Oi?aaeaiea – ioiineony e iaoaiaoe/aneie oai?ee oi?aaeaiey
aeaeaeaieai oaoie/aneie nenoaiu.
Iaiaoiaeeii iaienaoue aeai?eoi, ii eioi?iio iaeioi?ay nenoaia
oi?aaeyaony n iiiiuueth yia?aaoe/aneiai aicaeaenoaey, iai?eia? :
eaoaoaeueiue aiia?ao oi?aaeyaony n iiiiuueth ?oeaaie iaoeiu. Ieacuaaaony
nicaeaoue oi?aaeaiea yoi ia i/aiue neiaeii e yoi iiaeii naeaeaoue
eiooeoeaii. Iaeiaei nicaeaoue iioeiaeueiia oi?aaeaiea /?acau/aeii
neiaeii.
Oai?ey iioeiecaoeee – yoi iaoea i iaeeo/oeo aeai?eoiao
(oi?aaeaiey) nicaeaiiuo ii iaeioi?iio e?eoa?eth ea/anoaa
E?eoa?ee ea/anoaa – nicaeaiea (aano?aeoiia) iaeioi?ie ooieoeee
?enea, eioi?ay aeieaeia auoue a i?ioeanna iioeiecaoeee ieieiece?iaaiia
(yeno?aiaeueiay caaea/a).
Oi?aaeaiea auaaao iioeiaeueiui e eaaceiioeiaeueiui.
Iioeiaeueiia – ia aoiaaa,
Eaaceiioeiaeueiia – ?aaeueiia, no?aieony e eaeaaeueiiio.
Oi?aaeaiea auaaao :
1) I?ia?aiiiia
N iiiiuueth io?eoeaoaeueiie ia?aoiie nayce
I?ia?aiiiia oi?aaeaiea –
o?aaoaony nicaeaoue i?ia?aiio, eioi?ay aeaao iioeiaeueioth o?aaeoi?eth
(caeiaeaia a YAI) aeaeaeaiey iaeioi?ie nenoaiu.
I?eia? 1 : Ia?aaiae eaoaoaeueiiai aiia?aoa ec oi/ee A a
oi/eo A.
E?eoa?ee – ieieiece?iaaoue ?anoiae ai?th/aai.
Aeey ?aaeecaoeee oaeie caaea/e nicaeaii aeaa nenoaiu – Novstar
(NOA) e Aeiiann (?inney), noieiinoue eo i/aiue auniea.
I?eia? 2 : Iaaei nicaeaoue oaeoth o?aaeoi?eth, /oiau oa?ee neaoeeny ec
oi/ee ‘A’ a oi/eo ‘A’ ca ieieiaeueiia a?aiy.
A
A – Iioeiaeueiay
A
A
o?aaeoi?ey
Oi?aaeaiea n iiiiuueth io?eoeaoaeueiie ia?aoiie nayce
Io?eoeaoaeueiie ia?aoiie naycueth – iacuaaaony ia?aaea/a yia?aee n
auoiaea ia aoiae iaeioi?ie oi?aaeyaiie nenoaiie
ao + Nenoaia auo
ia?aoiay naycue
Auaaao aeaa aeaea ia?aoiie nayce : Iieiaeeoaeueiay IN e io?eoeaoaeueiay
IN.
Io?eoeaoaeueiay IN oiaiueoaao aoiaeiia aicaeaenoaea ia nenoaio
i?iii?oeeiiaeueii auoiaeiiio ioeeeeo (aeaiioe?oao nenoaio a oeaeii).
Aaoiiaoeea – iaoea eco/athuay oai?eth aiaeeca e neioaca
nenoai oi?aaeaiey (ei??aeoe?iaea aeaeaeaiey, iioeiecaoeey
ia?aoiaeiuo i?ioeannia) e nicaeaiea iioeiaeueiiai oi?aaeaiey.
?aaeeiaaoiiaoeea – iaoea, eco/athuay aii?inu oi?aaeaiey
aeaeaeaieai ?aaeeioaoie/aneeo nenoai.
No?oeoo?iay noaia nenoaiu ?aaeeioi?aaeaiey :
?aaeei- ((( Ono?ienoai (-(( Iauaeo (( Aeao/ee
i?eaiiee Oi?aaeaiey Oi?aaeaiey
IIN
?aaeeii?eaiiia ono?ienoai – ono?ienoai auaeaeaiey neaiaea
ii iaeioi?iio ?aaeeieaiaeo.
Iniaaiiinoue auaeaeaiey neaiaea ninoieo a oii, /oi neaiae
auaeaeyaony ia oiia aioo?aiieo ooiia e iiiao.
Aioo?aiiea ooiu – oaieiaua ooiu, eioi?ua anaaaea eiatho
ianoi a ?aaeeii?eaiiii ono?ienoaa.
Oaeei ia?acii a ?aaeeiaaoiiaoeea neo/aeiua i?ioeannu eco/athony iniai
(ooi, iiiaoa, naia o?aaeoi?ey aeaeaeaiey)
Ono?ienoai oi?aaeaiey – eae i?aaeei – au/eneeoaeueiay nen-
oaia n i?eaiaeii e yia?aaoe/aneie
onoaiiaeie.
I?eaiae – i?aia?aciaaoaeue iaoaie/aneeo eieaaaiee a yeae-
o?e/aneea.
Iauaeo oi?aaeaiey – iaeioi?ay aeeiaie/aneay nenoaia.
Aeeiaie/aneay nenoaia – nenoaia, eioi?ay iienuaaaony ee-
iaeiuie e iaeeiaeiuie aeeooa?ai-
oeeaeueiuie o?aaiaieyie aunieiai
ii?yaeea.
