Ogata - 5ta Sistemas Dinamicos Mecanicos
September 22, 2022 | Author: Anonymous | Category: N/A
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8ª hfngn÷k
Nkchknhrêo fh gbktrba jbfhrko
Iotsumnib Bcoto
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Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs 7-? Nktrbfuggn÷k Hsth gopêtuab prhshkto ha jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y fh snsthjos haîgtrngbs. Hk ha Gopêtuab 4 sh bdtuvnhrbk abs jbfhabs jothjïtngbs fh uk gnrguntb haîgtrngb snjpah y fh uk snsthjo jhgïkngb shkgnaab. Hk hsth gopêtuab sh gbksnfhro ha jbfhaofb jothjïtngb fh uko vornhfof fh snsthjos jhgïkngbs y snsthjos haîgtrngbs quh puhfhk oporhghr hk abs snsthjos fh gbktrba. Ao ahy eukfojhktoa quh gbktrbao abs snsthjos jhgïkngbs hs ao shcukfo ahy fh Khwtbk. Hk ao Whggn÷k 7-4 sh opango hsto ahy o fnvhrsbs snsthjos jhgïkngbs y sh goaguaok abs jbfhabs gbjb eukgn÷k fh troksehrhkgno y hk ha hspognb fh hstofbs. Aos ahyhs dïsngos quh gbktrbaok abs gnrguntbs haîgtrngbs sbk aos ahyhs fh Inrgmmbee. Hk ao Whggn÷k 7-7 sh bdtnhkhk abs jbfhabs gbjb eukgn÷k fh troksehrhkgno y hk ha hspognb fh hstofbs fh fnvhrsbs gnrguntbs haîgtrngbs y snsthjos fh ojpanengofbrhs bphrognbkoahs quh puhfhk oporhghr hk jugmbss snsthjos jugmb snsthjos fh gbktrba. gbktrba.
7-4 Jbfhaofb
jothjïtngb fh snsthjos jhgïkngbs
Hsto shggn÷k prhshkto hk prnjhr aucor snsthjos shkgnaabs fh rhsbrths y snsthjos snjpahs fh ojbrtncuofbrhs. Fhspuîs goaguao abs jbfhabs gbjb eukgn÷k fh troksehrhkgno y hk ha hspognb fh hstofbs fh fnvhrsbs fnvhrsbs snsthjos snsthjos jhgïkngbs. jhgïkngbs.
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56
Nkchknhrêo fh gbktrba jbfhrko
bdthkhrr ao gbksto gbkstokth kth fha rhsbrth fh abs snsthjos quh sh juhstrok hk aos Encuros 7-?(o) y (d), HLHJPAB 7-? Wh vo o bdthkh rhsphgtnvojhkth. Poro abs rhsbrths hk poroaha poroahab b YEncur YEncuroo 7-?(o) 7-?(o)Z, Z, ao gbkstok gbkstokth th fha rhsbr rhsbrth th hqunvoahkth i hq sh bdtnhkh fh i ? x ! i 4 x % E % i hq x
b i hq % i ? ! i 4
Poro abs rhsbrths hk shrnh YEncuro 7-?(d)Z, ao euhrzo hk gofo rhsbrth hs ao jnsjo. Osê, i ? y % E ,
i 4( x . y) % E
Wn sh hanjnko y fh hsos fbs hguognbkhs sh bdtnhkh
O D
i 4 x .
E
i ?
% E
b dnhk i 4 x % E !
i 4 i ?
E %
i ? ! i 4 i ?
E
Ao gbksto gbkstokth kth hqunvo hqunvoahkth ahkth fha rhsbr rhsbrth th i hq poro hsth gosb hs
i hq %
E
i ?i 4
x
i ? ! i 4
%
%
? ? i ?
!
? i 4
Encuro 7-?. (o) Wnsthjo ebrjofb ebrjofb pbr fbs rhsbr rhsbrths ths hk poroahab9 (d) snsthjo ebrjofb pbr fbs rhsbrths hk shrnh.
HLHJPAB 7-4 Wh vo o bdthkhr ha gbhengnhkth fh ernggn÷k vnsgbso hqunvoahkth d hq poro gofo ukb fh abs snsthjos quh
sh juhstrok hk aos Encuros 7-4(o) y (d). Xk ojbrtncuofbr hs uk fnspbsntnvb quh prbpbrgnbko ernggn÷k vnsgbso b ojbrtncuojnhktb. Hstï ebrjofb pbr uk pnst÷k y uk gnankfrb aahkb fh oghnth. Ha oghnth rhsnsth rhsns th guoaqunhr jbvnjn jbvnjnhktb hktb rhaotnvb hktrh ao vornaa vornaaoo fha pnst÷k y ha gnankfrb gnankfrb,, fhdnfb o quh ha oghnt oghnthh fhdh eaunr oarhfhfbr fha pnst÷k (b o trovîs fh brnengnbs hk ha pnst÷k) fh uk aofb fha pnst÷k oa btrb. Ha ojbrtncuofbr ojbrt ncuofbr hshkgn hshkgnoajhkt oajhkthh odsbr odsbrdh dh hkhrcêo. Hsto hkhrc hkhrcêo êo odsbr odsbrdnfo dnfo sh fnsnpo gbjb goabr y ha ojbrtncuofbr ojbrt ncuofbr kb oajog oajoghko hko hkhrc hkhrcêo êo gnkîtng gnkîtngoo kn pbthkg pbthkgnoa. noa.
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Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
58
Encuro 7-4. (o) Fbs ojbrtncuofbrhs ojbrtncuofbrhs gbkhgtofbs hk poroahab9 (d) fbs ojbrtncuofbrhs gbkhgtofbs hk shrnh.
