MIT 6 003 - LECTURE NOTES (8 pages)

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LECTURE NOTES



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LECTURE NOTES

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Pages:
8
School:
Massachusetts Institute of Technology
Course:
6 003 - Signals and Systems
Signals and Systems Documents
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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 terms Appendix F GLOSSARY OF COMMONLY USED SYMBOLS Section references indicate where symbols of a given significance are introduced grouped symbols are accompanied by their respective references The absence of a section reference indicates that a symbol has been applied for a variety of purposes Nomenclature used in examples is not included Symbol A Ai At A A a a a a ab a b c a1 a B Br B B Bo B0 Br Bra Brb Br Br Bri av b b C C Ca Cb Co C C C C Meaning Section cross sectional area 5 1 1 coefficient in differential equation complex amplitudes of components of nth 9 2 1 mode cross sectional area of armature conductor 6 4 1 8 5 1 spacing of pole faces in magnetic circuit 13 2 1 11 4 1 phase velocity of acoustic related waves 12 2 3 Alfv6n velocity 11 1 Lagrangian coordinates constant coefficient in differential equation 5 1 1 instantaneous acceleration of point p fixed 2 2 1c in material damping constant for linear angular and 2 2 1b 4 1 1 5 2 2 square law dampers 1 1 1a 8 1 6 4 2 magnetic flux density 7 0 induced flux density radial components of air gap flux 4 1 4 densities 6 4 1 radial flux density due to field current 8 5 width of pole faces in magnetic circuit half thickness of thin beam 11 4 2b 1 1 2a contour of integration 2 1 2 7 2 1a 5 2 1 capacitance 9 1 1 coefficient in boundary condition 11 4 the curl of the displacement 9 1 1 designation of characteristic lines Glossary of Commonly Used Symbols Symbol C c D d da df dl dT dV E E E Eo E Et ell eil Fij F F f fP fffFo ifff f fi f ff G G G G g g g H H H h I 1 it I lf i il i4 ik ia ia br i0 ia iYa ib id if id Or id Section Meaning specific heat capacity at constant pressure specific heat capacity at constant volume electric displacement length elemental area total elemental force on material in rigid body elemental line segment torque on elemental volume of material elemental volume constant of motion Young s modulus or the modulus of elasticity electric field intensity magnitude of armature voltage generated by field current in a synchronous machine induced electric field intensity strain tensor strain rate tensor magnetomotive force mmf force density complex amplitude off t amplitude of sinusoidal driving force equilibrium tension of string driving function force arbitrary scalar function scalar function in moving coordinate system three dimensional surface integration constant a constant shear modulus of elasticity speed coefficient conductance air gap length acceleration of gravity magnetic field intensity specific enthalpy electrical current electrical current 13 1 2 13 1 2 1 1 1a 1 1 2a 2 2 1e 1 1 2a 2 2 1c 1 1 2b 5 2 1 9 1 1 1 1a 5 1 2d 4 1 6a 7 0 9 1 11 2 14 1 1a 13 2 2 1 1 1a 5 1 1 9 1 3 9 2 5 1 1 2 2 1 2 2 1c 3 1 5 1 2a 3 1 2b 8 1 9 1 6 1 6 1 6 2 11 4 2a 5 1 2c 11 2 2 6 4 1 3 1 5 2 1 5 1 2c 12 1 3 1 1 1a 13 1 2 10 4 3 12 2 1a 4 1 2 6 4 1 2 1 4 1 3 6 4 1 4 1 7 6 4 1 4 1 Appendix F is i i t J i2 is 3 J Ji j K K Kf K Ki k k5 kr kj k k k L LI L2 La Lf Section Meaning Symbol unit vector perpendicular to area of integration unit vector normal to surface of integration unit vectors in coordinate directions current density moment of inertia products of inertia loading factor surface current density linear or torsional spring constant induced surface current density wavenumber summation index maximum coefficient of coupling nth eigenvalue inductance Lm Lo L2 4 L L 0 L L PsOPoa PMPr length of incremental line segment value of relative displacement for which spring force is zero length Hartmann number mass of one mole of gas in kilograms Mach number mass number of mechanical terminal pairs mutual inductance magnetization density mass unit length of string number of electrical terminal pairs number of turns number density of ions integer unit normal vector polarization density power number of pole pairs in a machine power per unit area pressure power Q q q q electric charge electric charge R RA Ro radius 1I 1 1 M M M M M M M M m N N Pn nt n P P P P P I 6 2 1 6 2 1 2 2 1c 7 0 1 1 la 5 1 2b 4 1 1 2 2 1c 2 2 1c 4 1 6a 13 2 2 7 0 1 1 1a 2 2 1a 7 0 7 1 3 10 1 3 10 0 2 1 1 4 1 6b 9 2 2 1 1 6 4 1 2 1 1 4 2 1 4 1 1 4 2 4 6 2 1 2 2 1a 14 2 2 13 1 2 13 2 1 2 2 1c 2 1 1 4 1 1 4 2 4 1 1 1a 9 2 2 1 1 5 2 2 12 3 1 7 1 1 1 1 2 1 1 la 12 2 1a 4 1 8 14 2 1 5 1 2d and 12 1 4 4 1 6a 4 1 6b 4 1 2 4 1 6b 7 2 1a 1 1 3 and 2 1 2 8 1 2 1 2 Glossary of Commonly Used Symbols Symbol Meaning R Ra Rb Rf Rr R resistance gas constant electric Reynolds number magnetic Reynolds number radial coordinate position vector of material position vector in moving reference frame center of mass of rigid body reciprocal modulus of elasticity surface of integration normalized frequency membrane tension transverse force unit length acting on string complex frequency slip ith root of characteristic equation a natural frequency period of oscillation temperature torque R R R Rm r r r rm S S S S Sz s smT Si T T T T TP Tem Tm To T t t U U It U a X0 u 1 t V Vm V V VP V V V surface force mechanical stress tensor the component of the stress tensor in the mth direction …


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