Aeao/ee – ono?ienoai, eioi?ia ecia?yao iieiaeaiea eaoaoaeue-
iiai aiia?aoa a i?ino?ainoaa.
Aeaaa 1 Noioanoe/aneia oi?aaeaiea
A neo/aa noioanoe/aneiai oi?aaeaiey, oi?aaeyaiua i?ioeannu yaeythony
neo/aeiuie (noioanoe/aneeie). Ia/aeueiay oi/ea oi?aaeaiey A e eiia/iay A
ia ecaanoiu. A yoii neo/aa nai
oi?aaeyaiue i?ioeann iienuaaaony noioanoe/aneeie o?aaiaie-
yie, eioi?ua, eae i?aaeei, ai?ieneie?othony ia?eianeeie i?ioeannaie.
I?eia?u nenoai aaoiiaoe/aneiai oi?aaeaiey
Nenoaiu aaoiiaoe/aneiai oi?aaeaiey iiaeii iienaoue i?eaee-
aeaiii eniieuecoy eeiaeiua eee iaeeiaeiua aeeooa?aioeeaeueiua
o?aaiaiey (aeaoa?ieie?iaaiiue iiaeoiae aac o/aoa ooiia).Yoi
auei aei 60o aiaeia: ana iiaeoiaeu auee noioanoe/aneea eeiaeiua e
iaeeiaeiua aeeooa?aioeeaeueiua o?aaiaiey.
I?eia? 1 (aeaoa?ieie?iaaiiue)
Oi?aaeaiea aeaeaeaieai einie/aneiai aiia?aoa a a?aae-
oaoeeiiiii iiea caiee (caaea/a aeaoo oae).
A aaioeaio?e/aneie nenoaia eii?aeeiao
Z r – ?annoiyiea io oeaio?a caiee
C – oeaio? caiee (any aa ianna)
E.A.
r E.A. – einie/aneee aiia?ao
X Ia einie/aneee aiia?ao aeaenoaoao
C i?eoyaeaiea :
E.A. F2 – oi?aaeythuay neea
F3 – nii?ioeaeaiea n?aaeu
O?aoee caeii Iuethoiia :
Anee yoi o?aaiaiea ni?iaeoe?iaaoue ia ine ei-
i?aeeiao, oi iieo/ei neaaeothuea o?e o?aaiaiey :
(1)- nenoaia eeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee 2-ai ii-
?yaeea, eioi?ay iienuaaao aeaeaeaiea einie/aneiai aiia-
?aoa.
Neeu U1,U2,U3 – neeu oi?aaeaiey.
r(t) – o?aaeoi?ey
Ieacuaaaony, /oi a caaeneiinoe io ia/aeueiuo oneiaee e ia-
?aiao?ia K1,K2,K3 o?aaeoi?ey r(t) iiaeao auoue e?oaiaay,
yeeeinieaeiay, ia?aaiee/aneay.
I?eia? 2 : Iaeeiaeiay nenoaia. Iienuaaaony iaeeiaeiui
aeeooa?aioeeaeueiui o?aaiaieai.
Aaia?aoi? eieaaaiee :
Iiaeii iieacaoue, /oi i?ioeann
x(t) iienuaaaony aeeooa?ai-
x(t) oeeaeueiui o?aaiaieai 2-ai
M ii?yaeea n iaeeiaeiui
.
R
C Anee aieinoue aa?uee?iaaoue,
iiaeao noaoue io-
eai e oiaaea iu iieo/ei ne-
ionieaeaeueiia eieaaaiea:
x(t)=a sin((t+()
(aaoieieaaaiey)
– iieiaeeoaeueii, oi aiieeooaea eieaaaiee oaaee-
/eaaaony n oa/aieai a?aiaie.
– io?eoeaoaeueii – aiieeooaea eieaaaiee oiaiueoa-
aony n oa/aieai a?aiaie aei ioey.
Aeaaa 2
Iaoaiaoe/aneia iienaiea nenoai (aeaoa?ieie?iaaiiay oa?ey) (eaeaaeueiue
neo/ae)
Eeiaeiua nenoaiu, eioi?ua iienuaathony aeeooa?aioeeaeueiuie
o?aaiaieyie iacuaathony aeeiaie/aneeie nenoaiaie.
Anee nenoaia iienuaaaony aeaaa?ae/aneeie o?aaiaieyie –
– yoi iienaiea ninoiyiey ?aaiiaaney (noaoe/aneea nenoaiu)
(1)
(1)- eeiaeiia aeeooa?aioeeaeueiia o?aaiaiea n-ai ii?yaeea.
I?aaay /anoue – yoi aeeooa?aioeeaeueiia o?aaiaiea aic-
aeaenoaey. Anee Ly=0 (2) ,oi Ly=Px.
(2)- iaeii?iaeiia aeeooa?aioeeaeueiia o?aaiaiea – iienuaaao
eeiaeiua aeeiaie/aneea nenoaiu aac aicaeaenoaey ia
ieo. Iai?eia? eieaaaoaeueiue eiioo?.
I?aaay /anoue o?aaiaiey (1) iienuaaao aicaeaenoaea ia ee-
iaeioth nenoaio eee iacuaaaony oi?aaeaieai.
Ly=x – oi?aaeaiea.
Anee anoue /anoue Px – oi yoi neiaeiia oi?aaeaiea, o/eouaa-
thuaa nei?inoue, onei?aiea.
Ia?aaeaoi/iay ooieoeey eeiaeiie nenoaiu
Io aeeooa?aioeeaeueiiai o?aaiaiey (1) iiaeii ia?aeoe e eeiae-
iie nenoaia, o.a. e iaeioi?iio /aou?aoiiethnieeo.
