lecture18 - SGLJHQN 0F" wAve—Bobv INTERACT/0N...

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Unformatted text preview: SGLJHQN 0F" wAve—Bobv INTERACT/0N PROBLEMS a Two ‘WPES OF uwwE Boov (VIEW/PACTVON PROBLEMS A25 E—UQouAfl‘ERED FrzaQuaJ—rw w APPLICAT(ON$‘ AND so LVED 87 71—15— METHODS DE3CEIBEO IN THIS SECTION ZEROQSPEED LIVEMZ wAVE BODY WTEEACNOMS (N THE FREcQUEMCv DO‘HMM ,.—~ 1M 21‘.) AND SD FoEMAfiDvSPEED SEA KEE PING PEDBLEHS IN THE FREQUENCY W‘HHSDONAIN HU ,— (HEEE DNENSWNS C LINEflFE <1 NONLlwaqe) 6 A CGMSENSUS HA: BEEN REAcHEOOVEeTm—Z (PAST T000 DEC/H353 THAT THE HOS‘T EFFKVW Am) ROBUST SOLUTION METF‘EODS‘ A25 BASSOON GREENS THEOREM USrua an! ER A come-Souch VOTEU‘TIAL GK THE Kafmmme swear/*3 THE GZEEM FUNCTIGNe.» 0 THE N UNEfizQH, Soufle OF‘THE RESULT—(HQ INTEGRAL. EcQuATmus w FRAcTzcE (S m ALHOJ‘T ALI, CASES CAKQIED XOOT BY PANEL METHODS. x L l ‘ FREcQU‘E-NCV—IDOHAIN IZADIA'now—DIFF/PALWOM 02c; ____~_________________________ EOQMDAW~VALUE Przozsuau: :2 = waif" OUTS?me me9 W Z A9 {C 4 DO VZLP t ‘94:" Y3}, ) £21, ,6 3 EADIA'UON 1 @ GREENS T245025»! 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Qszia: G GREEN EVA/ACTION VALuE AT FOHU—T >< DUE m A Sm CULARITY CENTERED AT P02th ‘g; .Two TYPES OF C({eeg—M FUNCTIZHUS (NH/L (323 o EAMKWE Somme; VXG—Tb JAN: 4 u—L v!"— GCX1€)=—~«/x—‘g\— CW 475 2 ~:; {(X-E): (7~H)L+[2-§)Z§ ~—. .— [/2 MCB’Tc; THAT THE FLUX OF FLuao EMlT‘TE—D ,.._> Haw g [S EcQuAL‘tO 1.0/6sz?) — THxs KAN}:th SOURCE AND 1T3 GRADIENT ban-H RES‘PECT To E CDH’OLES) IS THE; CREE—M FWCTION TH—AT wlLL (35 USED IN THS$HHD SEA KEEPm/C ‘Pfio B LEM @ HAUEL—Ocu’s ooAvE SOUIZCQ PUTEUT/AL ...ALSO rwoww AS THE 020 WAVL-ZG‘REEM FuwCTzow lN’THE Fmewuewu DWAIIV. _” 9A‘TISFIES THE FREE S‘UfZF-‘ACE CON Dl'TIOiU “‘5 Am; New“: 2:0 BEHRVES‘ LIKEA RANK/ME gouficg : [MAQEABw-r %=o T145 FoLmer-ua CHOtQE Fog Q<><f§§ SATzSFIES THE LAFLACE EQUATION AND THE FREE—50 {CFAcc-I CoMDIT(O‘f\J3 ‘ .4 —" __ __L __[_‘ +_4__ GCX)§\’”4T<V °° Ci Luau”) __ k i. 8 Team.) 2.7: O u—K, T001423: BESSEL «FUNCTzo—r/ OFsz—DEK £520 \D» : Comwfi (NDEN’TEDABGVE 1,701.5 14:1»; VEKIF‘I THAT WITH RES‘PECT 17) THE ARCuueu-r ’51,, THE VELOCITY PWEMTML LPL(§)3G(§5§) SATISFlas THE FQEE S‘UKFACE CON DITlON .- 3-2 I ‘l ._> '4 __.._r x—a LP: N 4? ’ E AS Lac—>03: ~ k(%+§) (7.) GA, _.£L La 8 HO (NZ) (7.] . ” CUHEKE Ha (tea) :9 THE HANKEL Fuwcnw 0+ THE SECOND bum“) AND “2059. ZERO . As W390i“ (2,) , ‘L(k’2"‘:“r3 H0 (102) N 2‘ e #— «FCC/K) 7tka 0 “(Half—,ng THE REAL VELOCL'CY FU—rEwT/AL REPZESEN‘TS‘ mamua'zwa cum) es 0F THE FoRM {mt—m) , A DC 6 Hch §ATISFYHUG THE (ZAP/H‘UOM .C<>worrzcow....w a A SIMILAR FAIZ~FIELD RADIATION CONDITION (3 §ATlSFIED BY THE VELOCITY Pche-M‘UAL L91 L32) :5:— LPG-2f I 4 kz—ikfl LQ1~(/L:::3”Le +004) [T Fa LLOUOS THAT ON $90? (3.3.: '5‘“ -qu), ._ .- v — ‘ ’bn w: “Bsz . o M: H :___ a 14 .._ in ?R Q; *THEQEFO 253 BED; 1% - _ Let .bn_L‘P?