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# Lecture12 - Figure 3-16 Interrelationships between...

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Unformatted text preview: Figure 3-16: Interrelationships between Cartesian coordinates (x, y, z) and cylindrical coordinates (r, 4), 2). Figure 3-17:AInterrelationships between base vectors (in f) and (f. ¢)- ® 6“: @36924- and} la éc‘de? 1 Co§z¢§+smrb®3® a @ (gammaped ma NOTE ' ® 1(- SNM ("SKW — SWYQ QbsdDX + g‘nlch La QB) (7.2»:erst Ar EDCCbQD =~sm®®\$di §+ cole-Wab @ AV = Ax®\$¢ +A\j \$\(\Cb A4; = ~Ax \$§ﬁ<b +Ay<o\$<b Mnsgcrm —' A 6% A=Av\$ +A¢¢+Azé Ax = AVCoﬁdi’ AQSkXC‘Q Ax, : AVéWWQ +J‘\<\) CG\$<D Figure 3-18: Interrelationships between (x, y, z) and (R, 6, 43). AQ ® m. C Am + 1Q A6 Aao é mw @ A6 + AU0 AON 4 [email protected] AK 9 Aphm % Awo a = : Ax? Aka A¢A® Q m+ AGAG mm as; 6 :m ++s AKADN. ¢ wﬂﬁa age :: aam A9 2 km @555 'L‘ Aymseglﬂd) " #43308 k A30 : «Axsmd? *AYCOSC‘D K Ax = AﬂémeCQﬁD+AeCO\$9Coscb - Amsmcb ' AY : AKSIHQ \$If‘xd3 +Ae®£ \$10®~+ A¢CO\$¢ A2. a AKCOSQ ~46st Cxl \xnc3v<m\ 3V0 SPMCRCQ\ Tmmsccxmaﬁon 3 Figure 3-18: Interrelationships between (x, y, z) and . (R.0,¢)- Ar : AK\$me +AeCose AZ 9 AK (0&6 —' qusme M = M 3-3 TRANSFORMATIONS BETWEEN COORDINATE SYSTEMS 125 Table 3-2: Coordinate transformation relations. Coordinate Variables Unit Vectors Vector Components Cartesian to cylindrical Cylindrical to Cartesian Cartesian to = fr sin 0 cos¢ spherical + 3'sin 0 sind) + icos 0 9: icosecosd) +9cos0sin¢ —isin0 \$ = —isin¢ + S'cosd) Spherical to x = R sine cos¢ i = Rsine cos¢ Cartesian +§cost9cos¢ —\$sin¢ y=Rsin0sin¢ 9=Rsin0sin¢ +§cos0sin¢ +\$cos¢ 2=Rcos0 —§sin0 Cylindrical to it = fsin a + 2 cos 9 spherical 5 = i- cos 0 — 2 sin 0 «3 ti Spherical to cylindrical A, = Ax cos¢+ Ay sin¢ A¢ = —Ax sind) + Ay cosd: Az=Az Ax = A,cos¢ — A¢ sin¢ Ay = A, sin¢+ A¢ cosd: Az=Az AR = A, sinecosd) + Ay sin0sin¢+ Azcose A9 = AJr cos0cos¢ + Aycosesin¢ — Az sine A4, = —Ax sind) + Ay cos¢ A, = AR sin0¢os¢ + A9 cosecosd) — A4, sin¢ Ay 2 AR sin0sin¢ + A9 cos0sin¢+ A¢ cos¢ Az = AR cos0 — A9 sine AR = A, sine + Azcose A9 = A, cos0 — Az sine A¢=A¢ A, = AR sin0+ A9 cose A¢ =A¢ Az = 14126089 — A9 Sine i @mxw cg a sum PM ® I . \$Cq\c1\‘ Qdd °o Tm emfwﬂ— eﬂ‘ T as q Cundrkcm 6‘; “ﬂaw? 2‘ RXth 0“ Change— 09 T we?