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ɉɪɢV = constD ~ T
x
j
U
P = constD ~ T
ɉɪɢɧɢɡɤɢɯɞɚɜɥɟɧɢɹɯɄɧɭɞɫɟɧɚȜɪɚɡɦɟɪɨɜɫɨɫɭɞɚɂɡɜɟɫɬɧɨ
ɱɬɨɞɢɮɮɭɡɢɹɡɚɜɢɫɢɬɨɬ ɪɚɡɦɟɪɨɜ ɫɨɫɭɞɚ Ʉɨɥɢɱɟɫɬɜɨɝɚɡɚɩɪɨɯɨɞɹ
ɳɟɟ ɱɟɪɟɡ ɥɸɛɨɟ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟɬɪɭɛɵɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜɵ
ɪɚɠɟɧɢɟɦ
d
S
j
S
CCLRTM
ɝɞɟ d±ɞɢɚɦɟɬɪɬɪɭɛɵ
L±ɟɝɨɞɥɢɧɚ
ɢɋ2±ɤɨɧɰɟɧɬɪɚɰɢɹɝɚɡɚɧɚɤɨɧɭɫɚɯɬɪɭɛɵ
ɋ
1
Ⱦɢɮɮɭɡɢɸɜɟɞɢɧɢɱɧɨɣɩɨɪɟɰɢɥɢɧɞɪɵ±ɜɫɟɩɨɪɵɩɚɪɚɥɥɟɥɶɧɵ
ɞɪɭɝɞɪɭɝɭɦɨɠɧɨɩɪɟɞɫɬɚɜɢɬɶɫɩɨɦɨɳɶɸɡɚɤɨɧɚɎɢɤɚ
D
w
ɚɩɪɢɷɬɨɦ
oo
mD c
S
p
DDm
mp
cc
ww
t
w
ɝɞɟ m
±ɨɛɴɟɦɧɚɹɞɨɥɹɩɨɪɡɚɩɨɥɧɟɧɧɵɯɢɦɨɝɭɬɛɵɬɶɡɚɩɨɥɧɟɧɧɵɦɢ
p
ɠɢɞɤɨɫɬɶɸ
um
±ɦɚɫɫɚɪɚɫɬɜɨɪɚɜɟɞɢɧɢɰɟɨɛɴɟɦɚɩɨɪɢɫɬɨɝɨɬɟɥɚ
ɝɞɟ u
p
ȡ
±ɟɝɨɩɥɨɬɧɨɫɬɶ
ɪ
ppp
Ɂɚɦɟɞɥɟɧɢɟɞɢɮɮɭɡɢɢ ɜɩɨɪɢɫɬɵɯ ɫɪɟɞɚɯɨɛɭɫɥɨɜɥɟɧɨɦɟɯɚɧɢɱɟ
ɫɤɨɣ ɛɥɨɤɢɪɨɜɤɨɣ ɞɢɮɮɭɡɢɨɧɧɨɝɨ ɩɨɬɨɤɚ ɬɜɟɪɞɵɦ ɫɤɟɥɟɬɨɦ ɭɦɟɧɶ
ɲɟɧɢɟɦɩɭɬɢɞɢɮɮɭɡɢɢɜɫɥɟɞɫɬɜɢɟɢɡɜɢɥɢɫɬɨɫɬɢɤɚɩɢɥɥɹɪɨɜɬɨɪɦɨ
ɠɟɧɢɟɦɦɨɥɟɤɭɥɹɪɧɨɝɨɞɜɢɠɟɧɢɹ ɫɬɟɧɤɚɦɢ ɤɚɩɢɥɥɹɪɚɢɩɨɜɵɲɟɧɢɟɦ
ɜɹɡɤɨɫɬɢɠɢɞɤɨɫɬɢ ɢɡɡɚɜɨɡɦɨɠɧɨɣɪɚɫɬɜɨɪɢɦɨɫɬɢɜɟɳɟɫɬɜɚɫɤɟɥɟɬɚ
ɆɨɠɧɨɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶDmɤɚɤɩɪɨɢɡɜɟɞɟɧɢɟɫɜɨɛɨɞɧɨɣ ɞɢɮɮɭɡɢɢ
