lecture9 - LIN EAR WAVE— BODY )WERACTIONS o ConoEe A...

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Unformatted text preview: LIN EAR WAVE— BODY )WERACTIONS o ConoEe A PLANE PFZOGRESS‘IVE REGULAR wAvE {MTERACUNQ ooz'rH A * FLoATINQ 8007 (M Two DIMENS’MHUS, 9 THE HArw CONCEPTS guewve ALA-{097' wLTH ND CHANGE (v THE MORE PRACTICAL THREE—DIMENS‘IQNAL PEoBLEH , [3%) L gEgm -~ ——o~v --'- I’m -~ EGG} Ems) \\\ \\\\\\\\\\'\\\\\\\\\\\\\\ \\\ AMBIENT (NAME E—LEvA‘T/(DN. REGULAR 01a (LAmDo—M OJITH DEFINITWNS To BE GWEN BEww‘ E (a o. 2.4%) 3, “800‘! SURGE DISPLACEMENT Egvc) ': BODY HEAVE DISPLACEMeMT .S406): 800‘] ROLL; DISPLACEMENT LwEvua THEORY © ASSUME: /3%x/=:O(£) <‘</ SMALL. WAVE §T56PNES§. veky qu ASSUMP'UON Fotz GRAw'Ty WAVES (N HOST CASES ,EXCEPT com-EN WAVE-S ARE NeAe BREAKING CGNDITION§ 0 Assoua 1l'?;‘,/A[=CDC£) <<l fl§M[=O&)«I IE4! =O(s) <<( These AssuHPT/oms A25 VALID w HOST CASES Auo HOST BODIES OF PEACTICAL. IUTE-fZEST, UNLESS THE VESSEL. RESPONSE AT KES‘DMANCE ls HIGHLY TUNED 0T1 24¢wa DAN-PED.TH13 13 OFTEN THE CASE FOR EOLL' <0 HEN A SMALL AMPLITUDE wAUE rm’LaeAcTS iaer A ‘VES§EL (nemcw VAH?EDIN KOLL.__ 0 THE \JESSEL DYMAch (ZES‘PONSES‘ IN wwegww BE MODEL—ED Accotzowa To LlpE—AR SYSTEM THEORY : \I II VES3LEL... :05) FHA/EAR Eff) T’HE HHEHNVARM DOMAIN i‘wt em”; 358 Famewcy 9‘UTCH OOH/MN ‘ RES - 1,—(w): 1965;13:5— AMPLJTU'Dt: O PERATCDR GAUSSIAN s [CHAL- 3713046774 259% uses [3y VIRTUE OF LlNEfirEIT?’ ) A RANDOM SEASTATE HAN BE REPRES'EN'TED AS ’THE LIN 849 $UPE~RPOSITI0N 0F PLANE P?OGRESS‘NE (UM/53; ACCORDING TU “we THEOPY 0? ST. DEM§ Am; PIERS‘ON) THE PHASES é; ARE RANDOM AND umFmaMLy 913116; swap RETWEEN <__,—C)7tj Rafa New we ASSUME THE-N KN WN Co NS‘TA‘LTE‘S3 Awe THE comesPowpwa VESSEL Rt‘SFONSES w HERE EEK (w) :3 THE COMPLEX 2A0 FOR M006 K. 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AS‘ FOLLowJ‘.’ SURGE pl“ Ew UL): X1C£)"A::§,’Alz gs“ “4143+ B.” E, — BIS E3"Bye+‘§q_ NAMELY HEAVE (1:3) AND mu. (5:4). HUS‘uH‘.’ F Lt: X ~ Z .‘ . W > K JEAKJEJJrBflgdi—ckdgfl 14:1231’4‘ THE ADDED~H4§S MATEIX AK,- KEPIZESEN’TS‘ T‘HE Aooeo meaTIA pug TO THE Accaearflow m: we 60W w wmea (mm ACCELERATION ' J C THE DAHPINC‘ HATE/K {3K3 Govefzws THE ENERGY DISSIPAT/ow w-r-o THE. FLU H> DON/MN (N THE. (—29er 0P smegma: WA us: 0 THE HflDQDSTATleZF/STDZING MATzzx ¥~CK5 REPRESENTS 'THE 575T5M STIFMESS Due To THE HYDQOS'TA‘TIC RESTG mum Peace: MOMENTS Foiz HAEHawc Mafiwwsj TH; MATRICES AKA AND {El/e; AQE FUNCTIONS aF cu Jog Ala; [60) , Coo) Tms‘ Fuwcmmwm FoeM emu. ~85 DISCUSSED Baow. 