“ \QQ\%\¢\‘\‘ :. ﬂ d2. Mm.) Cmﬁdu‘ f \Quhﬁ q Qunc\im 6Q Xﬂﬁfzr. Membed \n \Ums o9 ' In Quiver Cc\\m\us cog use 3 Qndqm’wb \ +0 dgﬁﬁnbe &\'QCQCU\*TQ\ SPOCHCA UQﬁqX—cng O?Q¢q CV3 Che \$©\QV\$ pd Cadre? , 0 G 3 c9 Ogmd\m+/ dxvmamm de cur\ owFCﬁ‘cfS P2(x+dx, y+dy, z+dz) Figure 3- 19: Differential distance vector d] between points P1 and P2. 116‘; U312) 0‘5 W9 q\' P\ T6<+d>gué+ Au&,1‘r37_3 \5 km? 01* 92 &X A\),c\17_ om. Comm a? \$\\‘Q‘Q€£e.h*\q\ AmehL/L Vector di: mh+%éﬁ+nﬁz The. dKQchm’n‘ c1\ 1m patchm 1% 2 M .-.- 1m z'é:\$‘*£:&8*§:dz Bx &% BL Coﬁcsmémak to oaks? drum??— “‘ Pom‘ﬁom AL éVQA\U\-\- (39 T v T : %<‘QC3T AQA / citodkh¥ 09%:ka NOTE : émAxm‘r ORR-ﬁe? \Hcﬁ no @Nsimx mszmk by \JVEGXQ’ I r\- oc\*\*qm\$ Q §>\\\l SEGA mmn‘rﬁz OﬂCL l3? ORQQXVC\$ On Q may)? \DhqstcA quen‘vd'be‘. The, mam/«“739 W ope¢q~*\c(\ \S Q Uec,\-c¢ (Amuse Wﬂnx’ruok. 5 QchA +6: +\ru. mammum rcérv. o9 QNOQ‘L 39 W PVK‘QCCA quam‘nhg QU‘ unﬁr dxsstnLLJ and wheat aoruhcﬂ \b o‘\on5 ﬁrm. chmcén’on O‘Q‘ mwxmum {anac‘SQ \Q a = AZ 2% JMMW m o\\mc}r'\cnc.\ Asmwoémﬂ- o\0<\§ a 1; [5 95., ,A AL“VT cm. .- 1:? VT \5 \LWDJUJC Cm 90\$ 6; ‘TD "Hﬁﬁ— ® JVWVQSTQXVUVC— &\Q‘Q€£U\U_ \Oerwmﬂ V? S K) 3 § 1 \ é) VOCXQOBV G «aros‘ov \ C \ 5M Mﬂmk * CW 2 vTa CW (Lab d¢erd \n CQV\‘L5{Q('\ Coo \AV Smokd be, wo\\6 \ﬁ ohxl <3?kach Véumk Sq :km E“)? m\ W\M\C \$\[\$\'€N VT: 9:; + \$ch +gjé 3% \$2— 5: gig; gAaw—xgt swam 5“ a? 5x 86) av 37. 3y emu, Z ts oerognacA *OX/ M \OL‘S‘T +£sz Q ﬂag“ V: X2*%2 Jmﬁ Cb : 0%. 6V Co cg: =_—( s¢~ \ ¢:‘:C;X +(é; .smdﬁib CQQ 23 ——\— 2 " t buA‘ (CCQ\\ “*HQ‘BV .' C7) —L- W 3PM“ Qq\ COOVc§\f‘Q\{\$ ”Baa. QVQAWRB“ "5 QKLD \Ox/ AV\(\€L Qo\\csug\ﬁ% (—XYQ‘ﬁimg \JCOVQRHLB & m 6mm Opemxmx‘ U, \/ are. «530? Qméxxom TN. oyoA'an‘v 053 q wuércr V: thh&\lb\$ ...
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Lecture12 - Figure 3-16 Interrelationships between...

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