h is o b la b , ta v s if o ‘lch am in i k ic h ra y tiris h .
- T a v sifn in g statsio n arlig i yo k i k v a z is ta tsio n a rlig i g ip o te z a s in i q a b u l
q ilis h
(«qolirilgan» koeffitsiyentlar usuli).
- T izim n in g fazoviy x u su siy atlarin i h is o b g a olm aslik (p a ra m e trla ri
to 'p la n g a n ta v s ifla rg a k e ltirish ) y o k i h ar b ir fa z o d a p a ra m e trla r
o 'z g a ris h in i hiso b g a o lm a y d ig a n
s o h a la rg a ajratish
(xujayrasimon
tavsiflar usuli).
-
T izim o ‘z g a ru v c h ila rin in g o 'z g a ris h s o h a la rid a c h iz iq li b o ‘lm ag an
tiz im la r n i c h iziq li tiz im la rg a k e ltiris h i
(kichik chetlanishlar usuli).
M a z k u r b o b d a soni c h e k la n g a n o 'z g a r u v c h ila r y o rd a m id a t o ‘la ta v s i-
fla n u v c h i, p a ra m e trla ri to ‘p la n g a n c h iz iq li tiz im g a k elu v ch i av to m atik tiz im la r
k o ‘rilad i. A m a ld a b u nday av to m atik b o sh q arish tiz im la rin i tav siflash u ch u n ik-
k ita u su ld a n fo y d a la n ila d i:
1)
«kirish y o 'li
—
chiqish yo'li»
x a r a k t e r i s tik a la r i y o rd a m id a ;
2)
holat o'zgaruvchilari
u ch u n te n g la m a la r (u m u m la sh tirilg a n k o o rd in a -
ta la r) y o rd a m id a .
A B T n i « k irish y o 'li — ch iq ish y o 'li» x arak teristik alari y o rd a m id a ta v s i
flash q u y id a g ila r orqali am alg a o sh irilish i m um kin:
1. T iz im o 'z g a ru v c h ila rin in g v a q t b o ‘y ic h a v a fa z o d a o ‘z g a rish in i ta v s i-
flo v c h i d if fe re n s ia l te n g la m a la r.
2. V a q t
fu n k siy asi
sifa tid a
b e rilg a n
o 'z g a ru v c h ila r
o rasid ag i
b o g ‘la n ish n i ak s ettiruvchi v a q t x arak teristik alari.
3. O 'z g a r u v c h il a r n in g F u re v a L a p la s
b o ‘y ic h a ifo d a la ri o ra s id a g i
b o g 'la n is h n i a k s e ttiru v c h i c h a s to ta x a ra k te ris tik a la ri.
A B T n i u m u m la s h tirilg a n k o o rd in a ta la r y o rd a m id a m a te m a tik ta v sifla sh
k la s s ik
m ex an ik ad an
b o sh la n g a n .
K e y in ch alik
u
e le k trik
va
e le k tro m e x a n ik
tiz im la rn i,
y a q in d a n
esa
ijtim o iy ,
b io lo g ik
v a
b o s h q a
tiz im la rn i
ta v s ifla s h d a
is h la tila
b o sh la n d i.
B u n d a
« u m u m la s h tirilg a n
k o o rd in a ta »
te rm in i o ‘rn ig a k o 'p in c h a « h o lat o ‘zg a ru v c h isi» te rm in i ish latiiad i.
Real sistemani, ixtiyoriy vaqt onida, holat o'zgaruvchilari deb ataluvchi
x , , x 2,...,
xn, kattaliklar gunihi yordamida to ‘la tavsiflash mumkin.
X/ x2 . .
.,
x,,
o ‘zg aru v ch ilarn i h o lat v e k to ri
X
nin g kom ponentlari sifatida
q arash m u m k in . E rkin holat o 'z g a ru v c h ila rin in g
en g k ic h ik soni
p
tiz im n in g
erkinlik darajasi
deb a ta la d i. H o lat tu sh u n c h a sin i m isol o rq ali tu sh u n tirib , unga
xos b e lg ila rn i k o ‘rsa tish m um kin.
0 ‘z g a rm a s k o e ffits iy e n tli c h iz iq li d iffe re n s ia l te n g la m a n i y e c h is h n i
k o 'r a y l ik . M a ’lu m k i, b u n d ay d iffe re n s ia l te n g la m a n i y ech ish d a
t0
berilgan
o ‘z g a r m a s la r n in g b o s h la n g 'ic h q iy m a tla ri a n iq b o 'lis h i k erak . T u rli b o sh -
la n g ‘ich
s h a r tla r tu rli
y e c h im la rg a o lib
k e la d i.
H o lat o 'z g a ru v c h ila ri
k o 'r in is h id a o ra liq p aram etrlarn in g k iritilish id a n aso siy m aq sad — b o sh q a ru
v ch i t a ’s irla r b ilan o b y e k t chiqish y o 'li koordinatalari o'rtasidagi bunday k o 'p
m a ’n o lik n i y o 'q o tish d ir.
H o la tn in g y u q o rid a keltirilgan x u su siy atlarin i h iso b g a olgan h o ld a bosh-
14
t
qarilu v ch i tizim larn in g (1 .1 ) v a (1 .2 ) b o g ‘lanish te n g la m a la rin i b irin c h i d a ra ja li
te n g la m a la rn in g h o la t te n g la m a la ri s h a k lid a ifo d alash m u m k in :
(X = f(X,U,Z),X(i„)=X0
1
Y = g(X),
bu y e rd a
f g
— b ir q iy m atli fu n k s iy a la r.
Y uqorida keltirilgan u su llarn in g birortasi ham k o ‘zga tash lan u v ch an , o d d iy
fiz ik m a ’n o g a ega em as y o k i b ir o r a m aliy m asalalarn i y ech ish d a q u lay em as.
M asalan ,
keng
q o 'lla n ilu v c h i
A B T n in g
norm al
sh ak lid ag i
d iffe re n sia l
te n g la m a la r o rq ali ta v s ifi b e rilg a n ta ’s irla r va c h iq ish y o ‘li o 'z g a ru v c h ila ri
o 'rta s id a g i b o g 'la n ish n i ifo d a la sh v a ta h lil q ilish d a ju d a n o q u lay b o 'ls a , b u n
day ta v s i f h is o b la sh m a s h in a s id a tiz im n i ta v sifla sh d a ju d a q o 'l k elad i.
A k sin -
cha, A B T n in g v a q t x u su siy a tla ri o d d iy fizik m a ’n o g a ega b o ‘lsa-da, am aliy
h is o b la sh la rd a v a ta v s ifla s h d a n o q u lay . S hu n d ay q ilib , differensial te n g la m a la r
h a m d a v a q t x a ra k te ristik a la ri o rq ali ta v s ifla sh o d d iy fizik m a ’noga ega, am m o
d iffe re n s ia l v a integral te n g la m a la rn in g y e c h ilis h in i ta q o z o
e tg an lig i sababli
am aliy h iso b lash lard a n o q u la y lik tu g 'd ira d i. M a ’lum b o 'lish ich a, m uhandislik
m asalalari tadqiqini chastota x arak teristik alari y o rd a m id a am alg a o sh irish q u lay .
F u re v a L ap las o 'z g a ru v c h ila ri m a te m a tik apparati tizim ni tavsiflash va tadqiq
qilish d a qulaylikka ega, c h u n k i b u n d a in te g ro -d iffe re n sia l te n g la m a la r o 'r n ig a
faq at a lg eb raik te n g la m a la r y e c h ila d i.
2.2.