(o) Ao euhrzo e fhdnfo o abs ojbrtncuofbrhs hs 8
8
8
8
8
8
e % d?( y . x) ! d4( y . x) % (d? ! d4) ( y . x)
Hk tîrjnkbs fha gbhengnhk gbhengnhkth th fh ernggn÷k ernggn÷k vnsgbs vnsgbsoo hqunvo hqunvoahkth ahkth d hq, ao euhrzo e hstï fofo pbr 8
8
e % dhq( y . x)
Fh omê, dhq % d? ! d4
(d) Ao euhrzo e fhdnfo o abs ojbrtncuofbrhs hs 8
8
8
8
e % d?( z . x) % d4( y . z)
(7-?)
fbkfh z hs ha fhspaozojnhktb fh uk puktb hktrh ha ojbrtncuofbr d? y ha ojbrtncuofbr d4. (Bdshrvh quh ao jnsjo euhrzo sh troksjnth o trovîs fha hlh.) Fh ao Hguogn÷k (7-?), sh tnhkh 8
8
8
(d? ! k4) z % d4 y ! d? x b dnhk ?
8
z %
8
8
d? ! d4
(d4 y ! d? x)
(7-4)
Hk tîrjn tîrjnkbs kbs fha gbhen gbhengnhkt gnhkthh fh ernggn÷k vnsgbso hqunvo hqunvoahkth ahkth d hq, ao euhrzo e hstï fofo pbr e % dhq( y . x) 8
8
Wn sh sustntuyh ao Hguogn÷k (7-4) hk ao Hguogn÷k (7-?), sh tnhkh 8
G
8
%
d?d4
8
d? ! d4
?
8
e % d4( y . z) % d4 y .
8
8
(d4 y ! d? x)
d? ! d4
F
8
( y . x)
Osê, 8
d?d4
8
e % dhq( y . x) %
8
d? ! d4
8
( y . x)
Fh omê, dhq %
d?d4
%
?
www rhhAndrbs brc d? ! d4
?
d?
!
?
d4
55
Nkchknhrêo fh gbktrba jbfhrko
Gbksnfîrhsh rhsh ha snsthjo joso-rhsb joso-rhsbrthrth-ojbrtn ojbrtncuofbr cuofbr jbktofb hk uk gorrb, snk joso, quh oporhgh hk HLHJPAB 7-7 Gbksnfî ao Encuro 7-7. Wh vo o bdthkhr uk jbfhab jothjïtngb fh hsth snsthjo, supbknhkfb quh ha gorrb hstï nkj÷vna furokth uk t o 0 y quh ha snsth snsthjo jo joso-rhs joso-rhsbrthbrth- ojbrtncu ojbrtncuofbr ofbr tojdnîk hstï nkj÷vna furokth uk t o 0. Hk hsth snsthjo, u(t ) hs ha fhspaozojnhktb fha gorrb y ao hktrofo poro ha snsthjo. Hk t % 0, ha gorrb sh juhvh o uko vhabgnfof gbkstokth b dnhk u % gbkstokth. Ha fhspaozojnhktb y (t ) fh ao joso hs ao soanfo. (Ha fhspaozojnhktb hk rhaogn÷k gbk ha pnsb.) Hk hsth snsthjo, j rhprhshkto ao 8
joso, dfh fhkbto ha gbhengnhkth fh ernggn÷k vnsgbso y i o hs ao gbkstokth rhsbrth. Wh supbkh quh ao euhrzo ernggn÷k fha ojbrtncuofbr hs prbpbrgnbkoa y . u y quh hafha rhsbrth hs ankhoa9 hs fhgnr, ao euhrzo fha rhsbrth hs prbpbrgnbkoa o y . u. 8
8
Encuro 7-7. Wnsthjo rhsbrth-joso-ojbrtncuofbr rhsbrth-joso-ojbrtncuofbr jbktofb sbdrh uk gorrb. gorrb.
Poro snsthjos trosaognbkoahs, ao shcukfo ahy fh Khwtbk hstodahgh quh jo % 9 E
fbkfh j hs uko joso, o hs ao oghahrogn÷k fh ao joso y C E hs hs ao sujo fh aos euhrzos quh ogtüok sbdrh ao joso. Opangokfb ao shcukfo ahy fh Khwtbk oa snsthjo prhshktofb y gbksnfhrokfb quh ha gorrb kb tnhkh joso, sh bdtnhkh f 4 y j
fy
.d 4 %
ft
b dnhk j
f 4 y 4
ft
!d
O
fu .
ft
fy ft
D
.
ft
! iy % d
i ( y . u)
fu ft
! iu
Ao hguogn÷k rhprhshkto uk jbfhab jothjïtngb fha snsthjo gbksnfhrofb. Wn sh tbjo ao troksebrjofo fh Aopaogh fh gofo tîrjnkb fh hsto üatnjo hguogn÷k sh bdtnhkh (js4 ! ds ! i )^ (s) % (ds ! i )X (s) Wn sh tbjo ha gbgnhkth hktrh ^ (s) y X (s), sh hkg hkguhk uhktro tro quh ao euk eukgn÷k gn÷k fh tro trokse ksehrh hrhkgn kgnoo fha snsthjo hs ^ (s) ds ! i Eukgn÷k fh troksehrhkgno % C(s) % X (s) % js4 ! ds ! i
www rhhAndrbs brc Voa rhprhshktogn÷k jhfnokth ao eukgn÷k fh troksehrhkgno fh uk jbfhab jothjïtngb sh uso gbk jugmo erhguhkgno hk ao nkchknhrêo fh gbktrba.
Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
53
O gbktnkuogn÷k sh bdthkfrï uk jbfhab hk ha hspognb fh hstofbs fh hsth snsthjo. Prnjhrb sh gbjpororï gbjpor orï ao hguog hguogn÷k n÷k fnehr fnehrhkgno hkgnoaa poro hsth snsthj snsthjoo ¨ % y¨
d j
8
y !
i j
y %
d
i
8
j
u!
j
u
gbk ao ebrjo hstïkfor 8
8
y¨¨ ! o? y ! o4 y % d0nn ! d?u ! d4u
h nfhktnengorhjbs o?, o 4, d 0, d ? y d 4 fha jbfb sncunhkth< o? %
d j
,
i
o4 %
j
,
d0 % 0,
d? %
d j
,
d4 %
i j
Thenrnîkfbsh o ao Hguogn÷k (4-78), sh tnhkh quh
d0 % d0 % 0 d? % d? . o?d0 %
d j
d4 % d4 . o?d? . o4d0 %
4
d
i .
j
j
OD
Pbr toktb, rhenrnîkfbsh ao Hguogn÷k (4-76), sh fhenkh x? % y . d0u % y 8
d
8
x4 % x? . d?u % x? .
j
u
O portnr fh ao Hguogn÷k (4-75), sh tnhkh quh 8
x? % x4 ! d?u % x4 %
d j
u
8
x4 % .o4 x? . o? x4 ! d4u % .
i j
x? .
d j
i
x4 !
4
d
u
.
j
j
G O DF
y ao hguogn÷k fh soanfo sh gbkvnhrth hk y % x?
b dnhk
8
GF x? 8
x4
%
G
0
? i
.
d .
j
j
F
G O DF d
GF x? x4
j
!
i
d
4
u
(7-7)
.
j
j
y y % Y?
0Z
GF x? x4
(7-6)
Aos Hguognbkhs (7-7) y (7-6) fok uko rhprhshktogn÷k hk ha hspognb fh hstofbs fha snsthjo. (Bdshrvh quh hsto kb hs ao ükngo rhprhshktogn÷k hk ha hspognb fh hstofbs. Moy nkenkntos rhprhshktognbkhs jïs hk ha hspognb fh hstofbs poro ha snsthjo.)
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5=
Nkchknhrêo fh gbktrba jbfhrko
HLHJPAB 7-6 Bdthk Bdthkco co ao eukgn eukgn÷k ÷k fh troksehr troksehrhkgno hkgno ] ?(s) / X X (s) fha snsthjo jhgïkngb quh sh juhstro hk ao Encu-
ro 7-6.
Encuro 7-6. Wnsthjo jhgïkngb.
Aos hguognbkhs fha jbvnjnhktb poro ha snsthjo prhshktofb hk ao Encuro 7-6 sbk 8
8
8
8
¨ ? % .i ? x? . i 4( x? . x4) . d( x? . x4) ! u j? x¨ ¨ 4 % .i 7 x4 . i 4( x4 . x?) . d( x4 . x?) j4 x¨
Wnjpanengokfb, sh bdtnhkh 8
8
8
8
j? x¨¨ ? ! dx? ! (i ? ! i 4) x? % dx4 ! i 4 x4 ! u j4 x¨¨ 4 ! dx4 ! (i 4 ! i 7) x4 % dx? ! i 4 x?
Vbjokfb aos troks Vbjokfb troksebrjo ebrjofos fos fh Aopaogh fh hstos fbs hguognbkhs, hguognbkhs, supbknhkfb gbkfngnbk gbkfngnbkhs hs nkngno nkngnoahs ahs kuaos, sh bdtnhkh Yj?s4 ! ds ! (i ? ! i 4)Z ] ?(s) % (ds ! i 4) ] 4(s) ! X (s)
(7-8)
Yj4s4 ! ds ! (i 4 ! i 7)Z ] 4( x) % (ds ! i 4) ] ?(s)
(7-5)
Wn sh rhsuhavh ao Hguogn÷k (7-5) poro ] 4(s), sh sustntuyh hk ao Hguogn÷k (7-8) y sh snjpanengo, sh bdtnhkh Y(j?s4 ! ds ! i ? ! i 4)( j4s4 ! ds ! i 4 ! i 7) . (ds ! i 4)4Z ] ?(s) 4 % (j4s ! ds ! i 4 ! i 7)X (s)
fh fbkfh sh sncuh ] ?(s) X (s)
%
j4s4 ! ds ! i 4 ! i 7
(j?s4 ! ds ! i ? ! i 4)( j4s4 ! ds ! i 4 ! i 7) . (ds ! i 4)4
(7-3)
(7-=)
Fh aos Hguognbkhs (7-5) y (7-3) sh tnhkh ] 4(s) X (s)
%
ds ! i 4
(j?s4 ! ds ! i ? ! i 4)( j4s4 ! ds ! i 4 ! i 7) . (ds ! i 4)4
Aos Hguognbkhs (7-3) y (7-=) sbk aos eukgnbkhs fh troksehrhkgno ] ?(s)/ X X (s) y ] 4(s)/ X X (s), rhsph rhsphgtnvo gtnvo-jhkth.
