Matematik fizika metodlari fanidan
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- Ελεφθέριος Φωτόπουλος
- 6 χρόνια πριν
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1 O sto Rspls Ol v o rt mss t lm vrlg Z.M.Bor omdg do dvlt vrstt FIZIK fdrs Mtmt f mtodlr fd m r mtlr Tvch: dots M.Nosrov do-6
2 qold. -mv. Krsh. Kompls solr v lr std mllr R:. Kompls sog shllr.. Kompls solr std mllr 3. Kompls sog drs v ld XVI-XVII srlrd mtmt f qdgg o shsh msllr chshd osh r o chg r -3+4= s= 3 l-5=? cos 4 d Bd qtlsh ch ompls solr tshchs rtld. Kompls so d- t hqq solr ftg tld v qdgch old: =+ o qdg o rshd tsvrld rd - ompls sog hqq -mvhm qsm. =R =Im = r Rsmd o r trd r cos r s 3 3 g qo s =rcos+s 4 gr Elr formlsg qo s =cos+s =r 5 = - forml ompls sog lgr shl - gomtr shl 3- trgoomtr shl 4- o rstchl shl dld. gr ompls so trgoomtr o o rstchl shld rlg o ls lgr shlg o tsh ch 3 formld fodlld sch o tsh ch s rctg r 6 Ifodlrd fodlld. -msol: Kopls so trgoomtr shld lgrc shlg o tls =cos/6+s/6
3 chsh: =cos/6=3/= 3 =s/6=/= = 3 + gr t ompls so rlg o ls Ko' ptrshvolsh Ko rstchl o rshd rlg t ompls sog o ptms topm: =r =r =r r + =r r cos + +s + 7 Dm ompls solr o rstchl shld rlg o ls lr o ptrsh ch modllr o ptrld rgmtlr qo shld. Xdd shgd t ompls so o ptrm: 3 =r r r 3 r =r =r cos+s 8 Kompls so - drsg o trsh ch modl - drg o trld rgmt s g o ptrld. gr ompls so =rcosφ+sφ o rshd os v g qo s cosφ+sφ =r cosφ+sφ B rd cosφ+sφ =cosφ+sφ 9 B forml Mvr formls dld. Msl o lgd cosφ+sφ = cos φ+sφcosφ-s φ=cosφ-sφ Dm cos φ-s φ=cosφ sφcosφ=sφ Kompls sog ld. r cos s r cos s =3 - o grvch Kompls sod - drl ld chqrsh ch modld - drl ld chqrld rgmt s π dvr qo shl g o ld. Msol: 3+I =? Ychsh: r= 3 4 φ=rctg/=/ 3=π/6 3+I = cosπ/6+sπ/6=5-3 Nort svollr.. Kompls sog shllr og.. Kompls solr std qd mllr rsh mm. 3. Mvr formls og 3
4 4. Kompls sog ld qd hsold? -mv. Kompls o grvchl fslr R:. Kompls o grvchl fslr. Kosh-Rm shrtlr 3. Trgoomtr fslr 4. Logrfm fslr 5. Tsr trgoomtrc fslr 6. Tsr gprol fslr 7. Kompls o grvchl fsd olg tgrl gr D sohd olg g hr r qmtg G sohd olg g hr r qmt ror qot o ch mos ltrlg o ls D sohd ompls o grvchl fs rlg dld v qdgch old: =f= f=+v= +v -fsg hqq qsm v- mvhm qsm dld. Msol: f= =+ = - - = - v= Kompls o grvchl fsg hosls d-fs ortrmsg rgmt ortrmsg stg rgmt ortrmsg tor o l l g tgdg lmtg tld. f lm lm Hoslg t rfd qdg shrtlr l chqd v v B shrtlr Kosh Rm shrtlr dld. B shtlr qotltrvch fslr lt fslr dld Msol:= = cos v= s v v cos cos s s Trgoomtr fslr S= - - / shα= α - -α / Cos= + - / chα= α + -α / fodlr l qlg fslr ompls o grvchl trgomtr fslr dld. B fslr hqq o grvchl trgoomtr fslrg rch osslrg g. Blrd tshqr t ossg g..b fslrg modl tor o lsh mm.lt Msol. s= s+=scos+ coss=sch+cossh rd cos= - + /=ch s= - - /=sh Logrfm fslr Kompls o grvchl logrfm fslr d =L g tld. B rd - ompls o grvch o l hqq mvhm ompls o lsh mm. B fs hm hqq o grvchl logrfm fsg rch 4
5 ssrlrg g. U hsolsh ch o rstchl o rshd om. L=Lr φ =Lr+L φ =lr+φ Msol:L=? Ychsh: = = r=φ=π/ L=l+ π/= π/ Tsr trgoomtr fslr Tsr trgoomtr fs d. =rcs. =rccos 3. =rctg 4. =rcctg lrg tld Ulr hsolsh ch rcs tsrs om. s== - - / g o ptrm = - = --= = L 4 4 L L L L rcs cos g o ptrm = -+= 4 4 L L L L rccos L - g optrs tg g o ptrm 5
6 L / g o ptrs L rctg L cos 4 rcctg s w L g o ptrm rcctg L Tsr gprol fslr Tsr gprol fslr d 5=rcsh 6=rcch 7=rcth 8=rccth lrg tld. 5sh== = - --= g o ptrm = 6
7 7 4 4 L rcsh L 6 ch== g o ptrm -+= 4 4 L rcch L 7 th= ch sh g o ptrs L ½ g o ptrs = l rcth l 8 cth= sh ch w g o ptrs =
8 w L ½ g o ptrs L rccth l I G Kompls o grvchl fsd olg tgrl d f d fodg tld. B rd G tgrllsh sohs. f=+v =+ I f d vd d vd d vd G B tgrl hqq o grvchl fslrd olg tgrlg rch osslrg g. Itgrlg ts tgrllsh sohsg o lg og lq. gr tgrllsh o lg osh v or rtrls stm-st tshs r sohg ld v tgrl qdgch lgld: C C f G C o l qold Kosh torms: hr qd lt fslrd r soh o ch olg tgrl g tg : d. Qdg tgrl or chqm d? o lgd fs rch sohlrd lt hsold. v tgrlg qmt tormg sos g tg o ld =- o lgd hol or;. c otrg tshqrsd. c otrg chd - hold otr chd fs lt o lglg ch hold hm tgrl g tg - hol ch -=r o grtrsh rtm v tomo hosls ols d r d dm C C d r d r d d. ctshqrd. cgchd Kosh formls 8
9 . d c d. tshq ch. f 3. d tshq. ch. 3 tgrl Kosh formls dld. Msol:. d C: =3 =3 4=8I - 4 tshq f.. d f ' B Kosh formlsg ts dld. 3 Msol. d C 3 3 =3 =6 =- N= t Nort svollr. Kompls o grvchl fs d mg tld?. Qd ompls o grvchl fslr ls? 3. Kosh torms tg.. Lor qtor. Mss qtlr 3. Chgrmlr rs 3-mv. Chgrmlr rs R: Lor qtor F=f +f +f 3 + += f. o rshdg qtor ompls hdl qtor dld. f=c +C -+C - +C = o rshdg qtor drl qtor dld. Drl qtorg hss hollrd r C - 9
10 f=f+f``+f`` +..= f! o rshdg qtor Tlor qtor dld. B lmtr fslrg Tlor qtorlr qdgch. = = s=- 6 cos=- +.= + = +.= 4 + 4!!! - =! Hr qq lt fsg Tlor qtorg osh mm v sch. 3 Msol: rcs -l =-l =-l = 4 6 6! Lor qtor d F= + c c c o rshdg qtorg tld. Lor qtor qsmd ort:. f = c - to g r qsm.. f c - osh qsm. c c... c Mss qtlr Fsg lt o lg qtlr odd qtlr lt o lmg qtlr mss qtlr dld. Mss qtlr ch l o ld.. Qtl o ldg mss qtlr. Bd qtd fsg Lor qtorg olmsd mf drlr qtshmd. Fsg qtdg lmt chl qmtg rshd. Msl: s F= fs ch = qtl o ldg mss qt o l g Lor qtor ' ' 5 s F= lm f= lm. -Mss qt qt dld. Qtd fsg Lor qtorg olmsd mf drlr so chl o ld. Eg tt mf dr qtg trt dld. B qtd fsg lmt chs o ld. cos Msl : f= fs ch = 3 cos lm f lm 3-trtl qtl hsold. 3. Mhm mss qt. B qtd fsg Lor qtor olmsd mf drlr so chs o ld. B qtd fsg lmt mvd o lmd.
