotential energy13.1.27.07.02.2.1c6.12.2.1c11.5.2c1.1.2a7.2.49.29.25.1.14.1.6b5.1.15.2.113.1.22.2.1c, 5.1.2b, 3.1.1,4.1.6b, 4.1.1, 6.4.1,6.4.18.413.1.28.14.1.19.1.19.1.19.211.4.2b1.1.16.112.1.310.213.1.111.39.2.110.4.35.1.2b7.0, 13.2.31.1.25.2.1SymbolSection__ Appendix DSymbolv, v(v, v, ..., v)VI', (Va, Vb, Ve),Vy, Voc, VvnVoVrv,VV(WI, WM)(W,, WM, W')W"www'X(x, 1, X2, .. )x,(XI, X2, x3), (x, Y, z)(z', y', z')(W, Y)(c, j)(2, #)AtaccV, o, y'AoArAs6( ), 61, 606&MeaningSectionvelocityvoltagevoltagevelocity of surface in normal direction 6.2.1initial velocity distribution on thin rod
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