Ao W(p) Auo
Yoio /aou?aoiiethniee iiaeii nicaeaoue ia yeaiaioiie aaca eee
niiaeaee?iaaoue ia YAI.
Io aeeooa?aioeeaeueiiai o?aaiaiey (1) e W(p) iiaeii ia?aeoe
aeaoiy iooyie – eniieuecoy neiaiee/aneee iaoiae e 2-a i?ai-
a?aciaaiea Eaieana.
Neaiiee/aneee iaoiae Oeae Naeaea.
I?eiaiea neiaiee/aneee iaoiae e (1) iieo/ei :
(3)
Oi?ioea (3) i?aaenoaaeyao niaie ioiioaiea aeaoo iieeiiiia –
iienaiea ia?aaeaoi/iie ooieoeee.
Eniieueciaaiea i?aia?aciaaiey Eaieana
– i?aia?aciaaiea Eaieana, p=j(
Anee iu i?eiaiei i?aia?aciaaiea Eaieana e eaaie /anoe (1)
, iieo/ei :
(4)
X(p) Y(p)
W(p)
Anee i?aaay /anoue ia?aaeaoi/iie ooieoeee i?inoaeoay –
, oi aicaeaenoaea iau/iia. Ia?aaeaoi/-
iay ooieoeey aoaeao eiaoue aeae :
, aaea ciaiaia-
oaeue ae?iae anoue oa?aeoa?enoe/aneia o?aaia-
iea.
I?eia? : Aeeooa?aioeeaeueiia o?aaiaiea 2-ai ii?yaeea iienu-
aaaony ia?aaeaoi/iie ooieoeeae :
(6)
Aeey iaoiaeaeaiey ?aoaiey aeeooa?aioeeaeueiiai o?aaiaiey nia/a-
ea iaiaoiaeeii ?aoeoue neaaeothuaa o?aaiaiea :
Ecaanoii, /oi aeeooa?aioeeaeueiia o?aaiaiea 2-ai ii?yaeea
eiaao ?aoaiea a aeaea eiiieaeniie yeniiiaiou eee aeaenoaee
iaae iae. (Yoi caaeneo io ei?iae oa?aeoa?enoe/aneiai o?aa-
iaiey). Anee ei?ie eiiieaeniua, oiaaea ?aoaiea aoaeao :
(t)
(7)(
(7) e (7)’ – ?aoaiea a aeaea ia?anoathuae eee caoooathuae neionieaeu,
eeai iau/iie neionieaeu, anee (=0.
Onoie/eainoue eeiaeiuo nenoai
Eeiaeiay nenoaia iieiinoueth iienuaaaony ia?aaeaoi/iie ooie-
oeeae, eioi?ay i?aaenoaaeyao niaie :
a eiiieaneiie ieineinoe
p=(+j( . Yoe iieeiiiu iieo/aiu ec aeeooa?aioeeaeueiuo o?aa-
iaiee iooai i?aia?aciaaiey Eaieana.
Noaaeony i?iaeaia: eae enneaaeiaaoue nenoaio n iiiiuueth W(p)
Ieacuaaaony, /oi yoi i?iua naeaeaoue /ai enneaaeiaaoue aeeooa-
?aioeeaeueiua o?aaiaiey. Enneaaeiaaiea ii W(p) i?iecaiaeeony n iiiiuueth
aiaeeca iiethnia e ioeae.
Iiethnii iacuaaaony oi cia/aiea ei?iy o?aaiaiey a ciaiaiaoaea, i?e
eioi?ii Q(p)=0.
Eiee/anoai ei?iae ii?aaeaeyaony noaiaiueth iieeiiia. Anee
)=0,
W(p)=( – iiethn.
Ioeyie W(p) iacuaathony oi/ee ia eiiieaeniie ieineinoe,
aaea iieeiii P(p)=0.
Eiee/anoai ioeae ii?aaeaeyaony ii?yaeeii iiee-
iiia.
j(
( > 0 iiethnu
( > 0
– iiethnu (ei?ie oa?aeoa?enoe/aneiai o?aa-
iaiey). Anee ei?ie eiiieaeniua, oi iie nii?yaeaiiua.
Auaiaeu :
1. Anee ei?ie oa?aeoa?enoe/aneiai o?aaiaiey Q(p)
iaoiaeyony a eaaie iieoieineinoe , oi nenoaia on-
((t(() – ?aoaiea aeey eiiieaeniuo
ei?iae.
((t(().
Nenoaia iaonoie/eaa.
?aniieiaeaiea ioeae ii?aaeaeyao ei??aeoe?othuea naienoaa nenoaiu,
o.a. ieacuaatho aicaeaenoaea ia ia?aoiaeiie i?ioeann
Anee ioee a eaaie iieoieineinoe, oi oaeay nenoaia iacuaaaony
ieieiaeueii oaciaie.
Anee ioee a i?aaie iieoieineinoe – iaeeiaeii oaciaay
nenoaia.
Anee iiethnu ia iieiie ine, o.a. (=0, oi nenoaia iaoi-
aeeony a eieaaaoaeueiii ?aaeeia (Nenoaia aac iioa?ue).
Ia?aaeaoi/iay ooieoeey eeiaeiie nenoaiu ia iieiie ine
A yoii neo/aa iinea i?aia?aciaaiee iieo/ei:
W(j()=A(()+jB(() –
Ia?aaeaoi/iay ooieoeey anoue eiiieaeniia /enei.
Caia/aiea: Ia iooaoue n ei?iyie ia iieiie ine.