11 Msol: f = fs ch = mhm mss qt o l g Lor qtor F=+... to g r ld. 3 6 Chgrmlr rs Chgrm qoldq vыcht- rsd rs r -c o rshd olsh mm. Fsg mss qtdg chgrms d fsg sh qt trofd Lor qtorg olmsdg mf ofstg tld. 5 3 Msl : f= = B rd fsg chgrms 3 g Rsf==3 = mss qts Fsg mss qtdg chgrms qdgch hsold..qtl o ldg mss qtdg chgrm chgrms g tg. rs =. Qtdg chgrm rs f== lm f! forml orql hsold. 3. Mm mss qtdg chgrm fs Lor qtorg osh orql hsold. d d 3 Msol:. rsf=-= lm f lm lm 3 3! s. F=? =3 = d s 3 rsf= lm 4! d d lm s lm s d lm d 3. Rsf =-= 4 = F= s? Lor qtorg osh f= ! 6 5! 3 rsf ==- 6 ; 4 d d 3 lm d s lm Lor qtor d mg tld?. Mss qtlr t rflg? 3. Chgrm d mg tld? Nort svollr. Umm hol. 4-mv. Chgrmlr ordmd tgrllr hsolsh R:
12 . Tromotr fs qtshg tgrllr. 3. Xosms tgrllr. Kosh torms formllr v chgrmlr rsd o rd ompls o grvchl fsd r soh oých olg tgrl rs chd m ssqt f d c tshdm ssqt fod ordmd qld. 4 Msol: s d? c c c=. s d = ; r= 5! 6 4 f= 4 d s lm 4 3 3! d ! 5! 3! 5! rs f== 5!.Trgoomtr fslr qtshg tgrllr. f s cos d? s = cos= d= d d d d= f s cos d c: f. Msol:. d d d d cos c; c lm 3 3 = rsf == rschd tshd d 3 3 = = -
13 =+ 3 - =- 3 3 f d. d rsf = = f d rs qorrmqsmd pstd d lm = lm Nort svollr. Chgrmlr ordmd tgrllr qd hsold?. Trgoomtr fslr qtshg tgrllr qsd hsold? 3. Xosms tgrllr qd hsold? 5-mv. Oprtso hso R:. Lpls lmshtrsh v g sos osslr. Elmtr fslrg tsvrlr 3. Tsvrlr ordmd dffrsl tglmlr chsh Xqq o grvchl t> d qlg stlg trtgch ls osllrg g o lg ft fs ch shd lmshtrsh rsh mm d osl v tgrl mllr odd o ptvchg ld.ntd dffrsl v tgrl tglmlr odd lgrc tglmlrg ld. Yqordg shrtlr rvch ft fs ch Lpls lmshtrshlr qdgch qld. L f t =fp= pt f t dt P-ompls o grvch. F ft o ft Fp. B rd ft orgl Fp tsvr dld. F t tsvr topsh ch f t formlg qoým. pt pt dv f ' t dt pt pt f ' t dt pt = f t p f t dt d P v f t p pt f t dt f Dm ft tsvr L{ft}=pFp-f g tg.. c? Elmtr fslrg tsvrlr hsolm. Fp= cdt c pt pt p c p ; dm c c p o ld. 3
14 . t? Fp= Fp= pt f t dt ; pt pt t t pt tdt pt =- d dt v p p dv Dm t g tg o ld. p t? Fp= pt t = ; dm t 3 p p p! Dm t fod l qlr. p 3 c t? p dt pt dt p p p pt t dv dt pt d tdt v pt pt =t tdt p p p 3 p Fp= d pt 3 pt 3 t 3 pt 3 p t dt pt =t d 3t v t dt p p 3 6 = ; dm t 3 4 p p p t 3.? dm Dm 4. S t? Fp= Fp= t p pt t p t dt St p 6 p 4 ; p t dt p cost. fod l qld. t t p t ; p pt p t p t s tdt dt p p S t. p = 5. Cos t? F P pt Cost costdt p Cos t. p t t p t p t dt p p p p t 6. t? 4
15 FP= t pt dt p t t dt t t! p -dvl Orgl ft Tsvr F P C t 3 t 4 t 5 S t 6 Cos t 7 t t c P p! p p p p p p! 7. f " t? 8 f t ' PF P f 9 f " t " P F P Pf f ' pt pt dv f " t dt F p f " t dt f ' t pt d p v f t f ' p pf p f f ' p F Pf P = 8. f "' t? F p p pt F"' t dt p d p v f " t dv f " dt pt = P f t = pt dt F p pf f ' pt pt = f " t P f " t dt f " p f ' p F p pf 3 =p F p P f pf ' f ". Tsvrlr ordmd dffrsl tglmlr chsh Tsvrlr ordmd dffrsl tglmlr chsh ch dvld fodl hosllrg tsvrlr qdg tglmg tsvr topld v f t Pt F p dp forml ordmd tgrl hsold. 5
16 Msol: Pt f t F p dp pfp+fp = Fp p+=3 3 F p p pt 3 f t dp 3 p rs f p p lm p t 6 t pt p p. t. Nort svollr. Oprtso hso d mg tld?. Elmtr fslr tsvrlr og? 3. Tsvrlr ordmd dffrsl tglmlr qd chld?. Ldr polom. Chshv-Ermt polom 3. Chshv-Lgrr polom 4. Gmm fs 5. Sldr fslr 6-mv. Mss fslr R: Kvt ms tom fs v r fd c o rshdg tglmlr chshg to g r ld v lrg chmlr mss fslr dld. Bd tglmg rchs. o rshd o l Ldr tglms dld. B tglm chm o rshd qdrm. Nom lm lr topsh ch hosllr ol tglmg oor qo m B forml om lm offstlr topsh ch rrt forml dld. olg tg o lgd ft hdlr olg tg o lgd toq hdlr olg ld. B hdlr top formlg qo s tglmg chm 6
17 P d! d 3. o rshd o ld. B Ldr pololr dld. Pol o phd m os ldrd. Dstl omrl Ldr polomlr hsolm. d! d Msol. P. Tglmlrg -chs 4 o rshd o l Chshv- Ermt tglms dld tglm chm hm o rshd qdrm. Hosllr ol tglmg qo om lmlr tops tglmg chm H d d o rshd o ld. B forml Chshv Ermt polomlr dld. H Tglmlrg 3-ch o rsh qdgch 6. 6 Chshv Lgrr tglms dld. Yqordg mllr rgd tglmg chm L d d 5 7. o rshd o ld. B Chshv Lgrr polomlr dld. L. Mss fslrg 4-chs F p p d 8. orql ql gmm fs dld. B rd p Г d Г! UdV U V VdU Dm Gmm fs tor d tt qq sog ftorl. Sldr fslr Mss fslrg5 sldr fslr dld g tglms qdgch P 9 Ko rshd o ld. B fslrg sldr dlshg s Lpls tglmsg sldr oordtlr sstmsdg o rsh sh o ld. Sldr v Drt oordtlr sstms orsdg og lsh: r cos r s tglmg chm o rshd qdrm 7
18 Y v g hosllr tglmg orm. X g r ldg drlr olddg offstlr tglm v om lm offstlr topm. Ntd tglmg chm J V V G V V V o rshd o ld. B fslr sldr fslr o Bssl fss dld. offstlrg qr sldr fslr 4 l o ld J J v! v 4 v v 4 64 v... v v v! v! Mss fslr d mg tld?. Mss fslr trlr tg? 3. Rrt forml dgd m tss? Nort svollr 7-mv. Xss hosll dffrsl tglmlr R:. Xss hosll dffrsl tglmlr v lrg chm.. Xrtrst form tshchs. 3. Ich trtl dffrsl tglmlrg lssftss 4. Erl o grvchlr lmshtrsh. 5. Ellpt tpdg tglmlrg o shl. 6. Gprol tpdg tglmlrg o shl. 7. Prol tpdg tglmlrg o shl.. Xss hosll dffrsl tglmlr v lrg chm... D E o l D -ochq og lml soh o ls. ortogol drt oordtlr sstmsdg qt- g oordtlr. Trtlg mf o lmg t t sog... tm-tlg -trtl m ltds dld... fsg D D D D Xss hod o rshd lglshm... E -Evld fos... - so m ltdsg g lg dld. qtdg... trtl hosls D o lgd D 8