-§;’_= “’ (LPILPZ—LPZLP1)—O ‘ , -3 00m: ERLCDRS THAT DbCAY LIKE [Z [2, HENCE FAb’TEK THAN K ,meH 15‘ THE Risa; AT meH THE SUKHCE SA, GrZowS AS 119%.; O [T FoLLows THAT UPON APPLICATION 0P CAP—556$ THEOREM ON THE uuxmoww Pcfl—EWAL L94 Eclo AND THE wAue GREEN FUNCTION (97,-; C; ONLY THE INTEGRALS oveav SB AMD Se $0szvE. O OVER $14 ) By VIflTUt: I B '37: OF THE BOUNDARY CONDlTwN IF THE cum-512. DEPTH (5 thTE OR Yip; —=;o, bike—>5 A5 3% 7:% 757—) ~00 '8‘! .VHZTUE 0F THE VANIS‘H'VC OF THE EVESPEC‘Twe Fww VELOCITIES A—T Mags DHTHS‘. <5 THERE Keumws'ro IwaePBE—r AND EVALUATE THE INTEGRAL ova: Se AND 38, START 031'”! Se 3 NW5 THAT THE twee 24L ovae Se Is muse Tue 3? VAmABLE MTH ‘g Bewa 7H5 FIX€D Pow-r Du HERE-THE Saunas (S CENTERED. , 4-7.:r “an Er 41W” L? —_.> LN?) .—_ LPG?) A: 5—90 326—)? H! THE. LtHITAS V390) ‘THEIUTEGRANDOVER ‘THE sPHErzE Se BECoHES SPHeezCAw/ S'YHHETIZ1L AND wlTH VANISHING Efiaofis w SUMMARY: LP(§ 7r” E”): 5:5 _ om SB: ELF = V00 2 koMM FRoH THE “MIX BbuupNzY CONDITION OF THE {ZAmerom AND D1FFIZACTmN PROBLEMS e \T FoLLows' ‘THAT A 125LA‘TmNsm P z: OBTAINED BETWEEN THE VALUE (5 F LN g) AT 305,45 POMIT' IN THE FLUID“ ooHAw AND ITS‘ VALUES LP 0?} Am) NOKHAL DeemATmES OVER THE BODY BOUNDARY 1' ~‘ ‘ a AS : mgwgiw T x X K GARE) Vb?) 45x 33 . I b 3TATED DWFEREUTLY) [CMDUULEDGEOF LP AND 37:70 oven THE BODY Bovup'mzv ALLOwS THE DETEEH7UA'TMN 0‘: q) ,wp UPoN biFFeeEwTI/rnow QF Vg? m TneFuuvo DOHAwJ; lu maven ‘TD DETERHHUE Leo?) on “me 809‘! BOUNDARY 5’13 ,31HPL‘I ALLow- E'A 98 IN WHICH CASE THE SPHERE Se (35cc; Mes A, V; SPHERE A5 eeo : \Se ‘ .f.‘ 0 NOTE THAT ‘gl w A FIXED POINT-WHERE ‘THE Pmm’ murace :9 cam-green Am; 32 is A DDHM‘I IMTEfiQA‘TION VA ENABLE Nowuz; muse THE 1500‘! eouumev 3,3, 0 THE Reoumom 0F GREENE THEOfPfEM Dazpr Agave SUEVNES ALMOST lDEUT/CA-LLY waH A FACTGf at: ya New MULTIPLY/IUC “me I; INTEG ram, syncs (mm ’/2 OF Tm»; 36 squ 06 L153! N ‘THE Puma Dmme w THELIHlTAS é—>o AND P02 A Baby §uIZFAce our—(mu :3 SfHocJ'TH . (T FOLLOWS ’ THAT: d wHaze Now 80TH >< A-MD “E we om "We I Bow war—Ace. THIS Becomes AN INTEGKAL ECQUA‘TION [:08 UN?) OVER A SUEFAQE $8 or $ouwoer> EXTBUT . (Ts sow—now [S CAEKIED 001' thH PAMELHETH®D$ DEScezggo 851,0“;— ,1 THE INTERPRETATWM OFTHE DEPvUA‘Tn/g UNDER THE MUTEG EAL S‘IGN‘ IS AS FOLLOWS‘.‘ ‘bnx x X — l .2. .9. A “ =(n1}x+n2}a+v/332\ Gch'g’) couture DEEWATNES M25 “('4 KEN 0027 THE WEST AKCUHEMT FOR A PmN-rSzpufice came—Ra) AT ‘Q ’ . (Poim INFINITE DOHArN PJTEMT/AL 1:on soufnoms .Mfi—u IN THE ABSENCE OF THE: FREESURFACE) THE; Demwrmm 0F THE CREE-M IUTEGML EcQUHTloN RWAINS ALMOST umcwuaeo usw (“2‘ @202): — —L (52%" 4m :— GBng‘) THE EAMLUME Somme AS THE GREEN FUNCTION AND WIN THE PfiOFEféTY THAT As {2—390 / Fem CLOSED BouppAaues SB Dorm NO SHED Tue zesuvrwa (NTEG EAL ECOUA'TIOM FOR CPU?) ovaz THE Boov BoUNDARY BECaHES: BGC 33; Ci; BAX X o Jig?” j] L952) s3 cum: -VL§): 2;? EXAMPLE! UyNtFoRH Fww PAST 35 “J 5.) UsUL i gs 1(\\‘ SO THE EHS‘ OF THE GREEN ELQUH‘TION BECOHES“. 12H: = Sfl 652;?) (~Uw,,)clsx ._ 33 . ...
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.24 taught by Professor Pauld.sclavounos during the Spring '02 term at MIT.

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lecture18 - SGLJHQN 0F" wAve—Bobv INTERACT/0N...

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