Formula_Sheets_for_Exam_1

Formula_Sheets_for_Exam_1 - Coordinate system Unit Vectors...

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Unformatted text preview: Coordinate system Unit Vectors Coordinates Cartesian to Cylindrical F3: iCOS(¢)+ S’Sin(¢) p = x E + y 3 (132-02 3111((1) +§Icos(¢) ¢ = tan _1[L] 2 r 2 x z = z “=‘ _” x=pcos(¢) Cylindrical to Cartesian x pcosm) (fsmwa y = p Sin (‘3) §=fisin(¢)+¢cos(¢) Z _ . 2 = 2 _ f:fischosQ-JrSlsinesin¢+icosfl 9 co |[ z J . . = s ——-——-—-— cartesmn to Sphencal 9: icosecos¢+Srcosesincp—isine Vx'” +2— A _ 4 y ¢=—xsin(¢)+§cos(¢) t-w" [:J i=Psm6cos +écos€cos —Asin _ Spherical to Cartesian ¢ A ¢ ? ¢ y — rsm(9)s:n(¢) SI=Fsmfisin¢+Bcosfisin¢+¢cos¢ z=rcos(e) 2: fcosflmésinfi (i’E-f)=sin9cosq) i ézcosecosq) :—sm¢ (fi‘§)=‘305(¢) :_Sln(¢) ()2 3:0 (§.f)=sinesin¢ $7 é =cosesinq) =COS¢ (9'6):Sin(¢) 39056?) (y‘i)=0 (fi-f‘)=cose 2 6) =—sin9 2-$)=0 (2:920 24;} =0 (2-2)=1 ‘ WWWWWWWWWW‘WM” imminmm. WWWWWWMWWWWW wwwwwmm.Wmmmmmmmmwmmmmmwwmmv—w' WEfiQFflE? eewmwee Cartesian Coordinates (x. y, z) A = Axa, + Ayn, + Aznz 61/ 6V 6V VV = Eax+$ay+gm v . A = LA: + e: + air a): fly a: a, 2-,, 3x V x A = i a a 6x By 62 Ax A, A, fife--2422 eke” wanna 8y 62 62 6x ’ 6x 6y ‘ 1 1 2 vii) = 9.! fl 9,}: + ., + (it: fly El:2 (1) differential dis—placement is given by di = alxaI + dya, + £123, (2) differential normal area is given by (3) differential volume is given by dv = dxdydz Cylindrical Coordinates (p, :15, z) A = Apap+lt¢a¢+maz 9V 16V 5V VV = —a +—-«-a +—— 6p " p345 "’ 323‘ la 13A 314 V A = m__(A +__£+_.t pappp) paqb 62 2,, p2,, :11 WA =11 i .6. p 6p ad 62 16, 6A, 6.4 at, l a M = ____ __ __h -mee [p 6:15 .3213" [.32 ap 39+ 6pm“) 51¢ '1. 2 Viv =ia(pav) 126”; all: 133.0 3P pad) 62 WWWWW‘WWW (1) differential displacement is given by cl! = elm-Ip + pddua¢ + dza, (2} differential normal area is given by (15 = pdqbdzap dpdza¢ pd¢dpaz (3) differentiai volume is given by Spherical Coordinates (r. 6, (1)) A 5 Arar+Agflg+A¢fl¢ _ av lying + 1 E W _ ar 8' r36 9 rsinflaqba" la 1 a _ 1 Milk - : ——» —A a + — V A r23r(rA')+rsinflal9(6sm) rsinflada a, ma (rsin9)a¢ 1 a a a VXA = «- —— M risinfl 6r art! 39 A, Ma (1‘ sin 9) Ad, 6A 1 131% a = .1 [imls‘me———‘1]ar+»~[————(m¢)]as r sm 6 63 6:1: r sin 8 all Br 1 a 6A + “it (rAg) — 3,; 1 9 av 1 a av E 32V 2 _ __ _ _ M _ V V ' r2 er (’2 Br) r2 sm 9 39 (51“ a .36) r2 smz 3 ad): ! (l) the differential disPIacement is (11 = dra, + rdflaa + r sinfldqbaé (2) the differential normal area is :15 a r2 sinfldfla‘daar r sinfil dr dqb as 1' dr £163., (3) and the differential volume is dv = ,3 sinB air all) dd; WWW ...
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This note was uploaded on 10/19/2010 for the course ECE 280 taught by Professor Mukkamala/udpa during the Fall '08 term at Michigan State University.

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Formula_Sheets_for_Exam_1 - Coordinate system Unit Vectors...

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