19 D D D F F... p... fs D sohd qtg v p p p p D F m m hosl old frql hqq o grvchg rlg fss o l md tt o ls. Ush p m F D... fsg st m tgl om lm trtl ss hosll dffrsl tglm dld. tglmg o g tomo s ss hosll dffrsl oprtor dld. gr F rch m o grvchlrg st chql fs o ls tglm p chql dffrsl tglm dld. grd F m o lgd rch p o grvchlrg st chql fs o ls tglm vchql dffrsl tglm dld. Msollr: 3 - chch trtl o grvchl chql tglm ch trtl ch o grvchl vchql tglm chch trtl o grvchl chql o lmg tglm. D sohd qlg fs tglmd shtro tvch rch hosllrr l ls o l tg ltrs g tglmg rglr lss chm dld. Xss hosll m trtl chql dffrsl tglm sh L D f m o rshd o olsh mm. Brch D lr ch tglmg o g tomo f olg tg ols tglm r sl f fs olg tg o lms r sl o lmg tglm dld. gr v v fslr r sl o lmg tglmg chmlr o ls rvsh w v rm r sl f tglmg chm o ld. grd fslr r sl f tglmg chmlr o ls c fs hm rd c hqq o grmslr sh tglmg chm o ld. Xss hosll ch trtl chql dffrsl tglm o rshd old rd rch m B C F B C F 3 D sohd rlg hqq fslrdr. 3 tglmg offstlr olg tg o lg D qtlrd tglm ch trtl o lm qold qtlrd tglmg trt ld. Bd rch D d 9
20 d hsolm. 3 tglmd tm l lrg g ds o lgd lohd-lohd qo shlvchlr shtro shtro td. Sh sl hm mmtl o tm hmm vqt d hsolm. Eslt o tm D sohd qlg v K trtgch ss hosllr l ls o lg hqq fslrg to plm C K D orql lglm.. Xrtrst form tshchs. Fr qll tglmd shtro totg F F... p... fs p p... m o grvchlr o ch ls hoslg g o ls. tglmlr r sd hqq o grvchlrg st sh F K m p m trtl form m drl r sl o phd mhm ro l o d. B form tglmg mos o lg rtrst form dld. 3. Ich trtl dffrsl tglmlrg lssftss v o o rsh. Ich trtl vchql... 5 dffrsl tglm ch 4 form... Q 6 vdrt formd ort. 5 tglm rl o grvchlr lmshtr soddroq o rshg ltrshg hrt qlm.... o rg C D v sh o d hsolm. U hold D D......
21 B 5 tglmg qo sh tglmg lm... Yo... 7 B rd tglm tshrlotg D sohd qt olm v sh lglshlr rtm. U hold 8 form qtd qdgch old 9 6 vdrt form qtd o olm Q Mss o lmg sh dt ff lmshtrsh ordmd vdrt form Q g ld. B vdrt formg offtstlr hm 9 forml l qld. Shd ql 5 tglm qtd o grvchlr o rg g o grvchlr rt soddlshtrsh ch sh qtd vdrt form mss o lmg chql lmshtrsh ordm
22 l soddlshtrhs trldr. lgr rsd sot qld hmm vqt shd mss o lmg lmshtrsh mvd o l g ordm l vdrt form qdg o rshg ol ld. rd Q 3 offtstlr - qmtlr ql qld. Sh l rg mst mf offtstlr so rts ds v olg o lg offtstlr so form dft ff lmshtrshg st vrt solr fqt form l ql lmshtrshg tl olshg og lq o lmd. B rs 5 dffrsl tglm offtstlrg qtd ql qldg qmtlrg qr lssfts qlsh mo rd. Yqord tlglrg sos 7 tglm... 4 o rshd old. Ich trtl dffrsl tglmg rlsh hosllr qtshmg d o rsh odtd g o orsh dld. 5 tglm tt qtd ms ch o lmgd D qtg ror ch trofd o o rshg ol lvch mmm dg svol tg ld. B svolg o vo fqt o lgdg m lm. B ol lohd o rm. gr rch o rch ols Q form mos rvshd mst o mf qlg gft o ls 5 tglm D qtd llpt tpdg o llpt tglm dld. gr offstlrd tts mf qolglr mst o sch o ls 5 tglm D qtd gprol tglm d tld. offstlrd ts mst qolg ts mf o ls 5 tglmg ltrgprol tpdg tglm dld. gr offstlrd md tts olg tg o ls 5 tglm g mod D qtd prol tglm d tld. gr 5 tglm D sohg r r qtsd llpt gprol o prol o ls old D sohd mos rvshd llpt gprol o prol tpdg tglm d tld. Eslt o tm mtrtsg rtrst solr sh dt E lgr tglmg ldlrd ort rd E - rll mtrts 5 tglm rlg D sohg tor qtg mtrts rtrst solrg shors ql 5 tglm qs tpg tgshl lg ql olsh mm. Ush tglm 5 dffrsl tglm rtrst tglms dld. gr... fs rtrstlr tglms qotltrs... c c cost tglm l qlg srt rlg 5 dffrsl tglm rtrst srt o rtrsts dld. O grvchlr so t o lgd rtrst gr chq hqd so ord. 4. Erl o grvchlr lmshtrsh. Ich trtl o grvchl vchql ss hosll dffrrsl tglmlrg shd sst or lr r qtd ms l t r sohd hm o orshg ltrsh mm v sohg qtlrd tglm tp o grmd. B C B C 5
23 Tglm mtrtss o olm B B C v mtrtsg rtrst solr tglms sh o rshd o ld. o dt E B B C v tglm hqq chmg g C C B C C 4 C B C C 4B v ldlr v r l shorl gr C B o ls; hr l shorl gr C B o ls; ldlrd r olg tg gr C B o ls. B rd 5 tglm C B o ls tglm llpt tpd C B ols tglm gprol tpd 3 C B o ls tglm prol tpd lg l chqd. B C rtrst tglm hold odd dffrsl tglmg ol lsh mm. -6 tglmg chm o ls. Ush rtrst qrm cost sh rtrst o lsh o l sh most o rldr. o d d : d : d 7 g sos 6 tglm rch trtl odd dffrsl tglm o rsh old. 7 d B d d C d 8 Tsrs gr C tglmg chm o ld 8 tglm sh t tglmg rld 8 tglmg mm chm o ls hold 6 fs 6 d d d d B B B C B C tglmd rl o grvchlr qdgch lmshtrl. hold tglm sh o rsh old 9 3
24 4 C B C B C B C C B B Bvost o rg qo sh l sotlsh mm C B C B osms lmshtrsh tglm tp o grtrmd. Horch lmshtrshlr tor lmshtrshlr d. 5. Ellpt tpdg tglmlrg o shl. Fr qll tglm llpt tpg tgshl o ls. U hold 5 tglm t qo shm chmg g o l c 7 tglm rchs mm tgrl o ls. 5 rtrst tglmg qo sh tgl g o lm C B C B o C B B C B o ompls solrg olg tglg osssd C B C B C B Bd C B tglm qdg o rshd o ld Shd ql B C o lgd 6 tglm ch c mm chmg o r lmshtrsh r tglm o rshg ol lsh mm 6. Gprol tpdg tglmlrg o shl. tglm ch B C ols. U hold 5 tglm t chmg g v lrg mm tgrllr sh o rshd o ls c c 3 hold 3 g sos C B