'T’HE HYDKOSTATIC HATRFK CH— 15 WOEPENOENTOF 00 Am) HAW 0F ITS ELEHEWS ARE IDENTICALL‘Y ECQUALTU 25420 COLLECTING TERMS (N THE- LEF'T" HAND SIDE AND Gems-nus {31H K3 THE Bony warn/4 M47121x; SURGE Z [—wz(H,5+A4J-)+I'w 8.; «LCM-331?; 2x44.» 3 ‘ , 3: I,3,’+ HEAVE V [‘UQ?’(H33‘ +A33‘B +1.0) + : X3610) J <' . ‘ (Jr-,2 321+ RoLL j u N43 THE EXTENSMDM oF—THESE ECQUH‘TIOIU S "m $tx DEGREES 0F FQEE-OoN IS STRAIGHTFOTEMARD How‘évaz BEFoee ozscosswa THE GENEEAI. CASE we (mu, $‘TUD‘I $PECthc ?on P501115; OF THE 20 P20 132,534 FOR THE SAKE of: Gwen-ml . CONSIDER A fioov SYHMEletc ABov-T T145 X:— FOR A Boov firms-rem. P0127 Km EBoAraD: o VERIFY TH"? HEAVEIS DEcouPng F1259“ soace AND ROLL. IN OTHER 0001633 THE Suace AND @oLLMUTwNS DONUTINFLUENQE HE'AV’E AND wce V5234: [wt/OZCH +A33>+ {00 1333 +C33] E3 =A . THE om»! NONZERO HYDEosTATlc COEFFICIENTS Mae C33 AND C44. veeum THAT THIS IS THE CASE EVE—M Foe NON—$5! HHETeec Sear/mus a SUR—GE AMD 20 [email protected] Cou PLED Fora SYMMETEICLAMD NON— SYMMETQIC 860:55‘ THE CDUPLED Ecpun'rlou 0? MOTION BECOMES; . DUI—{EN NMON'S LAN 19 5x91253350 AGO-J7- THE cemaa oi: GRAVITY: Hal—1.: H41 :02 H” = H > H‘H‘ = I6 CnHe'zE IG :3 THE BODY MOMENT OFmeva A‘SOU'FTHE CEAFI‘EROF GRAVITY. IF THE . EQUATIONS ARE TO BE ExPzesseo A6007" ‘THE ORIGIN OF THE coozowm'e S‘VS‘TEM) THEN ‘T‘HE FGENULA‘TION MUST START worm {ZESeECT TO G AND EXPRESSIONS DEENED own 0, VIA A CoogowATa—S TMNSFWHATIQN 6 THE EXCtTrMG Fof2c€3 >\<,, ) X3 A—IZE DEFINED IN AN oBvravs HANNE/e Auwc THE x- AND E+A7<E§ .‘THE raou, MOMENT X4 [3 DEFIKNED NWT/A LLV ABNTG, NEED To 05:2:sz DEFINITIONS FOR THE COEFFICJEMTS‘ THAT ENTER 1—145 HEAVE 2r suzce'raou. EcQUflTIo/US’ oF‘ fiCFTmN: a M: 94¢) 40L2VOLUHE OFLJATEJZ DISPLACEO Ev Baoy AlZcHrMEomM PRINCIPLE 0F ' TSUOYANCY ° C33: {Di/AV" : €38 Aw : Boov WATEZPLA—NE AREA : [5 (85AM w Two DIMENSIONS) . 3 x. ' _ , B _ R = 3 - mu, 1257-0122914 MDHEUT . (CM) \ % o/l'z. q DUE ‘TO A S‘HALLAUCULAR DISPLACEMENT Aew—T THE CENTER OF GRAVITY. VERIFY FOR ALL WALL X Now» (DALI, 5 “>60 SECTIONS. C. E C . C r . DERIVE AN 4% ( “JG 75C 4430 3 EXPRESSION FC’Q(CL+4) m Teens“: (CH) ' O 5*: G , ‘—" ...
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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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lecture9 - LIN EAR WAVE— BODY )WERACTIONS o ConoEe A...

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