Ieacuaaaony i/aiue oaeiaii enneaaeiaaoue W(j()ia iieiie ine ia n
iiiiuueth ioeae e iiethnia, a n eniieueciaaieai eiiieae-
niie ia?aaeaoi/iie ooieoeee.
Eiiieaeniay ooieoeey :
A*O
O*O
A*O iieacuaaao naeaeoeaiinoue nenoaiu ii
aiieeooaeiiio niaeo?o.
O*O iieacuaaao – eaeie naeaea oac iieo/aao ia
auoiaea oeeueo?a eaaeaeay aa?iiieea.
Caia/aiea: Ecaanoii, /oi niaeo? neaiaea (ii
Oo?uea) oaeiaii i?aaenoaaeyoue a eii-
ieaeniie aeaea, o.a. o niaeo?a anoue A*O (?an-
i?aaeaeaiea aa?iiiee ii aiieeooaea io /anoiou), e O*O (?an-
i?aaeaeaiea oac).
Auaiaeu: Eiiieaeniia i?aaenoaaeaiea niaeo?a eee ia?aaeaoi/-
iie ooieoeee W(p) i/aiue oaeiaii ?aaeeioaoieea. Yoi
iicaieyao eiiiaeoii caienaoue A*O e O*O.
Ia?aaeaoi/iay ooieoeey nenoai ?aaeeiaaoiiaoeee
1)
auo
Ia?aaeaoi/iay ooieoeey iineaaeiaaoaeueii niaaeeiaiiuo caaiue-
2)
Ia?aaeaoi/iay ooieoeey ia?ae-
eaeueii niaaeeiaiiuo caaiueaa:
ao auo
: :
: :
: :
3) y(t) Ia?aaeaoi/iay ooieoeey nenoaiu
(((( n ia?aoiie naycueth:
Oeiiaua caaiuey ?aaeeiaaoiiaoeee
1) Eia?oeeiiiia caaii
Ia?aaeaoi/iay ooieoeey :
C
W(() A*O
K
( (()= – arctgT( O*O
0
(
-45(
-90(
2) Eioaa?e?othuaa caaii
Ia?aaeaoi/iay ooieoeey :
3) Aeeooa?aioee?othuaa caaii
C
R
R L
W(() A*O Ia?aaeaoi/iay ooieoeey :
W(p)=Kp
A*O: W(()=K(
0 (
4) Oi?ne?othuaa caaii
W(() A*O
Ia?aaeaoi/iay ooieoeey:
0
( (()
0 (
5) Caiacaeuaathuaa caaii
=1 Ia?aaeaoi/iay ooieoeey :
((() O*O
A*O
1
Caiacaeuaathuaa caaii iacuaaaony eeieae caaea?aeee, aaea
5) Eieaaaoaeueiia caaii
Ia?aaeaoi/iay ooieoeey:
– ia?aiao? caoooaiey
1 – naiiaicaoaeaeathuayny
nenoaia
O*O
6) Iaieieiaeueii oaciaia caaii
Ia?aaeaoi/iay ooieoeey:
; W(()=1
A*O
O*O
Oeeo?iaua nenoaiu aaoiiaoe/aneiai oi?aaeaiey
Caaeai i?ioeann: Aoaeai ?anniao?eaaoue i?i-
y(t) oeann y(t) a aeene?aoiua ii-
iaiou a?aiaie.
Oaeie i?ioeann iacuaaaony n
aeene?aoiui a?aiaiai.
Cia/aiey yoiai i?ioeanna a
aeene?aoiua iiiaiou :
– cia/aiey
Nouanoaotho aeaa oeia i?ioeanna n aeene?aoiui a?aiaiai :
1)I?ioeann n aeene?aoiui a?aiaiai e iai?a?uaiui iiiaeanoaii
yaeyaony iai?a-
iai?a?uaia a
n?aaeiai eaaae?aoe/aneii).
ICN
– iai?a?uaiua ooieoeee
ICN – i?eai? n ca?yaeiaie naycueth
– eioa?aae aeene?aoecaoeee ai a?aiaie (eaaioiaaiea ii
a?aiaie)
Aeey oaeeo i?ioeannia ninoaaeythony ?aciinoiua o?aaiaiey :
– 1-a i?e?auaiea, eiia/iay ?aciinoue
– 2-y ?aciinoue
2) I?ioeann n aeene?aoiui a?aiaiai e aeene?aoiui iiiaeanoaii
ninoiyiee.
caienu-
aaaony a oeeo?iaii aeaea – aeene?aoiay ooieoeey, any aaca
enneaaeiaaiee ae?oaay. Eaaioiaaiea eaeao e ai a?aiaie e
ii o?iaith.
I/aiue /anoi aeaeaaony aeia?iia eaaioiaaiea 0;1. A yoii
neo/aa aiia?aoo?a neeueii oi?iuaaony.
Caia/aiea :
, oi auoiae-
, o.a. oaeie aea, ii aeene?ao-
iue.
– aeiiieaeueiia ?ani?aaeaeaiea.
Ieacuaaaony, anee /enei o?iaiae eaaioiaaiey ( 8,oi
eo iiaeii ioiaeaeanoaeoue n iai?a?uaiuie nenoaiaie.
I?aaenoaaeaiea aeeooa?aioeeaeueiuo o?aaiaiee, iienuaathueo
nenoaiu aaoiiaoe/aneiai oi?aaeaiey eiia/iuo ?aciinoae
– ia?aay ?aciinoue, aiaeia ia?-
aie i?iecaiaeiie
n – iai?a?uaiia a?aiy, iai?a?uaiia iiiaeanoai ninoi-
yiee.