25 v B C tgllr o rldr. Dm C Shd ql 6 tglm sh o rsh old B d lmshtrsh r sh tglmg lm B gprol tpdg tglmg o o rshdr Prol tpdg tglmlrg o shl. Fr qll tglm ch C B o ls. U hold 5 tglmlr tt cost mm tgrlg g o ld. 5 tglmd d -tor l l D D mostd o lg fs lmshtrsh rm hold v B C B C tgld C dm tglm o shlg g o lm. B l chqd d s B l C Nort svollr. Xss hosll dffrsl tglmg t rf rg lrg chm d qd fssg tm.. Kv chql tglm d qd tglmg tld. 3. Ich trtl chql ss hosll dffrsl tglm lssftslg. 4. dt E 5. Ich trtl o grvchl v chql tglmg rtrst tglms og. 6. Ellpt tpdg tglm ch o o rshg ltrsh rtrst solrg shors m qld. ch qd lmshtrsh rsh r. 7. Gprol tpdg tglm o o rshg ltrsh ch qd lmshtrsh rsh r. 8. Prol tpdg tglm o o rshg ltrsh ch qd lmshtrsh rsh r. 8-mv. Mtmt f tglmlr R:. Tor hqd tshch.. Tor trsh tglms ltr chqrsh. 3. Trsh ssql trqlsh sttsor tglmlr.. Tor hqd tshch. 5
26 Tor dgd r gldg gch p tshld oshqch tgd tor shd qttq sm g lg oshq o lchmlrd ch ortq o ld. Torg chl qtlr mhmlg o s qttq tortlg o ls. gr tor mvot holtd chtlshtrls tor tr oshld. B tor trsh r tsld ro rd d fr qlm. B tsld to g r rchl drt oordtlr sstms olm o. o o q torg oshlg ch tch holt o ch o ltrm. U hold torg mvot holtd slsh rd. Tor trsh rod -chtlsh v t g og lq o ld t. Hr r fsrlg t vqtd t fs grfg tor trsh grfg rd t s grfg qtsg o tlg rm rch offst rd. t t hrt tlg tt t hrt tlsh. Bg mqsdm tor hrt rvch t fs qotltrdg tglm tsh. Bg ch r chlshlr qlm. Tor st glvch. Torg t sr ql trg trgl ch trl tt d fr qlm. Sh sl torg glgd qrshlg trgl st hsog olms hm o ld. gr torg ror qtd r tomog otvch qsm ol tshls hold ol tshlg qsmg t sr lmshtrvch trgl ch. Sh qtd torg rms o ch o lg o ld. Tor cho lvch ms d fr qlm v G qog o sd trgl ch o grsh mqdor torg lg o grshg proporsoldr. Tor r sl d fr qlm v g chql chlg orql lglm rl l to g r lvch mss. Torg o o qg prlll chlr t sr td d fr qlm lr tor o l hrt qld v t g og lq lrg chlg g t d lgllm. Mhtg qrshl ch torg olmd. B fqt torg ch trshlr o rgm.. Tor trsh tglms ltr chqrsh. gr t tshl tg rchg lgls hold torg ch trsh t lg o d ttd. s g Mlor qtorg olmsg sos orql torg qtsd t vqtd o tlg rms o o qg mst o lsh l dm shrtg sos dm cos. rd B rd M M 3 s 3! s cos s B rd 4 tg s tg cos tg s L tg s 6 d d ch trshlr tor qsmlr cho lmd v qsqrmd. Ed trgl ch T o grms lg o rstm T v t g og lq mslg sotlm.
27 Bg ch torg M M o lg olm t momtd tshl orlg o llr t sr T v T trgl chlr l lmshtrm shrtg o r tor qtlr r tsld hrt qlmoqd dm tshq chlr hm o o qg prlll o lshd t sr o rstd. B chlrg o o qdg pross olg tg T cos T cos cos cos dm T T M v M qtlr ch M v momtg T t T t. L G qog o r dm T t K T t T cost cost 7 M qtlr tor o lg ch tor ch t Ed tor trsh tglms ltr chqrm. Bg ch torg chs ch M M o lg d o ls. Ud trgl chlr T v T t sr td. B olm v g o o qdg pross chlrg o o qdg pross T s T s T s s L Dm s tg ' s tg ' t d t T s s T[ ' d t ' t] T d t momtd torg M M qsmg t sr tvch rch tshq chlrg tg t sr tvchs F orql lglm. Dm F g t M M g t d g t - rl l t sr tvch chlr chlg. Ed M M qsm ch N tog ch qo qo llm. B qog o r M M chst msss tlsh o ptms. rch t sr tvsh chlr g dsg tg. gr -tor chlg o ls hold o d g qsqrtr d T d g t d t t g t T rd 4 tglmg tor trsh tglms dld o r o lchovl to lq tglms dld. 3. Trsh ssql trqlsh sttsor tglmlr. Mg tor str mmr ch o lchovl hmlrg trshlr fg ltr trshlr o p msllr dv p grd q F t t t om lm fs t fov p q - mtg osslr l qld. F t s tshq 5 o rshdg trsh tglmlrg ol ld. Bdg oordtlrg hmd t vqtg og lqdr. t srg tsvlg qld 5 tglmd grd 4
28 v gr p p p p p -o ls dm dv p p dv pgrd p Issql trqlsh o mhtd rrchlrg dff rolr sh mm dffrsl tglm l fodld dv pgrd q F t 6 t Sttsr tglmlr. Sttso vqtg og lq o lmg rolr ch F t F t 5 trsh hmd 6 dffr tglmlr sh dv pgrd q F t o rshd o ld. Nort svollr.. Trsh v dff tglmlrg mm o rsh og.. Issql trqlsh tglms mm o rsh og. 3. Sttsor tglmlrg mm o rsh og. 9--mv. Mtmt f tglmlr ch msllrg qo lsh R:. sos msllrg qo lsh.. Kosh msls v g qo lshd hrtrstlrg ro l. 3. Kosh Kovlvs torms. 4. Ellpt tpdg tglmlr ch chgrv msllr.. sos msllrg qo lsh. Bg hsh m lm trsh tglmlr ssql trqlsh tglms q dv p grd q F t t q dv p grd q F t t stsor rolr tglms dv p grd q F t 3 o rshd o ld. Bror f ro to l o rgsh ch ro tsvrlotg tglmlrd tshqr g oshlg holt v ro sodr o lotg sohg chgrsdg holt rsh rrdr. Mtmt qt rd rs dffrsl tglmlr chmg go mslg l og lq. Hss hosll dffrsl tglmlr ch mm chm htor fslrg og lq o l fslrg so tglm trtg tg o ld. Ihtor fslr rgmtlrg so chm rgmtlrg sod tt m o ld. Msollr: tglmg chm tglmg chm topsh ch f 8
29 lmshtrsh rm f f Xdd shg o shsh gr v o grms solr o ls tglmg mm chm o ld 3 Ush tglmg mm chm f f o ld. 4 f r sl o lmg tglmg chm o rshd o ld 5 Uchch trtl tglmg mm chm d ort o ld. f d d w Shd ql q f ro fodlovch chm rt olsh qo shmch shrtlr rsh rrdr. Bd qo shmch shrtlr oshlg ch v chgrv shrtlrd ortdr. Jro sodr o lotg soh G R o l S g chgrs o ls. S o llr sllq srt d hsolm. Ö Ò G T sos G soh ldlg T o lg sldr o ls g chgrs o srt T q G v qor G T S E soslrd ort. G S T 9