nkvhrtnfb nfb jbktofb hk uk gorr gorrb b jokhlofb pbr uk jbtbr oporh oporhgh gh hk ao Encuro 7-8(o). 7-8(o). HLHJPAB 7-8 Xk pîkfuab nkvhrt Hsth hs uk jbfhab fha gbktrba fh pbsngn÷k fh uk prbpuasbr prnjornb hspognoa poro fhsphcuhs. (Ha bdlhtnvb fha prbdahjo fha gbktrba fh pbsngn÷k hs gbkshrvor ha prbpuasbr prnjornb hspognoa hk uko pbsngn÷k pbsngn ÷k vhrtngoa. vhrtngoa.)) Ha pîkfuab nkvhrtnfb hs nkhstodah pbrquh puhfh cnror hk guoaq guoaqunhr unhr jbjhktb y hk
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Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
5>
Encuro 7-8. (o) Wnsthjo fh pîkfuab pîkfuab nkvhrtnfb9 (d) fnocrojo fh guhrpb andrh.
guoaqunhr fnrhggn÷k, o jhkbs quh sh ah opanquh uko euhrzo fh gbktrba gbkvhknhkth. Oquê sh gbksnfhro s÷ab uk prbdahjo hk fbs fnjhksnbkhs, hk ha guoa ha pîkfuab s÷ab sh juhvh hk ha paokb fh ao pïcnko. Wh opango oa gorrb ao euhrzo fh gbktrba u . Wup÷kcosh quh ha ghktrb fh crovhfof fh ao dorro fha pîkfuab hstï hk su ghktrb chbjîtrngb. Bdtîkcosh uk jbfhab jothjïtngb poro hsth snsthjo. Who m ha ïkcuab fh ao dorro rhsph rhsphgtb gtb fh ao aêkho vhrtngoa. Whok ofhjïs aos gbbrfhkofo gbbrfhkofoss ( x, y ) fha ghktrb fh crovhfof fh ao dorro fha pîkfuab ( xC, y C). Fh hsth jbfb, xC % x ! a shk m
www rhhAndrbs brc yC % a gbs m
30
Nkchknhrêo fh gbktrba jbfhrko
Poro bdthkhr aos hguognbkhs fh jbvnjnhktb poro ha snsthjo, gbksnfîrhsh ha fnocrojo fh guhrpb andrh quh oporhgh hk ao Encuro 7-8(d). Ha jbvnjnhktb rbtognbkoa fh ao dorro fha pîkfuab oarhfhfbr fh su ghktrb fh crovhfof sh fhsgrndh jhfnokth N m¨ % Ua shk m . Ma gbs m
(7->)
fbkfh N hs ha jbjhktb fh nkhrgno fh ao dorro oarhfhfbr fh su ghktrb fh crovhfof. Ha jbvnjnhktb mbrnzbktoa fha ghktrb fh crovhfof fh ao dorro fha pîkfuab sh bdtnhkh jhfnokth j
f 4 ft 4
( x ! a shk m) % M
(7-?0)
(7-??)
Ha jbvnjnhktb vhrtngoa fha ghktrb fh crovhfof fh ao dorro fha pîkfuab hs j
f 4 ft 4
( a gbs m) % U . jc
Ha jbvnjnhktb mbrnzbktoa fha gorrb sh fhsgrndh jhfnokth J
0
f 4 x ft 4
% u . M
(7-?4)
Gbjb sh fhdh jokthkhr ha pîkfuab nkvhrtnfb hk pbsngn÷k vhrtngoa, sh puhfh supbkhr quh m(t ) y
gbs m fh ebrjo quh shk m 0, gbs m(t ) sbkshphquhÿbs, (7-??) ankhoanzok fha jbfb sncunhkth<
%
0
4
? y mm
%
0. Hktbkghs, aos Hguognbkhs (7->) o
N m¨ % Uam . Ma
(7-?7)
¨ ! am¨ ) % M j( x¨
(7-?6)
0 % U . jc
(7-?8)
O portnr fh aos Hguognbkhs (7-?4) y (7-?6), sh bdtnhkh ¨ ! jam¨ % u ( J ! j) x¨
(7-?5)
O portnr fh aos Hguognbkhs (7-?7), (7-?6) y (7-?8), sh bdtnhkh N m¨ % jcam . Ma
m . a(jx¨ ¨ ! jam¨ )
% jca
b dnhk
¨ % jcam ( N ! ja 4)m¨ ! jax¨
(7-?3)
Aos Hguognbkhs (7-?5) y (7-?3) fhsgrndhk ha jbvnjnhktb fha snsthjo fha pîkfuab nkvhrtnfb hk ha gorrb. gorr b. Gbkstnt Gbkstntuyhk uyhk uk jbfhab jothjïtng jothjïtngb b fha snsthjo.
HLHJPAB 7-5 Gbksnfhrh ha snsthjo fh pîkfuab nkvhrtnfb quh sh juhstro hk ao Encuro 7-5. Gbjb hk hsth snsthjo ao
joso sh gbkghktro hk ab oatb fh ao vornaao, ha ghktrb fh crovhfof hs ha ghktrb fh ao dbao fha pîkfuab. Poro hsth gosb, ha jbjhktb fh nkhrgno fha pîkfuab rhsphgtb fh su ghktrb fh crovhfof hs phquhÿb, y sh supbkh quh N % 0 hk ao Hguogn÷k (7-?3). Hktbkghs ha jbfhab jothjïtngb poro hsth snsthjo hs ha sncunhkth< ¨ ! jam¨ % u (7-?=) ( J ! j) x¨ ¨ % jcam ja 4m¨ ! jax¨
(7-?>)
Aos Hguognbkhs (7-?=) y (7-?>) sh puhfhk jbfnengor gbjb
www rhhAndrbs brc Jam¨ % ( J ! j)cm . u ¨ % u . jcm Jx¨
(7-40)
(7-4?)
Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
3?
Encuro 7-5. Wnsthjo fh pîkfuab nkvhrtnfb. nkvhrtnfb.
Ao Hguogn÷k (7-40) sh bdtuvb hanjnkokfb x¨ fh fh aos Hguognbkhs (7-?=) y (7-?>). Ao Hguogn÷k (7-4?) sh bdtuvb hanjnkokfb m¨ fh aos Hguognbkhs (7-?=) y (7-?>). Fh ao Hguogn÷k (7-40) sh bdtnhkh quh ao eukgn÷k fh troksehrhkgno fh ao paokto hs
G(s) X (s)
.
%
?
Jas4 . ( J ! j)c
?
%
O L
Ja s !
J ! j Ja
c
D O L s.
J ! j Ja
D
c
Ao paokto fha pîkfuab nkvhrtnfb tnhkh uk pbab hk ha hlh rhoa khcotnvb Ys % .(∄ J ! j / ∄ ∄ Ja )∄ cZ y btrb hk ha hlh rhoa pbsntnvb Y s % (∄ J ! j / ∄ ∄ Ja )∄ cZ. Pbr toktb, ao paokto hs nkhstodah hk aozb odnhrtb. Whok aos vornodahs fh hstofb x ?, x 4, x 7 y x 6 sncunhkths< x? % m 0
x4 % m x7 % x 8
x6 % x
Bdshrvh quh ha ïkcuab m nkfngo ao rbtogn÷k fh ao vornaao fha pîkfuab rhsphgtb oa puktb P , y x hs ao pbsngn÷k fha gorrb. Wn sh gbksnfhrok m y x gbjb aos soanfos fha snsthjo, hktbkghs y%
G F GF G F y? y4
%
m
x
%
x? x7
(Bdshrvh quh toktb m gbjb x sbk goktnfofhs eïgnajhkth jhfndahs.) Hktbkghs, o portnr fh ao fhenkngn÷k fh vornodahs fh hstofb y fh aos Hguognbkhs (7-40) y (7-4?), sh bdtnhkh 8
x? % x4 J ! j ? x4 % cx? . u Ja Ja 8
8
x7 % x6
www rhhAndrbs brc j ? x6 % . cx? ! u J J 8
34
Nkchknhrêo fh gbktrba jbfhrko
Hk tîrjnkbs fh aos hguognbkhs vhgtbrnoahs, sh tnhkh 0 J ! j
8
x? 8
x4 8
x7
Ja
%
GF G
0 j
8
x6
.
J
y4
%
0
0
c 0
0
0
0
0
?
c 0
0
0
GF x?
GF G y?
?
?
0
0
0
0
0
?
0
F
x4
0
x? x4 x7
? .
!
GF F G x6
x7
Ja u 0 ? J
F
(7-44)
(7-47)
x6
Aos Hguognbkhs (7-44) y (7-47) fok uko rhprhshktogn÷k hk ha hspognb fh hstofbs fha snsthjo fha pîkfuab pîkfua b nkvhrtnfb. (Bdshrv (Bdshrvhh quh ao rhprhshk rhprhshktogn÷k togn÷k hk ha hspognb fh hstofb hstofbss fha snsthj snsthjoo kb hs ükngo. Moy nkenkntos rhprhshktognbkhs poro hsth snsthjo.)
7-7 Jbfhaofb
jothjïtngb fh snsthjos haîgtrngbs
Aos ahyhs eukfojhktoahs quh cbdnhrkok abs gnrguntbs haîgtrngbs sbk aos ahyhs fh gbrrnhkths y vbatolhs fh Inrgmmbee. Ao ahy fh gbrrnhkths fh Inrgmmbee (ao ahy fh kbfbs) paoktho quh ao sujo oachdrongo fh tbfos aos gbrrnhkths quh hktrok y soahk fh uk kbfb hs ghrb. (Hsto ahy tojdnîk puhfh paokthorsh fha jbfb sncunhkth< ao sujo fh aos gbrrnhkths quh hktrok o uk kbfb hs ncuoa o ao sujo fh aos gbrrnhkths quh soahk fha jnsjb.) Ao ahy fh vbatolhs fh Inrgmmbee (ao ahy fh joaaos) hstodahgh quh hk guoaqunhr nkstokth fhthrjnkofb ao sujo oachdrongo fh abs vbatolhs oarhfhfbr fh guoaqunhr joaao hk uk gnrguntb haîgtrngb hs ghrb. (Hsto ahy tojdnîk sh paoktho fha jbfb sncunhkth< ao sujo fh aos goêfos fh vbatolh hs ncuoa o ao sujo fh aos hahvognbkhs fh vbatolh oarhfhfbr fh uko joaao.) Xk jbfhab jothjïtngb fh uk gnrguntb haîgtrngb sh bdtnhkh opangokfb uko b ojdos ahyhs fh Inrgmmbee. Hsto shggn÷k troto prnjhrb abs gnrguntbs haîgtrngbs shkgnaabs y fhspuîs prhshkto ha jbfhaofb jothjïtngb jothjïtng b fh snsthjos snsthjos gbk ojpanengofbrh ojpanengofbrhss bphrognbkoah bphrognbkoahs. s. Gbksnfîrhsh ha gnrguntb gnrguntb haîgtrngb quh oporhgh oporhgh hk ao Encuro 7-3. Ha gnrguntb Gnrguntb ATG. Gbksnfîrhsh hstï ebrjofb pbr uko nkfugtokgno A (mhkrnbs), uko rhsnsthkgno T (bmjnbs) y uko gopogntokgno G (eorofnbs). Opangokfb ao ahy fh vbatolh fh Inrgmmbee oa snsthjo, sh bdtnhkhk aos hguognbkhs sncunhkths< fn
?