– aiaeia 2e
i?iecaiaeiie
…………………………………
– aiaeia E-oie i?iecaiaeiie
Anee yoi iiaenoaaeoue a iai?a?uaiia aeeooa?aioeeaeueiia o?aa-
iaiea oi iieo/ei neaaeothuaa :
Anee iiaenoaaeoue a (2) ?aciinoe, oi iieo/ei :
–
– ?aciinoiia o?aaiaiea n aeene?aioiui a?aiaiai.
Z -i?aia?aciaaiey
Aiaeiae/iu i?aia?aciaaieth Eaieana. Yoi i/aiue oaeiaiue aiia?ao aeey
enneaaeiaaiey nenoai n aeene?aoiui a?aiaiai a
/anoioiie iaeanoe. Aeey yoiai aianoi yeniiiaiou (aeey oi?i-
– yoi anoue Z-i?aia?aciaaiea. Aeey
oiai, /oiau aaanoe Z-i?aia?aciaaiea eniieuecoaony nea-
aeothuee i?eai nayce iai?a?uaiiai i?ioeanna X(t)e aeene?aoii-
(1)
X(1),X(2) – auai?ea n aeene?ao-
?anniio?ei i?aia?aciaaiea Eaieana :
(2)
Oi?iaeueii aaaaeai iiaoth ia?aiaiioth :
(3)
Eniieuecoy (2) e (3) iieo/ei
(4)
(4) – iacuaaaony Z-i?aia?aciaaiey, iieacuaaao eae ia?aeoe
io ooieoeee n aeene?aoiui a?aiaiai (X(n)) e niaeo?o
ia Z-ieineinoe.(Iii i?iua i?aia?aciaaiey Eaieana,
ii eiaao oa aea naienoaa e aeey ?aciuo aeene?aoiuo
ooieoeee eiathony niaoeeaeueiua oaaeeoeu.
Onoie/eainoue nenoai n aeene?aoiui a?aiaiai
Nenoaiu n iai?a?uaiui a?aiaiai oa?aeoa?ecothony ia?aaeaoi/-
iie ooieoeeae (ioiioaiey 2o iieeiiiia), oiaea naiia a Z-i?a
,
(ia eeiaeiie ine)
P-ieineinoue
Z-ieineinoue
(Nenoaia
onoie/eaa)
– ie?oaeiinoue, neaaeiaaoaeueii eaaay eiiieaeniay iieo-
ieineinoue eaa/a i?aia?acoaony ai aioo?aiiinoue e?oaa
Anee iiethnu ia?aaeaoi/iie ooieoeee iaoiaeyony ai aioo?aiiin-
oe e?oaa, oi nenoaia onoie/eaa, anee iiethnu iaoiaeyony ia
naiii e?oaa, oi aoaeao eieaaaoaeueiue i?ioeann, anee aia
e?oaa – nenoaia iaonoie/eaay.
– onoie/eaay nenoaia – eieaaaoaeueiay
nenoaia
n
– iaonoie/eaay nenoaia
n
Aeaaa 3
Iaeeiaeiua aeeiaie/aneea nenoaiu
Iaeeiaeiua aeeiaie/aneea nenoaiu iienuaathony aeeooa?aioee-
aeueiuie o?aaiaieyie :
Anee eeiaeiua aeeooa?aioeeaeueiua o?aaiaiey eiatho ?aoaiey
(yeniiiaioeeaeueiua), oi aeey iaeeiaeiuo aeeooa?aioeeaeueiuo
o?aaiaiee iao iaueo ?aoaiee (ca ?aaeeei eneeth/aieai), ii
ana ?aaeueiua aeeiaie/aneea nenoaiu iaeeiaeiu, iaeioi?ua
ec ieo iaeuecy eeiaa?ece?iaaoue, eae auoue ?
Auoiae : 1) Oai,aaea aiciiaeii, aeaeaaony eeiaa?ecaoeey i?aaie
/anoe o?aaiaiey (1).
Eeiaa?ecaoeey – caiaia iaeeiaeiie ooieoeee ia eeiaeioth.
(2) f(x,t)=A(t)x + B(t) + S(x,t)
S(x,t) – iaei, ei iiaeii i?eiaa?a/ue.
Anee i?aaay /anoue (1) ia caaeneo io a?aiaie, oi nenoaia
Eeiaa?ecaoeey eniieuecoaony,eae i?aaeei, aeey i?iaa?ee
onoie/eainoe nenoaiu. Aeey enneaaeiaaiey naienoa iaeeiae-
iuo aeeiaie/aneeo nenoai, iau/ii eniieuecothony ea/anoaaiiua
e /eneaiiua iaoiaeu ?aoaiey iaeeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee.
Oai?ey iaeeiaeiuo o?aaiaiee /anoi iacuaaaony
oai?eae iaeeiaeiuo eieaaaiee.
I?eia? : Iaeeiaeiie aeeiaie/aneie nenoaiu o?aaiaiee Aaiaea?
Iiey.
– iaeeiaeiinoue.
= const
Aeeooa?aioeeaeueiia o?aaiaiea iacuaaaony iaeeiaeiui, anee
iii iaeeiaeii ioiineoaeueii ?acuneeaaaiie ia?aiaiiie (na-
iie ia?aiaiiie eee aa i?iecaiaeiie) (iaeeiaeiinoue ec-ca
eaaae?aoa)
O?aaoaony iaeoe ?aoaiea x(t) .
Nouanoaotho /eneaiiua iaoiaeu ?aoaiey oaeeo aeeooa?aioeeaeue-
iuo o?aaiaiee ( /eneaiiua iaoiaeu ?anniao?eaathony ia nao-
) . ?aoaiea iieo/aaony ia iai?a?uaiia , a
aeene?aoiia.