30 C S Dffrsl tglmlr ch sos ch tpdg msllr r-rd frq qld. Kosh msls. B msl sos gprol v prol tpdg tglmlr ch qo ld. G soh t R fo l stm-st tshd hold chgrv shrtlr o lmd. v Chgrv msl llpt tpdg tglmlr ch qo ld S d chgrv shtrlr rld oshlg ch shrtlr t o lmd. g rlsh msl llpt tpdg tglmlr ch qo ld: G R o l oshlg ch v chgrv shrtlr rld.. Kosh msls v g qo lshd rtrstlrg rol. tglm ch Kosh msls d qo ld: Kosh msls: t c t c sfg tgshl t rm fod tglm v t t 4 t oshlg ch shrtlr qotltrvch t fs topls. tglm ch Kosh msls qdgch qo ld. Kosh msls: c t c t sfg tgshl t rm fod tglm v 3 t d t 5 oshlg ch shrtlr qotltrvch fs topls. Kltrlg Kosh msls mmlshtrsh mm. Sh mqsdd o grvchl ch trtl sh vchql dffrsl tglm tshrm:... Ô 6 Ytrl slq S : srt v srtg rm o lmg g hr r qtsd ror o lsh rlg o ls. Kosh msls: S srtg ror trofd 6 tglm v s 7 s Kosh shrtlr qotltrvch fs topls. B mmlshtrlg Kosh mslsdr. Kosh msls qo lshd S srt rtrst srt o lmslg mhmdr. gr S srt rtrst srt o ls oshlg ch shrtlrd vrlg v fslr o ro og lg o l qold. Dm rtrst srtd oshlg ch shrtlr tor rlsh mm ms. B hold Kosh msls mm chmg g o ls hm go o lmd. Msol: Ush tglmg 9 oshlg ch shrtlr qotltrvch chm topls. Rvsh cost cost to g r chqlr ols mld hm rlg tglmg rtrstlrd ort. Dm oshlg ch shrtlr rtrstd rlpt tshrlotg tglmg 8
31 mm chm d ort. Umml to tm f d hsolshm mm. Boshlg ch shrtlrg sos f f f ; f gr cost o ls org tglg rlsh mm ms hold Kosh msls chmg g o lmd. Shd ql cost o l gdg Kosh msls chmg g o ld. B hold f c rd c c sfg tgshl v c c shrtlr qot-ltrvch fs. gr c o ls Kosh mslsg chm mvd o l chm forml l qld l chm go ms. N t om lml c 3. Kosh Kovlvs torms. N fss t Ô t D D N t dffrsl tglmlr sstms qrm N. B hold tglmlr sstms t o grvchg st orml sstm dld. gr f fs qtg ror trofd ts qlshvch c f f c! c drl qtor l fodls qtd lt fs dld. gr f fs G sohg hr r qtsd lt o ls G sohd lt dld. t g st orml sstm ch Kosh msls d qo ld: sstmg t t d sh. t D..... N 3 oshlg ch shrtlr qotltrvch N chm topls. B rd -ror G R sohd rlg fslr. Brlg 3 oshlg ch shrtlrg sos fslrd shtro totg rch hosllr hsolsh mm. D t t t D Dt D t tt D Kosh-Kovlvs torms: gr rch fsl qtg ror trofd lt t... Ô fs s... t... D... qtg ror trofd lt o ls hold 3 Kosh msls t qtg ror trofd lt chmg g o ld sh l chm lt fslr sfd go o ld. B torm lt fslr sfd Kosh mslsg chm trl ch sohd mvd v go 3
32 lg tsdqld. 4. Ellpt tpdg tglmlr ch chgrv msllr. dv p grd q F 4 4 tglm llpt tp ch chgrv msl d qo ld; G sohd 4 tglm v S chgrd qdg shrtlrd tts qotltrvch fs topls: I. S. II. S. III. S B rd fslr. S srtg o tlg tshq orml v S d rlg ls Msllr qo shd drhol sh rs m lm I hold fs C G C G sfg II III hollrd s C G C G sfg tgshl o lsh r. B mslrd I rch chgrv msls o Drl msls II ch chgrv msl o Nm msls III s chch chgrv msl dld. Yqord ltrlg msllrd o mlm fs G sohd lg ch lr mos rvshd ch msllr d rtld. Xdd shg o shsh chgrlg G sohg tshqrsd tshq msllr chgrv msllr qo ld. Blrg frq shd S dg chgrv shrtlrd tshqr soh chs o lg ch chs oqlshg qtd hm shrt rld. Msl d shrtlr Lpls tglms ch d o o o o rshd o lsh mm. Yqordglrg o shsh G sohd rlg mm ch trtl chql B C f 5 tglm ch chgrv msllr qo ld. G sohd 5 tglmg S 6 shrt qotltrvch rglr chm topls. B rd... v S d rlg fslr; v dgd qt G sohg chd S qtsg tlgdg fslrg lmt qmtlr tshld. 5 6 msl Pr msls dld. Brch S d... o lg hold 5 chgrv shrt S 7 o rshd o olsh mm. B msl rch chgrv msl o Drl msls dld. o lgd Pr mslsg hss hol S d msl hosl o d. 5 8 msl q hosll msl dld. S srtg qtsdg o ltrvch osslr S 8 3
33 cos N cos o lg rl vtor oorml N orql lglm. B rd orml cos... N S srtg qtd o tlg tshq gr 8 chgrv shrtd rch S d cos o ls q osll msl ch chgrv msl o Nm msls dld. rlsh msl. Trshlr tglms gprol tp dv p grd q F t 9 t 9 tglm ch rlsh msl d qo ld: C ÖT C Ö T sfg tgshl Ö T sldrd 9 tglm q sos d t Ö T sldrg t G t t oshlg ch shrtlr v t T Ö T g o srtd I II o III chgrv shrtlrd tts qotltrvch t chm topls. Boshq msllr. Ich trtl o grvchl o o rshg ltrlg sh c f mm chql tglm rlg o ls. B tglmg rtrstlr tglms d d d ort. Bd drol cost cost to gr chqlr ols l chqd. Uchlr B C v D qtlrd tomolr tglmg rtrtlrd ort o lg to rtrch G orgl lgl olm. Odtd to rtrch rtrst to rtrch dld -chm. Grs msls. G to rtrchd rglr G d ls v B D shrtl qotltrvch tglmg chm topls. Mslg qo lshg sos v fslr rlg sohsd ls v shrt lsh rr. Dm Grs mslsds tglmg t sshdg rtrstlrd tt chgrv shrt rld. Grs mslsd shrtlr rtrstlrd rlg ch msl rtrst msl d hm rtld. 33
34 Ed G orql o qg tor B sms v tglmg C : BC : rtrstlr l chgrlg chrch lglm. B chrch rtrst chrch dld -chm. Dr Kosh-Grs g rch msls. G d rglr G d ls v C shrtlr qotltrvch tglmg chm topls d v rlg fslr sh l rg. Dr Kosh-Grs g ch msls. G d rglr G d ls B smgch rch trtl hosllrg g o ls v lm v C shrtlr qotltrvch tglmg chm topls d C C rlsh tpg tgshl m s g m cost Tglm tshrm m o lgd tglm Trom tglms l stm-st tshd m o lgd s tglm Lvrt v-bdsd tglms dld. rlsh tpdg tglm rlg soh rlsh soh d rtld. G o grvchlr tslgd o lgd chlr v B qtlrd o lg Jord gr chg l d s 8 tglmg m m C: BC : m m rtrstlr l chgrlg r og lml rlsh soh o ls 3-chm Trom msls. G sohd rglr C G G G sfg tgshl gr chqd v C o BC rtrstlrd ttsd msl C d rlg qmtlr ql qlvch 34