N N
A ft ! Tn ! G n ft % hn
?
G
n ft % hb
(7-46)
(7-48)
www rhhAndrbs brc
=5
Nkchknhrêo fh gbktrba jbfhrko
HLHJPABW FH PTBDAHJOW ^ WBAXGNBKHW O-7-?. Ao Encuro 7-40(o) juhs juhstro tro uk fnocrojo hsquhjïtngb fh uk snsthjo fh susphk susphksn÷k sn÷k fh uk outbj÷-
vna. Gbkebrjh ha outbj÷vna ovokzo pbr uk gojnkb, abs fhspaozojnhktbs vhrtngoahs fh aos aaoktos eukgnbkok gbjb uko hxgntogn÷k fh jbvnjnhktb poro ha snsthjo fh susphksn÷k fha outbj÷vna. Ha jbvnjnhktb fh hsth snsthjo gbksnsth hk uk fhspaozojnhktb fha ghktrb fh ao joso y uk cnrb oarhfhfbr fha ghktrb fh ao joso. Ha jbfhaofb jothjïtngb fha snsthjo gbjpahtb hs dostokth gbjpangofb. Xko vhrsn÷k juy snjpanengofo fha snsthjo fh susphksn÷k oporhgh hk ao Encuro 7-40(d). Wupbknhkfb quh ha jbvnjnhktb x n hk ha puktb P hs ao hktrofo oa snsthjo y ha jbvnjnhktb vhrtngoa x b fha guhrpb hs ao soanfo, bdthkco ao eukgn÷k fh troksehrhkgno ] b(s)/ ] n (s). (Gbksnfhrh ha jbvnjnhktb fha guhrpb s÷ab hk ao fnrhggn÷k vhrtngoa.) Ha fhspaozojnhktb x b sh jnfh o portnr fh ao pbsngn÷k fh hqunandrnb hk oushkgno fh ao hktrofo x n. Wbaugn÷k. Ao hguogn hguogn÷k ÷k fh jbvnj jbvnjnhktb nhktb por poroo ha snsthjo snsthjo fh ao Encuro Encuro 7-40 7-40(d) (d) hs
¨ b ! d( xb . xn) ! i ( xb . xn) % 0 jx¨ 8
8
b dnhk jx¨¨ b ! dxb ! ixb % dxn ! ixn 8
8
Wn sh tbjo ao troksebrjofo fh Aopaogh fh hsto üatnjo hguogn÷k, y sh supbkhk gbkfngnbkhs nkngnoahs fh ghrb, sh bdtnhkh (js4 ! ds ! i ) ] b(s) % (ds ! i ) ] n (s) Pbr toktb, ao eukgn÷k fh troksehrhkgno ] b(s)/ ] n(s) sh bdtnhkh jhfnokth ] b(s) ] n (s)
%
ds ! i 4
js
! ds ! i
Encuro 7-40. (o) Wnsthjo fh susphksn÷ susphksn÷k k fh uk outbj÷vna9 outbj÷vna9 (d) snsthjo fh susphksn÷k snjpanengofb.
www rhhAndrbs brc Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
=3
O-7-4. Bdthkco ao eukgn÷k fh trokseh troksehrhkgno rhkgno ^ (s)/ X X ( s) fha snsthjo fh ao Encuro 7-4?. Ao hktrofo u hs uk
fhspaozojnhktb. (Oa ncuoa quh ha snsthjo fha prbdahjo O-7-?, hsto hs uko vhrsn÷k snjpanengofo fh uk snsthjo fh susphksn÷k fh uk outbj÷vna b uko jbtbgngahto.) Wbaugn÷k. Wupbkco qu quhh abs fhspaozojnh fhspaozojnhktbs ktbs x h y sh jnfhk rhsphgtnvojhkth o portnr fh aos
pbsngnbkhs hk hstofb hstognbkornb hk oushkgno fh hktrofo u . Opangokfb ao shcukfo ahy fh Khwtbk oa snsthj snsthjo, o, sh bdtn bdtnhkh hkh j? x¨ ¨ % i 4( y . x) ! d( y . x) ! i ?(u . x) 8
8
¨ % .i 4( y . x) . d( y . x) j4 y¨ 8
8
Pbr toktb, sh tnhkh quh ¨ ! dx ! (i ? ! i 4) x % dy ! i 4 y ! i ?u j? x¨ 8
8
¨ ! dy ! i 4 y % dx ! i 4 x j4 y¨ 8
8
Vbjokfb ao troksebrjofo fh Aopaogh fh hstos fbs hguognbkhs y supbknhkfb gbkfngnbkhs nkngnoahs fh ghrb, sh bdtnhkh Yj?s4 ! ds ! (i ? ! i 4)Z ] (s) % (ds ! i 4)^ (s) ! i ?X (s) Yj4s4 ! ds ! i 4Z^ (s) % (ds ! i 4) ] (s) Hanjnkokfb ] (s) fh aos fbs üatnjos hguognbkhs, sh tnhkh 4
(j?s
! ds ! i ? ! i 4)
j4s4 ! ds ! i 4 ds ! i 4
^ (s) % (ds ! i 4)^ (s) ! i ?X (s)
fh ab guoa sh fhfugh ^ (s) X (s)
%
i ?(ds ! i 4) 6
j?j4s
7
4
! (j? ! j4)ds ! Yi ?j4 ! (j? ! j4)i 4Zs ! i ?ds ! i ?i 4
Encuro 7-4?. Wnsthjo fh susphksn÷k. O-7-7.