*eneaiiua iaoiaeu iienuaa-
t thony a eieaa: Yeuenaieueoe
‘Oai?ey aeeooa?aioeeaeueiuo
o?aaiaiee e aa?eaoeeiiiia
en/eneaiea’.
U
*eneaiiue iaoiae Yeea?a ( /eneaiiue iaoiae)
(5)
*eneaiiue iaoiae i?aaeiacia/ai aeey ?aoaiey ia-
eeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee.
,
iiaenoaaeyaony a i?aaoth /anoue o?aaiaiey (5) e
o.ae. Yoi iacuaaaony ?aeeo?aioiinoueth.
Ea/anoaaiiay oai?ey ?aoaiey iaeeiaeiuo aeeooa-
?aioeeaeueiuo o?aaiaiee (a i?eeiaeaiee e iaeeiaeiui nenoa-
iai)
A ioee/ea io /eneaiiiai iaoiaea (Iaoiae Yeea?a), eioi?ue
aeaao ?aoaiea a 1e oi/ea ( ia aeaao o?aaeoi?eth (ioaeii aea-
eaoue 1000 oi/ae, /oiau iieo/eoue o?aaeoi?eth)).
Ioai Ea?a a 19 aaea aeae ea/anoaaiioth oai?eth ?aoaiey aeeo-
oa?aioeeaeueiuo o?aaiaiee, iia eniieuecoaony aeey ?aoaiey ia-
eeiaeiuo aeeooa?aioeeaeueiuo o?aaiaiee a aeaea iaeioi?iai oa-
ciaiai ii?o?aoa (iaeioi?ue a?aoe/aneee iaoa?eae, ii ei-
oi?iio iiaeii aiaeece?iaaoue o?aaeoi?eth aeaeaeaiey aeeiaie/an-
eie nenoaiu, o.a. oaeoe/anee iieo/eoue ?aoaiea (1-ai ec
?aoaiee).
Ia i?eia?a X e Y :
f(x,y) – iaeioi?ay iaee-
( dy iaeiay ooieoeey
– iaeeiaeiay
ooieoeey
x
Iaeoe ?aoaiea icia/aao – iaeoe y=((x) (2),
eioi?ay oaeiaeaoai?yao (1).
Ioai Ea?a ?acaee iaoiae , eae iaeoe (2) i?yii ia
ieineinoe.
Iaoiae ecieeei
, ia e?eaie
f(x,y)=const ana i?iecaiaeiua eiatho iaeii e oiaea cia/aiea,
oaeay e?eaay iacuaaaony ecieeeiie. (tg(=const, (=const)
Iiaeii au/eneeoue iiiaeanoai ecieeei, yoi iiiaeanoai aeaao ii-
ea iai?aaeaiee. Eanaoaeueiay e yoiio iieth e anoue ?aoaiea,
o.i. yoi anoue o?aaeoi?ey, eioi?oth iu ?acuneeaaai.
y
– ?aoaiea aeeo. –
ecieeeia
o?aaiaiey
x
x
Aaee/eia ?aaeeona – cia/aiea i?iecaiaeiie, ethaay ie?oaeiinoue –
ecieeeia. ?aoaiea (eanaoaeueiay e iieth iai?aaeaiey) –
-anoue eanaoaeueiay e aaeoi?ai, ?aniieiaeaiiay ia ecieeeiao.
( – ecieeeia
( ?aoaiea
– O?aaiaiea Aaiaea? Iiey
x(t) – iai?yaeaiea ia eiioo?a aaoiaaia?aoi?a, oaciaay ia-
?aiaiiay
= const – ia?aiao?
– aoi?ay oaciaay ia?aiaiiay
O/eouaay yoi eiaai :
= 0
–
ecieeeia
– oaciaue ii?o?ao
– ?aoaiea aeeooa?aioeeaeue-
iiai o?aaiaiey Aaiaea?
Iiey – ie?oaeiinoue
= 0)
Anee ia aoiaeu X e Y inoeeeia?aoa iiaeaoue aeaa neionieaeu, oi
iieo/ei ie?oaeiinoue (oeao?a Eennaaeo), neaaeiaaoaeueii ie?oae-
iinoue aeaao ?aoaiey neionieaeaeueiiai eieaaaiey.
x Y
t t
( 0 (ni. o?-a (1)’) oaciaue ii?o?ao aoaeao 2o oe-
iia :
Y X(t)
X
t
Auaiaeu :
1) Aeeiaie/aneea nenoaiu ?aaeeiaaoiiaoeee iienuaa-
thony aeeooa?aioeeaeueiuie o?aaiaieyie 1, 2 e ai-
eaa aunieiai ii?yaeea ( iai?eia?: eieaaaoaeue-
iay nenoaia(nieia/iay nenoaia, aaoiaaia?aoi?,
iieao einie/aneiai aiia?aoa a iiea i?eoyaea-
iey caiee) iienuaaaony aeeo. o?aaiaieai 2-ai
ii?yaeea e auoa.
2) Eeiaeiua aeeiaie/aneea nenoaiu iienuaathony ee-
iaeiuie aeeo. o?aaiaieyie. Eeiaeiay aeeiaie/an-
eay nenoaia ninoaaeaiiay ec R,L,C – oeaii/ae e
aeoeaiuo yeaiaioia (o?aicenoi?ia e o.ae.).