35 35 C shrtlr qotltrvch 8 tglmg chm topls. Sh l rg C C C d rtld. v o lsh rr. Trom msls msl Korrt qo lg msl tshchs. B qord o rd mtmt f mslrg qo lshd rm fslr oshlg ch chgrrv shrtlr shtro td: qo lg mslg chm t sh fslrg og lq o ld. B fslr odtd tr sosd qld shg ch hm lr solt q topsh mm ms. Dm oshlgch v chgrv shrtlrd hmm vqt ror tolg o lsh mqrrrdr.b tol o vtd chmg hm t sr qld. Boshlg ch v chgrv msllr tshrshd chmg mvdlg v golgd tshqr oshlg ch v chgrv shrtlrd qo lg tolg chmg qd t sr qlsh qlsh hm mhm hmtg gdr. B fr qroq o qlsh ch tshrlotg msl M orql lgl olm. Hr qd M mslg moht rlg E fslrg sos E chm topshd ortdr rd E v E - mtrlr v o lg qddr mtr folr. B folr mslg qo lsh l E lmg go qld. M mslg chm tshchs qlg o l hr r R E chm mos ls. gr tor ch shd so o rstsh mm o l tgsld tgsl l chqs M msl E E folr ftd trg msl dld. Bd R E E... mslg chm rlg shrtlr oshlg ch v chgrv shrtlr tglmg offtstlr ood hd v h. g ls og lq o ld. gr tshrlotg M msl ch sh tor E ch E chm mvd; chm go; 3 msl E E folr ftlgd trg shrtlr rls M msl E E folr ftlgd orrt to g r qo lg o to g rd-to g r orrt msl dld. s hold msl orrt qo lmg msl dld hold qordg tllrd md tts rlmd. Sh rs t dl o tm orrt qo lg msl t rf rlg E E ftl tlqldr ch oshq mtrlrd sh mslg o orrt qo lg o lsh hm mm. Korrt qo lmg msllrg msollr. Kosh-Kovlvs torms g mml tvsfg g lgg qrmsd dffrsl tglmg orml sstms ch Kosh msls orrt qo lglg to l hl qlmd. Hqqtd hm torm msl chmg trl ch sohd mvd v golg t m td. Odtd dlllr vlld rlg mm ch o lmg sohlrd to g r lg o rstsh tl qld. Bd tshqr tglmg ood hd v oshlg ch shrtlr mm olgd lt o lmg fslr o ld
36 Nhot chm oshlg ch shrtlrg ls og lq o lmslg hm mm. B dll o rstvch msol rch mrt dmr tomod tlg. dmr msol. Ush Lpls tglmsg rm tsld 36 cos oshlg ch shrtlr qotltrvch rglr chm topls. Tshr o rsh q ms mslg rd-r chm o rshd o ld. cos sh... Ko r trd gr cos fs olg ts tld cos l chm old frql tor d cos sh o ld. Shd ql Lpls tglms ch Kosh msls orrt qo lmsg msl. Ush t ssql o tvchl tglmsg t sohd s t t shrtlr qotltrvch chm topls. B mslg chm t t s fsd ortdr. T hr r ch o g oshlg ch shrt v g mos o lmg chm or. Sh sl hm olg chm chmlr tm-tlg d qrsh r. s fs lmtg tlmd. 3 Tor trsh tglms ch Drl msls tshrm to rtrchd d olg tld l chm s hdd dmr msold hch qd s shrtlr qotltrch tor trsh tglmsg chm topls. B rd - mst rrtsol so. B mslg chm s s... s forml l qld. Rvsh m lm shd d chgrv shrtdg p v s fs olg tld. Solr rsd q t solr tm tlg mvd o l hr qd rrtsol so ch
37 p q q tgsllrd o rl o ld. Bg sos s q s q p q tgsl hosl qlm. B hold tshrlotg mslg chm fs ch q s q s q s q q s q s q tgslg g o lm. Bd tor trsh tglms ch Drl msls orrt qo lmg msl ms lg l chqd. Nort svollr.. Xss hosll dffrsl tglmg mm chm tlsh qd o ld.. Kosh msls qd tglmlr ch qo ld. 3. Chgrv msl qd tglm ch qo ld. 4. rlsh msl qd tglm ch qo ld 5. Boshlg ch shrtlr rtrstlrd rsh mmm. 6. Norml sstm d qd dffrsl tglmlr sstmsg tld. 7. Kosh-Kovlvs torms t rflg. 8. Ellpt tpdg tglmlr ch sos chgrv msllr t rflg. 9. Korrt qo lg msl t rf rg.. Tor trsh tglms ch Drl msls orrt mslg o rstg. -mv. Chs tor ch Dlmr formls R:. Br sl tor trsh tglms ch Kosh msls.. Kosh mslsg chm Dlmr sld topsh. 3. Xlos. I ch mhmlg o r ch mhmlg tor trsh hqdg msl chshd old osoroq o lg msl chs tor trsh hqdg msl o rl. Qdg t rsl tor trsh tglmsg t f t t t F oshlg ch shrtlr qotltrvch chm topsh r. Bdg f F lr - orlqd rlg fslrdr. Nom lm t fsg hch qd chgrv shrt qo lmg. tglmg oshlg ch shrtlr qotltrvch chm topsh msls Kosh msls dld. B msl chsh sl Dlmr sl dld. g mm chm t t t 3 o lshlg o rstm. Bd fslr mrt dffrsllvch fslrdr. Hqqt hm 37
38 t tt tt t t t t t t t t tt tgl o rl o ld. Dm 3 g mm chm o ld. Ed oshlg ch shrtlrd fodl om lm fslr topm. 3 d: t= o lgd +=f 4 hosl o ld. t t 5 5 d gch tgrlls d t 4 v 6 d: c f t t t t F d F d F d F d c 6 F d 7 dg o rg -t v +t qo s 3 g sos t f t f f t f t t F d F d t F d t F d t f t F d f t M lm t t t F d F d F d F d t t f t f t t F d. t hold t F d 8 8 forml tor trsh tglms ch Kosh mslsg Dlmr chm dld. t 7 F d t Msollr: tglmg tt 38
39 t t t f t F t t 9 tt t 3 f t t 6 3t s F oshlg ch shrtlr qotltrvch chm topg. 6. 3t t 3t 3t 3t t d tglmg 3 tt t t t cos 3t 6 39 t t oshlg ch shrtlr qotltrvch chm topg. t s cost cos st. Ed 3 chmg f m os qlshg to tlm. t t t. mm foddg fslr lohd qrm. t fs ol t g o svch t=t t=t t=t... qmtlrch grflr chm. vvl Ich grf rch grf st t mqdorg o g tomog qr slg chchs s t mqdorg o g tomog qr slg v h.. gr chmlr tm-t qo g lms rg protsls rch grf o g tomog qr grotg o rm. Ed 3 dg ch qo shlvch +t qrl. Xdd qordgd mloh rgs fs hm tl l chp tomog qr trqld. -t +t fslr l tvsflvch to lqlr grvch to lqlr dld. Shd ql tglmg mm chm -t v +t to lqlrg g dsd sprpotssd ort. 8 chm tshrl. F= o ls. B hold tor qtlrg oshlg ch tlg olg tg o l tor fqtg oshlg ch sltsh tsd trm hrt qld. B hold t f t f t g g o lm. f fs q o lg ch t g qmt hr qd v t lr ch hsolsh mm. f Xdd qord o rgm rd hm t fs t f t v t to lqlrg sprpotssd ort. Brch to lq tl l o g tomog qr trqld v to g r to lq dld. t= d s l to lqlrg profl stm-st tshd. gr f= o l F o ls t o ld. t F d t t t F dd fr qls hold t t f t f t t t t v tsr t o ld. B hold hm tor o l to g r Tor hrt tsvvr qlsh ch to lqlr trqld.