Bdthk Bdthkco co ao rhprhshk rhprhshktogn÷k togn÷k hk ha hspognb fh hstofb hstofbss fha snsthjo snsthjo jbstrofb jbstrofb hk ao Encuro 7-44. 7-44. Wbaugn÷k. Aos hgu hguognb ognbkhs khs fha snst snsthjo hjo sbk ¨ ? ! dy? ! i ( y? . y4) % 0 j? y¨ 8
¨ 4 ! i ( y4 . y?) % u j4 y¨
www rhhAndrbs brc ==
Nkchknhrêo fh gbktrba jbfhrko
Aos vornodahs fh soanfo poro hsth snsthjo sbk y ? h y 4. Wh fhenkhk aos vornodahs fh hstofb gbjb x? % y? x4 % y? 8
x7 % y4 x6 % y4 8
Hktbkghs sh bdtnhkhk aos sncunhkths hguognbkhs< x? % x4 8
x4 %
?
8
Y.dy? . i ( y? . y4)Z % .
i
8
j?
j?
x? .
d j?
x4 !
i j?
x7
x7 % x6 8
x6 %
?
8
j4
Y.i ( y4 . y?) ! uZ %
i j4
x? .
i j4
x7 !
? j4
u
Fh omê, ao hguogn÷k fh hstofb hs 0 i
x? 8
GF G x4 8
x7
%
0 i
. j? . j? 0
8
8
0
0 .
j4
0 0
x?
GF F G F FG F
j?
0
i
x6
y ao hguogn÷k fh soanfo hs
? d
i
j4
0
?
0
x4 x7
!
x6
0 0 ?
u
j4
x?
GF G y?
%
y4
?
0
0
0
0
0
?
0
x4 x7 x6
Encuro 7-44. Wnsthjo jhgïkngb. O-7-6. Bdthk Bdthkco co ao eukgn÷k fh troks troksehrh ehrhkgno kgno ] b(s) / ] n (s) fha snsthjo jhgïkngb quh oporhgh hk ao Encu-
ro 7-47( 7-47(o). o). Goa Goagüa güahsh hsh ofhjïs ofhjïs ao eukgn eukgn÷k ÷k fh tro trokse ksehrh hrhkgn kgnoo fha gnr gnrgun guntb tb haîgtr haîgtrngb ngb fh ao Encuro Encuro 7-47(d). Fhjuhstrh quh aos eukgnbkhs fh troksehrhkgno fh abs fbs snsthjos tnhkhk uko ebrjo nfîktngo y, pbr toktb, sbk snsthjos okïabcbs. Wbaugn÷k. b Hkrhpbsb. ao Encuro 7-4 7-47(o) 7(o)aos sh supbkh quh abs fhspaozojnhktbs nhktbs xnha , xsnsthjo h y sh jnfhk fhsfh pbsngnbkhs hk Hktbkghs hguognbkhs fh fhspaozoj jbvnjnhktb poro jhgïkngb fhsus ao Encuro 7-47(o) sbk d?( xn . xb) ! i ?( xn . xb) % d4( xb . y) 8
8
d4( xb . y) % i 4 y 8
8
8
8
www rhhAndrbs brc Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
=>
Vbjokfb ao troksebrjofo fh Aopaogh fh hstos fbs hguognbkhs y supbknhkfb gbkfngnbkhs nkngnoahs fh ghrb, thkhjbs d?Ys] n (s) . s] b(s)Z ! i ?Y ] n (s) . ] b(s)Z % d4Ys] b(s) . s^ (s)Z d4Ys] b(s) . s^ (s)Z % i 4^ (s)
Wn sh hanjnko ^ (s) fh aos fbs üatnjos hguognbkhs, sh bdtnhkh d?Ys] n (s) . s] b(s)Z ! i ?Y ] n (s) . ] b(s)Z % d4s] b(s) . d4s
d4s] b(s) d4s ! i 4
b dnhk
O
(d?s ! i ?) ] n (s) % d?s ! i ? ! d4s . d4s
d 4s d4s ! i 4
D
] b(s)
Pbr toktb, ao eukgn÷k fh troksehrhkgno ] b(s)/ ] n (s) sh bdtnhkh gbjb
O
d?
] b(s)
%
i ?
DO
s!?
d? s ! ? i ?
] n (s)
O
DO
d4 i 4
D
s!?
d4 s ! ? i 4
D
!
d4 s i ?
Poro ha snsthjo haîgtrngb fh ao Encuro 7-47(d), ao eukgn÷k fh troksehrhkgno H b(s)/ H n (s) rhsuato shr
H b(s) H n (s)
T? ! %
? (?/ T4) ! G 4s
? G ?s
! T? !
?
%
( T?G ?s ! ?)( T4G 4s ! ?) ( T?G ?s ! ?)( T4G 4s ! ?) ! T4G ?s
G ?s
Ao gbjporogn÷k fh aos eukgnbkhs fh troksehrhkgno fhjuhstro quh abs snsthjos fh aos Encuros 7-47(o) y (d) sbk okïabcbs.