Ethaay eeiaeiay nenoaia iooai i?aia?aciaaiey
Eaieana iiaeao auoue i?aaenoaaeaia a aeaea ia?a-
aeaoi/iie ooieoeee.(Aeeo. o?aaiaiea i?aia?acoao-
ny ii Eaieano). Ia?aaeaoi/iay ooieoeey caienu-
aaaony aeey oaeianoaa a eiiieaeniii aeaea, ia
iieiie ine p=j( iiaeii iaeoe A*O e O*O eeiae-
iie nenoaiu. Ia?aaeaoi/iay ooieoeey aeaao eioi?-
iaoeeth ia onoie/eainoe nenoaiu.
3) Iaeeiaeiua aeeiaie/aneea nenoaiu iienuaathony
iaeeiaeiuie aeeo. o?aaiaieyie, a yoeo nenoaiao
e ae?.), iaueo ?aoaiee e aiaeeca /a?ac ia?aaea-
oi/ioth ooieoeeth eae i?aaeei ia nouanoaoao, ii-
yoiio anoue aeaa iaoiaea :
a) /eneaiiue iaoiae (Yeea?a e ae?.) (ainnoaiiaea-
iea ii oi/eai)
a) ?aoaiea aeeo. o?aaiaiee iaoiaeii oaciaiai ii?o-
?aoa (ea/anoaaiiay oai?ey). (Yoi iaaeyaeiue
iooue auyniaiey iiaaaeaiey iaeeiaeiie nenoaiu)
Noioanoe/aneea nenoaiu
Noioanoeea – neo/aeiinoue.
Ii?aaeaeaiea: Aeeiaie/aneay nenoaia iacuaaaony noioanoe/an-
eie , anee iia iienuaaaony aeeooa?aioeeaeueiui
eee ?aciinoiui o?aaiaieai, a i?aaoth /anoue
eioi?iai aoiaeeo neo/aeiue i?ioeann.
Oaeoth nenoaio iiaeii i?aaenoaaeoue a aeaea eeiaeiiai eee ia-
eeiaeiiai /aou?aoiiethnieea, ia aoiae eioi?iai iiaeaaony ooi
Noioanoe/aneay
((t) nenoaia X(t)
((t)- ooi
X(t)- auoiaeiie i?ioeann
Ninoaaeaiea iiaeaee ethaie aeeiaie/aneie nenoaiu aeieaeii
a ?aaeueiuo oneiaeyo(iai?eia? aeaeaeaiea naiieaoa eee ?aea-
ou) ninoaaeyoueny n iiiiuueth i?aaeaa?eoaeueiuo yenia?eiaioia
iaae aeaeaeaieai ?aaeueiie nenoaiu. (Eae i?aaeei yoi aeeooa-
?aioeeaeueiua eee ?aciinoiua o?aaiaiey) e a yoe o?aaiaiey
anoaaeyaony iaeioi?ue ooi, eioi?ue yaeyaony neo/aeiui
i?ioeannii.
Aeey aeaeueiaeoaai ninoaaeaiey iiaeaee eniieuecoaony eaeai-
oeoeeaoeey iiaeaee ia iniiaaiee yenia?eiaioa eee yenia?e-
iaioaeueiuo aeaiiuo.
Eaeaioeoeeaoeeae iacuaaaony ioeaiea eiyooeoeeaioia ?aciino-
iiai o?aaiaiey e ioeaiea ia?aiao?ia ooia:
aeenia?nee, iao. iaeeaeaiey, eiaa?eaoeee e ae?.
Eaeaioeoeeaoeey neoaeeo aeey oiai, /oiau ?aaeueiue i?ioeann e
iiaeaeue auee aeecee.Iieo/ea iiaeaeue iu eiaai aiciiaeiinoue,
eniieuecoy yoo iiaeaeue, iieo/eoue aeeceoth e ?aaeueiie ea?oe-
ia neooaoeeth aeaeaeaiey nenoaiu e nicaeaoue oi?aaeaiea neooa-
oeeae ii iaoae iiaeaee.
Auaiae: Iiaeaeue ioaeia, /oiau ia YAI iao/eoueny i?iaeoe?iaaoue
oi?aaeyaiua aeeiaie/aneea nenoaiu aeey ethauo oaeoe-
/aneeo neooaoeee, ecaanoiuo ec i?aeoeee.
I?aaeeueii nicaeaiiay iiaeaeue – yoi iaeneioi oniaoa a i?iae-
oe?iaaiee yooaeoeaiie nenoa-
iu. Iinea nicaeaiey e io?aaioee iiaeaee noioanoe/aneie aee-
iaie/aneie nenoaiu nicaeaaony aiia?aoo?a ii yoie iiaeaee,
eioi?ay i?iaa?yaony ia aeeiaie/aneii noaiaea.
Aeeiaie/aneee noaiae – 2e yoai iiaeaee?iaaiey ?aaeueiie neoo-
aoeee oaea n aiia?aoo?ie.
3e yoai ninoieo a i?iaa?ea aiia?aoo?u ia iieeaiia.( Ia
ai?oo o?ainii?oiiai eee aiaiiiai n?aaenoaa).
Iiaeaee?iaaiea neo/aeiuo i?ioeannia n aeene?aoiui a?aiaiai
– auai?ea neo/aeiiai i?ioeanna n aeene?aoiui
a?aiaiai.
X(t) I?ioeann (1) a iauai aeaea i/aiue
o?oaeii aiaeece?iaaoue, yoio i?i-
oeann, eae i?aaeei, iieo/ai ec
yenia?eiaioa. Yoio ?aaeueiue
i?ioeann iau/ii aii?ieneie?oaony
ae?oaei i?ioeannii, eioi?ue iic-
aieeo iai iaoaiaoe/anee nicaea-
t aaoue iiaeaee, aeeceea e ?aaeueii-
io i?ioeanno.
