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 AGLOSSARY 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.SymbolMeaningSectionAAicoefficient in differential equation5.1.1+ , (AAn)complex amplitudes of components of nthmode9.2.1A,cross-sectional area of armature conductor6.4.1aspacing of pole faces in magnetic circuit8.5.1a, (ae, as)phase velocity of acoustic related waves13.2.1, 11.4.1abAlfvyn velocity12.2.3(a, b, c)Lagrangian coordinates11.1aiconstant coefficient in differential equation5.1.1a,instantaneous acceleration of point p fixedin material2.2.1cB, Br, B,damping constant for linear, angular andsquare law dampers2.2.1b, 4.1.1, 5.2.2B, Bi, Bmagnetic flux density1.1.1a, 8.1, 6.4.2oBiinduced flux density7.0(Br, Bra, Brb, Brm)radial components of air-gap fluxdensities4.1.4[Brt, (Brf)av]radial flux density due to field current6.4.1bwidth of pole faces in magnetic circuit8.5bhalf thickness of thin beam11.4.2bCcontour of integration1.1.2aC, (Ca, Cb), C,capacitance2.1.2, 7.2.1a, 5.2.1Ccoefficient in boundary condition9.1.1Cthe curl of the displacement11.4(C+, C-)designation of characteristic lines9.1.1cross-sectional area_~Glossary of Commonly Used SymbolsSymbolMeaningSectionC,specific heat capacity at constant pressure13.1.2Cvspecific heat capacity at constant volume13.1.2Delectric displacementl.l.ladlengthdaelemental area1.1.2adf,total elemental force on material in rigidbody2.2.1cdlelemental line segment1.1.2adT.torque on elemental volume of material2.2.1cdVelemental volume1.1.2bEconstant of motion5.2.1EYoung's modulus or the modulus ofelasticity9.1E, Eoelectric field intensity1.1.1a, 5.1.2dE,magnitude of armature voltage generatedby field current in a synchronousmachine4.1.6aEiinduced electric field intensity7.0e11, eijstrain tensor9.1, 11.2eijstrain-rate tensor14.1.1aFmagnetomotive force (mmf)13.2.2Fforce density1.1.1aF0complex amplitude off(t)5.1.1amplitude of sinusoidal driving force9.1.3fequilibrium tension of string9.2driving function5.1.1f, ffe,fSftfi lforce2.2.1, 2.2.1c, 3.1,5.1.2a, 3.1.2b, 8.1,9.1farbitrary scalar function6.1f'scalar function in moving coordinatesystem6.1fthree-dimensional surface6.2fintegration constant11.4.2aGa constant5.1.2cGshear modulus of elasticity11.2.2Gspeed coefficient6.4.1Gconductance3.1gair-gap length5.2.1acceleration of gravity5.1.2c, 12.1.3g, g(H, H., H,, Hz)magnetic field intensity1.1.1ahspecific enthalpy13.1.2I, I, (I, i)s), ifelectrical current10.4.3, 12.2.1a, 4.1.2,6.4.1(i, i, i2,.. . , ik),electrical current2.1,4.1.3, 6.4.1, 4.1.7,(iar,ias, ibr, ibs),6.4.1, 4.1(Of,it),('r,QsAppendix ASymbolMeaningSectioni,unit vector perpendicular to area ofintegration6.2.1i,unit vector normal to surface ofintegration6.2.1(i,'I, U, (ix,is,2is)unit vectors in coordinate directions2.2.1cJ,J1current density7.0, 1.1.1amoment of inertia5.1.2b, 4.1.1, 2.2.1cJ, J )products of inertia2.2.1cV-l4.1.6aKloading factor13.2.2K,K1surface current density7.0, 1.1.1aKlinear or torsional spring constant2.2.1aK, induced surface current density7.0k, ke, (kr, k,)wavenumber7.1.3, 10.1.3, 10.0ksummation index2.1.1kmaximum coefficient of coupling4.1.6bk.nth eigenvalue9.2(L, L2, (La, Lf),inductance2.1.1, 6.4.1, 2.1.1,L,, (Lo, LR),4.2.1, 4.1.1, 4.2.4(L,, L L.0) ),L.length of incremental line segment6.2.1value of relative displacement for which2.2.1aspring force is zero1,1,, 1,lengthMHartmann number14.2.2Mmass of one mole of gas in kilograms13.1.2MMach number13.2.1Mmass2.2.1cMnumber of mechanical terminal pairs2.1.1M, M,mutual inductance4.1.1, 4.2.4Mmagnetization density1.l.lammass/unit length of string9.2Nnumber of electrical terminal pairs2.1.1Nnumber of turns5.2.2nnumber density of ions12.3.1ninteger7.1.1nunit normal vector1.1.2Ppolarization density1.1.1aPpower12.2.1aPnumber of pole pairs in a machine4.1.8ppower per unit area14.2.1pressure5.1.2d and 12.1.4pe, Pg,pPm,Prpower4.1.6a, 4.1.6b, 4.1.2,Qelectric charge7.2.1aq, qi, qkelectric charge1.1.3 and 2.1.2, 8.1,2.1.2R,Rj,Roradius4.1.6bGlossary of Commonly Used SymbolsSymbolMeaningSectionR, Ra, Rb, R,, Rr, R,resistance(R, R,)gas constant13.1.2Reelectric Reynolds number7.0Rmmagnetic Reynolds number7.0rradial coordinaterposition vector of material2.2.1crposition vector in moving reference frame6.1rScenter of mass of rigid body2.2.1cSreciprocal modulus of elasticity11.5.2cSsurface of integration1.1.2aSnormalized frequency7.2.4Smembrane tension9.2S.transverse force/unit length acting on string9.2complex frequency5.1.1slip4.1.6bs,ith root of characteristic equation, a5.1.1natural frequencyTperiod of oscillation5.2.1Ttemperature13.1.2T, T, T, Tem, Tm,torque2.2.1c, 5.1.2b, 3.1.1,To,T,4.1.6b, 4.1.1, 6.4.1,6.4.1surface force8.4mechanical stress tensor13.1.2the component of the stress-tensor in themth-direction on a cartesian surface witha normal vector in the nth-direction8.1constant of coulomb damping4.1.1initial stress distribution on thin rod9.1.1longitudinal stress on a thin rod9.1.1transverse force per unit area onmembrane9.2transverse force per unit area acting onthin beam11.4.2b1.1.1time measured in moving reference frame6.1gravitational potential12.1.3longitudinal steady velocity of string ormembrane10.2uiinternal energy per unit mass13.1.1surface coordinate11.3uo(x -xo)unit impulse at x = 9.2.1zoutransverse deflection of wire in x-direction10.4.3u_-(t)unit step occurring at t = 05.1.2bV, v,velocity7.0, 13.2.3Vvolume1.1.2V, Va, V1, Vo, VIvoltageVpotential energy5.2.1Appendix ASymbolMeaningSectionv, Vvelocity(V,V1. V.k)voltage2.1.1v', (vC, Vb, vc),voltageVp,Voc, VjUnvelocity of surface in normal direction6.2.1Voinitial velocity distribution on thin rod9.1.1V',phase velocity9.1.1 and 10.2vrrelative velocity of inertial reference frames6.1VsV~flm for a string under tensionf and10.1.1having mass/unit length
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