Encuro 7-47. (o) Wnsthjo jhgïkngb9 jhgïkngb9 (d) snsthj snsthjo o haîgtrngb okïabcb. okïabcb.
www rhhAndrbs brc Gopêtuab 7. Jbfhaofb jothjïtngb fh snsthjos jhgïkngbs y snsthjos haîgtrngbs
>3
Ha tîrjnkb Yd0 ! (I 4I 7/ To)Zs nkfngo quh hehgtnvojhkth ao euhrzo gbktrohahgtrbjbtrnz fha jbtbr nkgbhengnhk nhkth th fh erngg ernggn÷k n÷k vns vnsgbs gbsoo grhjhk grh jhkto to ao ern ernggn ggn÷k ÷k vns vnsgbs gbsoo fha snst snsthjo hjo.. Ao nkh nkhrgn rgnoo L 0 y ha gbheng d0 ! (I 4I 7/ To) sh rhenhrhk oa hlh fha jbtbr. Guokfb sh juatnpangok L 0 y d0 ! (I 4I 7/ To) pbr ?/ k4, ao nkhrgno y ha gbhengnhkth fh ernggn÷k vnsgbso sh hxprhsok hk eukgn÷k fh ao soanfo fha hlh. Wn sh nktrbfughk kuhvbs porïjh porïjhtrbs trbs fhenknfbs pbr L % L 0/ k4 % jbjhktb fh nkhrgno rhehrnfb o ao soanfo fha hlh D % Yd0 ! (I 4I 7/ To)Z/ k4 % gbhengnhkth fh ernggn÷k vnsgbso rhehrnfb o ao soanfo fha hlh I % I 0I ?I 4/ k kT To
ao eukgn÷k fh troksehrhkgno C (s) fofo pbr ao Hguogn÷k (7-8?) sh snjpanengo fh ao ebrjo I C(s) % 4 Ls ! Ds
b dnhk C(s) %
I j s(V js ! ?)
fbkfh I I j % , D
L
To L
0 V j % % D Tod0 ! I 4I 7
Osê, ha fnocrojo fh dabquhs fha snsthjo fh ao Encuro 7-4>(d) sh puhfh snjpanengor oa quh oporhgh hk ao Encuro 7-4>(g).
PTBDAHJOW D-7-?. Bdthkco ha gbhengnhkth fh ernggn÷k vnsgbso hqun-
D-7-4. Bdthkco Bdthkco jbfhabs jothjï jothjïtngbs tngbs fh abs snsthjos
voahkth d hq fha snsthjo fh ao Encuro 7-70.
jhgïkngbs fh aos Encuros 7-7?(o) y (d).
Encuro 7-70. Wnsthjo fh oj ojbrtncuofbrhs. brtncuofbrhs.
Encuro 7-7?. Wnsthjos jhgïkngbs.
www rhhAndrbs brc
>=
Nkchknhrêo fh gbktrba jbfhrko
D-7-7. Bdthkco uko rhprhshktogn÷k hk ha hspognb fh hs-
tofbs fha snsthjo jhgïkngb fh ao Encur Encuroo 7-74, fbkfh u ? y u4 sbk hktrofos h y ? h y 4 sbk soanfos.
Encuro 7-76. Wnsthjo fh pîkfuab pîkfuab nkvhrt nkvhrtnfb. nfb. D-7-5. Bdthkco ao eukgn÷k fh troksehrhkgno ] ?(s)/ X X ( s) y
] 4(s)/ X X (s) fha snsthjo jhgïkngb quh sh juhstro hk ao Encuro 7-78. Encuro 7-74. Wnsthjo jhgïkngb. D-7-6. Gbksnfhrh ha snsthjo fha pîkfuab oggnbkofb pbr
rhsbrth fh ao Encuro 7-77. Wupbkco quh ao euhrzo fha rhsbrth quh ogtüo sbdrh ha pîkfuab hs ghrb guokfb ha pîkfuab hstï vhrtngoa, b dnhk m % 0. Wupbkco tojdnîk quh ao ernggn÷k nkvbaugrofo hs nksncknengokth y quh ha ïkcuab fh bsgnaogn÷k m hs phquhÿb. Bdthkco uk jbfhab jothjïtngb fha snsthjo.
Encuro 7-78. Wnsthjo jhgïkngb. D-7-3. Bdthkco ao eukgn÷k fh troksehrhkgno H b(s)/ H n (s)
fha gnrguntb haîgtrngb quh sh juhstro hk ao Encuro 7-75.
Encuro 7-75. Gnrguntb haîgtrngb. D-7-=. Gbksnfhrh ha gnrguntb haîgtrngb quh sh juhstro
Encuro 7-77. Wnsthjo fh pîkfuab gorco-rhsbrth. gorco-rhsbrth.
hk ao Encuro 7-73. Bdthkco ao eukgn÷k fh troksehrhkgno H b(s)/ H n (s) utnanzokfb ao oprbxnjogn÷k fh fnocrojos fh dabquhs.
D-7-8. Thjntn Thjntnîkfbsh îkfbsh o abs Hlhjpabs 7-8 y 7-5, gbksnfh-
rh ha snsthjo fha pîkfuab nkvhrtnfb fh ao Encuro 7-76. Wupbkco quh ao joso fha pîkfuab nkvhrtnfb hs j y quh hstï fnstrndunfo hquntotnvojhkth o ab aorcb fh ao abkcntuf fh ao dorro. (Ha ghktrb fh crovhfof fha pîkfuab sh udngo hk ha ghktrb fh ao dorro.) Wupbknhkfb quh m hs phquhÿb, bdthkco jbf jbfhab habss jot jothjï hjïtng tngbs bs por poroo ha snsthj snsthjoo hk ebr ebrjo jo fh hguognbkhs hguog nbkhs fnehr fnehrhkgno hkgnoahs, ahs, eukgn eukgnbkhs bkhs fh troks troksehrh ehrhkgno kgno y hguognbkhs hk ha hspognb fh hstofb.
Encuro 7-73. Gnrguntb haîgtrngb.
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