Oaeia nicaeaiea iiaeaeae iacuaaaony – aii?ieneiaoeeae.
Nai aii?ieneie?othuee i?ioeann iacuaaaony aa?aaao.
Ia?eianeay aii?ieneiaoeey neo/aeiuo i?ioeannia
Ia?eianeei i?ioeannii iacuaaaony oaeie i?ioeann, o eioi?iai
iiiaiia?iay ieioiinoue aa?iyoiinoe
. Iaeioi?ua
cia/aiey oaciauo ia?aiaiiuo a n-ia?iii i?ino?ainoaa – yoi
iiiaiia?iay ieioiinoue aa?iyoiinoe
Aeaoia?iay ieioiinoue Iiiaiia?iay OIA ianao anth ei-
aa?iyoiinoe oi?iaoeeth i neo//aeiii i?ioean-
W(x,y) na. Aieueoa eioi?iaoeee ia no-
uanoaoao.
Iaeiaei eniieueciaaoue yoo iii-
aiia?ioth OIA /?acau/aeii nei-
aeii ia i?aeoeea, iiyoiio /an-
oi i?eaaaatho e iaeioi?ui ai-
i?ieneiaoeeyi i?ioeanna :
Y
X
Aii?ieneie?iaaoue – aua?aoue oaeea ion/aou
auee
iacaaeneiu, oiaaea iiiaiia?iay OIA oaeoi?ecoaony neaaeoth-
– oaeoi?ecaoeey.
Iaeiaei i?e oaeie oaeoi?ecaoeee iiaeao iioa?youeny eioi?ia-
oeey i neo/aeiii i?ioeanna. Anoue iioa?y eioi?iaoeee aeey
i?iecaieueiuo ion/aoia (ei?aeee?iaaiiinoue i?ioeanna).
Nouanoaoao 2e niinia aii?ieneiaoeee – ia?eianeee niinia
aii?ieneiaoeee. Aeey ia?eianeeo i?ioeannia iiiaiia?iay OIA
oaeoi?ecoaony oae :
– on-
eiaiay ieioiinoue aa?iyoiinoe.
Oaeoi?ecaoeey (2) iicaieyao neeueii oi?inoeoue iaoaiaoe/an-
eea aueeaaeee a caaea/ao oeeueo?aoeee e oi?aaeaiey.
Ii?aaeaeaiea : I?ioeann iacuaaaony ia?eianeei, anee auiie-
iyaony oneiaea (2)
Ieacuaaaony, nouanoaoao i/aiue iiiai aaia?aoi?ia ia?eian-
eeo i?ioeannia. Iu ia?aoiaeei e eo ?anniio?aieth.
I?ioeannu aaoi?aa?annee
I?ioeann aaoi?aa?annee – i?inoie aaia?aoi? ia?eianeiai
i?ioeanna.
1. Iaeiinayciay ?aa?anney
– io aaia?aoi?a aaeiai ooia
– ei??aeyoeey.
(0 eiaai
onoie/eaue i?ioeann.
a1 iui e aeinoaoi/iui oneiaeai
onoie/eainoe nenoaiu.
Onoie/eainoue iaeeiaeiuo nenoai
Iaeeiaeiay noioanoe/aneay nenoaia :
Onoie/eainoue iaeeiaeiuo aeeiaie/aneeo nenoai ii?a-
aeaeyaony ooieoeeae Eyioiiaa.
Ii?aaeaeaiea onoie/eainoe ii Eyioiiao aeey aeaoa?ieie?iaai-
iie nenoaiu.
Aaiaeeony niaoeeaeueiay ooieoeey, iacuaaaiay ooieoeeae Eyioii-
. Ooieoeey oaeiaeaoai?yao neaaeothuei
oneiaeyi :
=0
0,
Aeey noioanoe/aneie nenoaiu (3)
iau/ii ooieoeeth Eyioiiaa auae-
. A oneiaea
onoie/eainoe aeey nenoaiu (3)
aoaeao neaaeothuei:
,
i(( (anneiioioe/anee)
Aiaeec ea/anoaa ?aaiou noioanoe/aneeo nenoai ?aaeeiaaoiia-
oeee
Ea/anoai eeiaeiuo e iaeeiaeiuo noioanoe/aneeo nenoai ii-
?aaeaeyaony ?aaeueiui ea/anoaii oeeueo?a. (ni. auoa)
Neioac i?aaeiieaaaao, /oi iiaeaeue niioaaonoaoao ?aaeueiiio neo/aeiiio
i?ioeanno, eioi?ue iu oeeueo?oai. A yoii neo/aa
ea/anoai ii?aaeaeyaony neaaeothuei ia?acii :
I?eia?: Iaeiiia?iue oeeueo? Eaeiaia.
– ooi iaaethaeaiee
– aiinoa?ei?iay aeenia?ney
– eiyooeoeeaio oneeaiey
oeeueo?a Eaeiaia
i – aeene?aoiia a?aiy
Ea/anoai oeeueo?aoeee ii?aaeaeyaony aaeaeaaoiinoueth iiaeaee e
?aaeueiiai i?ioeanna. Eae i?iaa?eoue aaeaeaaoiinoue iiaeaee
?aaeueiiio i?ioeanno ? Naeaeaoue yoi
,
.
i
Oai?aia : I?ioeann oiaaea e oieueei oiaaea aaeaeaaoai iiaeaee,
eiaaea iaaycea yaeyaony aaeui ooiii.
I?iaeaia ea/anoaa ii?aaeaeyaony i?iaeaiie yeno?aiieyoeee.
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