40 d olm. B hold F F l l V l l V V d l l l V l h V d l l V l V h V d l h Bd o rd toq fsdr. Nort svollr.. Chs tor ch Kosh msls qd qo ld?. Dlmr sl md ort? 3. Dlmr formls ordmd msollr chg. -mv. Chl tor ch Fr mtod R. O grvchlr rtsh mtod o Fr mtod hqd.. Fr mtod ordmd ch mhmlg torg r trsh tglms chsh. 3. Xlos. Mtmt f tglmlr chshd o p qo llldg mtodlrd r o grvchlr rtsh mtod o Fr mtoddr. B mtod ordmd ch rtrlg torg r trsh tglms chsh o rl. Bg tglmg oshlg ch shrtlr v t t f t t t F 4 t l t chgrv shrtlr qotltrvch chm topsh r. g chm r fqt t g fss -s fqt g fss o lg t fs o ptms shld lm 4 g qo s T T t t X X g g o lm t X T t B tglmg chp tomo fqt t g o g tomo fqt g og lq o lg ch stlr o grms sog tg o lsh r Bd T T t t X X
41 t T t X T 5 X 6 r sl odd -trtl dffrsl tglmg g o lm. tglmg 3 chgrv shrtlr qotltrvch ss chm t g tor qmtd t T t X t T t X l l o ld. Bd Tt= ds t= tglm trvl chmg = g o lm. Bg trvl o lmg chm r hold X X l d olm. Dm X fs topsh ch qdg msl chshg l qold. X topsh r. X tglmg X X l X o rshd lm v r Echm r B rd r ch hollr or. r c c o ls hold chm X Х l shrtg sos X shrt qotltrvch chm rtrst tglmg g o lm. d lgld o ld. c c c c c c c c c shg ch c c B hold X t ol chmg g o ld. o ls. B hold chm c c o ld. X c c l c l t B hold hm X trvl chmg g o ld. 3 o ls. B hold chm Chgrv shrtlrg sos: l c s l c X X c cos c s c X o ld. o lsh r s hold trvl chmg g o lm. Shg sl o lsh r. l l... ch = d trvl chm hosl o ld. X c s c c l d lgld. - rtrst solr X rtrst fslr dld. fs mos ld. B hold 5 tglm qdg l rtrst sog T t 4
42 T l t T t o rshg ld. O tg drslrg sos g mm chm B T t B cos t D s t 8 l l D lr tor o grms solr g qo s hosl o ld d l B c D c. t cos t s t s l l 9 tglm chql r sl o lg ch 9g g ds t cos t l s t s l l hm g chm o ld. Bd qtor qlshvch hmd qtorg hdlr mrt dffrsllvch d fr qlm. t ch lrg g ds t ss chmlr 3 chgrv shrtlr qotltrg hm 3 grv shrtlr qotltrd. Ed tor v o grmslr shd topsh r oshlg ch shrtlr qotltrs. t s f t t t t l s F l l lrd o rd l l s t l cos t s l l t tor l f s d 3 l l l l F s d F s d l 4 l l 34 lr g qo tglmg 3 shrtlr qotltrvch chm topm: t s cos t f s d s t F Ed U hold l l l l l l l l t cos t s t s s cos l rctg s d l l 5 4
43 t 6 dg hr r qo shlvch fl s s t l l s l mpltdl 6 chstotl grmo l trm hrt fodld. Shg ch 6 dg hr r qo shlvch grmo dld. Hrr grmo t to lq l tsvrld. Umm hold t t to lq s tglm l d cht chmg g o ls shch qo g lms qtlrg g o ld. l Nort svollr. Fr mtod m?.ich o grms ofstl r sl dffrsl tglmg mm chm qd o rshd o ld? -mv. Frdgol mg tgrl tglmr R:. Umm tshchlr.. Frdgol m ch tr tgrl tglms chsh. 3. Frdgol m tormlr.. Umm tshchlr. Itgrl tglmlr d om lm fs tgrl shors ostd o lg tglmlrg tld. M mtmt f v tg d o pl msllr sh K d f o rshdg tgrl tglmlrg tshrshg ol ld rd om lm fs K v f fslr mos rvshd v -o grms solr opq sohlrd rlg ls hqq fslr. f fs tgrl tglmg ood hd K tglmg dros sol o ptvch tglmg prmtr dld. Frdgol mg rch tr tglms d o rshdg tgrl tglmg tld. gr tglmd f o ls tglm mos o lg r sl tgrl tglm dld. Br sl K d f K d 3 K d 4 tglm 3 r sl tglmg qo shm tgrl tglm dld. 43
44 K d f 5 o rshd o ls Voltrrg ch tr tgrl tglms K d f 6 Tshr o rsh q ms gr ch tr Frdgoltgrl tglmsg mm chm mvd o ls 7 o rshg g o ld d 3 tglmg mm chm s tglmg mm v ss chmlr o ls lrg rms 3 tglmg chmd ort o ld. Bd drhol 7 tgl l chqd.. Frdgol m ch tr tgrl tglms prmtr ch o lgd tm-t qlshsh sl l chsh. ch tglm tshrm K v f fslr o lr qlg sohlrd ls o lg K M m f m 8 o ld. gr tglm prmtr 9 M shrt qotltrs hold tglmlrg go chm mvd o l tm-t qlshsh sl l topsh mm. Nolch qlshsh sftd tglmg ood hd ql qlm f Bch qlshsh f K f d most l qlm. B ro dvom ttr -qlshsh f K d... most l qlm. Shd ql rrrt mostlr qotltrvch fsol tm-tlgg g o lm. Mtmt ld m lm tm-tlg qlshsh qtorg qlshshg tg chldr. forml 44
45 d K d K d K f d K f 3 o rshd o olm. 8 g sos 3 d qdg tgsllr l chqd: M m M m M m m... Shd ql qtorg hr r hd mst sol M m 4 Frdgol mg rch torms. Frdgol mg ch tr f d K 5 tgrl tglmsg K dros q p K 6 o rshd o ls g lg dro d rtld. Bdg p v q -rlg hqq ls fslrdr. rm dotlrd 6 o rshdg dro Prl-Grs dros o qsqch PG-dro d hm tld. Umml o tm rch p fslr hm q fslr hm o ro og lq ms d hsolm. s hold 6 g dd qo shlvchlr so mtrsh mm. 6 fod 5 tgrl tglmg qo f d q p 7 tglm hosl qlm. 7 tgrl tglm p c f 8 o rshd osh mm d d q c... lr om lm fsg og lq o lg ch om lm o grmslrdr. Ed c... o grms solr shd tlshg hrt qlm td 8 foml l qlg fs 3 tgrl tglmg chmd ort o ls. Sh mqsdd 8 fod 7 tglmg chp tomog ol or qo m
46 f c p p q f c p d f o p c q f d c p q d Bd p fslr chql og lq o lmg ch tgl l chqd. Ush lglr rt vvlg tgl c q f d c p q d q f d p q d c c... 9 o rshd o olm. Shd ql 7 tgrl tglmg chm topsh msls 9 chql lgr tglmlr sstms chshg ol ld. 9 sstm rsd M mtrs mhm rol o d. B mtrsg dtrmt D orql lgl olm dt M D. Chql lgr rsd m lm gr D o ls 9 sstm tor o g tomohlr ch go chmg g o ld v chm Krmr formllr l qld. mmo D dtrmt g st -drl o phdd ortdr. Dm D o phdg ldlr o lg g shl sodg:... m qmtlr m K drosg o g mos 3 tgrl tglmg os ch 6 shrt ld. g qmtlr rtrst solr dld. Shd ql g lrd... m frql o lg hr r chl qmt ch 9 c...c sstm go chmg g o ld. B chm 8 tglg o g tomog qo 7 tgrl tglmg chmg g o lm. Ntd qdg torm sotld. Frdgol mg rch torms. gr K drog os so o lms tor ls f ch 7 tgrl tglm chmg g sh l rg chmg go o ld. Frdgol mg ch torms. 7 tgrl tglmg mos r sl tglm 9 g mos o lg sh p q d c c 46
47 r sl chql lg sstmsgs ld. tglmg qo shm o lg r sl tglm p q d 3 o rshg g o ld. 3 tglmg g g qo shm o lg r sl sstmg tg chldr d gr d d 47 d p d m o l M mtrsg rg r g tg o ls chql lgrd r t c... c d... d... r m lm r sl 8 sstm hm v g qo shm o lg sstm hm chql og lq o lmg chmlrg g o ld. B chmlr v 34 d osl o lg sh d q c p... r formllrg o g tomolrg qo v r g sl tgrl tglmlrg og lq o lmg chmlr hosl qlm. Frdgolmg ch torms. Br sl 9 tglm v g qo shm o lg r sl 9 tglm r l o lmg chmlr g o ld. Br sl 9 tglmg olg tg o lmg 4 r td chql r td chql og lq... r chmlr 7 tglmg o K drog os sog mos o lg os fslr dld. Frdgol mg chch torms. Y chql lgr rsg mrog t qlm. M lm o lgd 7... m sstm tor o g tomolr ch chmg g o lvrmd. B sstmg chmg g o lsh ch solr... d... r 5 shrtlr qotltrsh rr v trldr. 5 shrtlrd o rg g qmt qo 5 g tg chl o lg qdg tgllr sstmsg g o lm: d Bd 4 g sos d q f d f f d... r d q d tgllr hosl o ld. Bror D sohd ss orlqd t fsg o ptmsd olg tgrl olg tg o ls fslr ortogol d tld. Shd ql qdg torm sot qld. Frdgolmg chsh torms. m o lgd 7 tgrl tglmg chmg g o lsh ch g ood hd... f g qo shm r sl tglmg rch... r o lsh rr v trldr. chmlrg ortogol
48 Uls drol Frdgol mg ch tr tglms. Ush K d f K K d B C ls drol Frdgol mg ch tr tglms o rgm. Ed tglmg dros g o lmg hol tshrm. gr K fs vdrtd ls o ls mtmt l rsd sotldg Vrshtrss tormsg sos hr r ch v g st trl qor drl shd K o phd mvd o ld rch R d K K tgsl o rl o ld. Rvsh K o phdg hr r hd tts g ch g og lq o lg t o ptvchg o ptms sftd fodlsh mm. Sh sl K dro K p q K 6 o rshd o olshm mm. Bdg K fod R d K 7 shr qotltrvch ls fs. 6 tgl K dro ch v g drolr g dsg rttlglg fodlovch formldr. 6 g sos Frdgol m tglm K d F 8 o rshd o olm d F f p q d 9 prmtrg tor chl t qmt ch so shd ch tl olm tgsl o rl o ls. 6 tgslg sos 3 K d Dm 3 tglm 5 g o r rd-r chmg g o ld. K drog rol vts 48
49 R orql lgl 3 tglm chm F R F d 3 o rshd o olm. 9 tgldg F o rg g qmt 3 ol or qo m: sh f p q d R t f t p t q g f R t f t dt. ddt. r p R t p t dt. lglshlr rt r q d g 6 tglm hosl qlm. Shd ql g tor chl t qmt ch ls drol tglm g drol Frdgol mg ch tr 6 tglmsg vlt. 6 tglm ch vvlg dd o qlg Frdgol m tormlr o rl o lg ch ls drol tglm ch hm o rl o ld. B tormlrg sos qdg l trtv hosl o ld. Frdgol m ltrtvs. gr tglm mos r sl B tglm g hr r t qmt ch old frql chmg g o lms tglm tor ood hd f ch go chmg g o ld; grd B r sl tglm old frql chmlrg g o ls B tglm hm v g qo shm - r sl tglm hm r l chl sodg chql og lq o lmg chmlrg g o ld; hold tglm tor f ch chmg g o lvrmd tglmg chmg g o lsh ch g ood hd f qo shm C r sl tglmg rch chmlrg ortogol o lsh rr v trldr f d... d... - C tglmg rch chql og lq o lmg chmlr. olg tg o lmg fs rvsh r sl B tglmg v g qo shm o lg C tglmg chm o ld. Bd r sl o g qo shm tglmg chm dgd old frql chm tshm. Br sl B tglm... chmlrg g o lg g qmt K drog o B tglmg os so fslr s sh dro o tglmg os sog mos os fslr dld. Yqord o qlglrg sos r or t dl o tm rlg os sog mos chql og lq o lmg os fslrg so chldr. K drog rch os solr to plm drog sptr d tld. Voltrr tglms drosg sptr o sh to plmd ort g drol Frdgol m ch tr 49
50 tglmsg sptr s chl sodg lmtlrd ort. Ed tglm K t t dt f o rshd o ol g hr qsm K tgrllm. U hold tgl torg ol g o ptrm v o ch d gch K d f K t t dt f tglm hosl qlm d f f K f d B ro dvom ttr qdg tglmg g o lm: K d f 3 d f f K f d f f. Shd ql sh tg ld: gr K drog os so s os sog mos os fss o ls hold fssd ort o ld. v trtslg K drog os so v os Nort svollr. Frdgol mg rch torms t rflg.. Frdgol mg ch torms t rflg. 3. Frdgol mg chch torms t rflg. 4. Uls drol tgrl tglm g drol tgrl tglmsg ol lsh g os ltrg. 5. Frdgol m ltrtvs t rflg. chshg 6. Frdgol m ch tr tgrl tglms tm-t qlshsh sl l og. rrrt formls 3-mv. Vol trrg tgrl tglmlr. Rol vt. R:. Voltrrg ch tr tgrl tglms.. Itrslg dro. 3. Rol vt. 4. Voltrrg rch tr tgrl tglms.. Voltrrg ch tr tgrl tglms. 5
51 K d f Itgrl tglm tm-t qlshsh sl l chm. 7-m rdg mlohlr qrt fslr tm tlg hosl qlm d f K d m m f N m K lglshlr rtm. B hold m K d mn... N m... 3! tgslg g o lm. Mst hdl m o N N fsol qtor prmtrg tor chl qmtd ts qlshvch o lg ch 3 tgsllrg sos fslr tm tlg solt v ts qlshvch o l g lmt o lg m lm fs tglmg chmd ort o ld. Ed tglm chmg go lg o rstm. Fr qll tglm t v ls chmlrg g o ls. Blrg rms r sl K d 4 tglm qotltrd. * m m d lgl ols 4 d drhol K d tgsl l chqd. Bd fodl 4 tgld K d Nm tgsl hosl qlm. B ro dvom ttr tor trl * Nm ch * 5
52 * m N! d o lg l tgsl hosl qlm. B tgsld chqd. Shd ql qdg losg ld. Voltrrg ch tr tgrl tglms g dros K v ood hd fslr o lgd prmtrg hr r chl qmtd go chmg g o ld. Sh dll l Voltrrg ch tr tgrl tglms hr r ch chmg g o lvrmdg Frdgolmg ch tr tgrl tglmsd td frq qld.. Itrslg dro. m tgsl rlgd f ls 3 fslr tm tlg tglmg chmg qlshsh sotlg d. Ed sh tm t qlshsh strtrs tfsl o rgm. M lm f K f d So gr f K t t dt f K t f t dt K t dt K t f d Ilg tgrld tgrllsh trt o grtr K K t K t dt d lgl ol f K f d K f d tgl hosl qlm. B ro dvom ttr f K f d 5 Tglg g o lm d K lr K K K K t K t dt 3... rrrt mostlr l qld. K fslr trtslg trorlg drolr d tld. 5
53 3. Rol vt. 3 tm tlg qlshsh sotlgdg mlohlr qtr rlgd vdrtd m shrt K qtorg ts qlshshg shoch hosl qlsh mm. B qtorg g ds R K drog o tgrl tglmg rol vts o hl qlvch dros dld. 5 d d lmtg o t tglmg chm rol vt ordmd f R f d o rshd oshm mm. 4. Voltrrg rch tr tgrl tglms. Voltrrg rch tr K d f 6 tgrl tglms tshrm Fr qll 6 tglmg dros v ood hd qdg shrtlr qotltrs: K f ' lr mvd ls fslr K hch qrd olg lmd. B hold 6 tglm o ch dffrsll Voltrrg ch tr tgrl tglmsg ol lm: o K K d f ' 7 K * d f * d K f ' K * f * K K Yqord ltrlg shrtlrd g mhm K g olg lmsl shrtdr ch g ror qmt K olg tg o l qols Voltrrg rch tr tgrl tglms tshrshd tt qchllrg dch ld. Nort svollr..itrslg tgrl tglm l dstl tgrl tglm o rtsd og lsh.. Kchs drol tgrl tglmlr. 3. Voltrrg rch tr tgrl tglms. 4. K drog rol vts og 5. Tglm chm rol vt orql fodlg. 53
54 54
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Alterazioni del sistema cardiovascolare nel volo spaziale
POLITECNICO DI TORINO Corso di Laurea in Ingegneria Aerospaziale Alterazioni del sistema cardiovascolare nel volo spaziale Relatore Ing. Stefania Scarsoglio Studente Marco Enea Anno accademico 2015 2016
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