M
I
ɧɚɮɚɤɬɨɪɵɭɱɢɬɵɜɚɸɳɢɟɪɚɡɥɢɱɧɵɟɜɥɢɹɧɢɹ
D
ɟ
ɇɚɩɪɢɦɟɪɭɞɥɢɧɟɧɢɟɩɭɬɢlɧɚɩɪɚɜɥɟɧɢɟɜɞɨɥɶɤɚɩɢɥɥɹɪɚɬɟ
VLQxl
D
w
w
VLQ
l
dc c
dt
ɬ ɤ lx
ɠɢɬɟɥɶɪɚɜɟɧĮ
D
ɤɨɷɮɮɢɰɢɟɧɬ ɭɞɥɢɧɟɧɢɹɩɨɪ ɬɨ ɤɨɪɪɟɤɬɢɪɭɸɳɢɣ ɦɧɨ
ȿɫɥɢɪɚɡɦɟɪɞɢɮɮɭɡɢɨɧɧɵɯ ɱɚɫɬɢɰ rɫɪɚɜɧɢɦɫɪɚɡɦɟɪɨɦɩɨɪr
n
ɬɨ ɫɤɚɡɵɜɚɟɬɫɹ ɬɨɪɦɨɡɹɳɟɟ ɡɧɚɱɟɧɢɟ ɫɬɟɧɨɤ ɤɨɬɨɪɵɟ ɭɱɢɬɵɜɚɸɬ
ɦɧɨɠɢɬɟɥɟɦ
r
r
n
ȽɅȺȼȺȺȾɋɈɊȻɐɂə
f
Ɋɚɫɫɦɚɬɪɢɜɚɹɚɞɫɨɪɛɰɢɸɨɛɵɱɧɨɨɩɪɟɞɟɥɹɸɬɤɨɥɢɱɟɫɬɜɨ ɚɞɫɨɪ
ɛɢɪɨɜɚɧɧɨɝɨɜɟɳɟɫɬɜɚɩɪɢɊ = constɢɌ = constɢɡɨɬɟɪɦɚɚɛɫɨɪɛɰɢɢ
vfPT
Ɍɚɤɠɟɟɟɦɨɠɧɨɩɪɟɞɫɬɚɜɢɬɶɢɜɜɢɞɟɢɡɨɛɚɪɵɚɛɫɨɪɛɰɢɢv
v
P
t
T
p
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɦɟɠɞɭ ɫɢɫɬɟɦɚɦɢ ɚɞɫɨɪɛɰɢɢ
ɞɟɥɹɬɧɚɮɢɡɢɱɟɫɤɭɸ ɚɞɫɨɪɛɰɢɸɢɯɟɦɚɞɫɨɪɛɰɢɸɏɟɦɚɞɫɨɪɛɰɢɹ ɦɨ
ɠɟɬɩɪɨɢɫɯɨɞɢɬɶɜɞɜɟɫɬɚɞɢɢɫɧɚɱɚɥɚɩɪɨɢɫɯɨɞɢɬɮɢɡɢɱɟɫɤɚɹɚɞɨɪɛ
ɰɢɹɝɚɡɚɚɡɚɬɟɦɨɧɜɫɬɭɩɚɟɬɜɦɟɞɥɟɧɧɭɸɯɢɦɢɱɟɫɤɭɸɪɟɚɤɰɢɸɫɩɨ
ɜɟɪɯɧɨɫɬɶɸɬɜɟɪɞɨɝɨɬɟɥɚȼɪɟɦɹɚɞɫɨɪɛɰɢɢ±ɷɬɨɜɪɟɦɹɜɬɟɱɟɧɢɢɤɨ
ɬɨɪɨɝɨ ɚɞɫɨɪɛɢɪɨɜɚɧɧɚɹ ɦɨɥɟɤɭɥɚ ɧɚɯɨɞɢɬɫɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɚɞɫɨɪ
ɛɟɧɬɚ ȿɫɥɢ ɫɭɳɟɫɬɜɭɟɬ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɨɥɟɤɭɥɵ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ
ɬɨɝɞɚɩɨɎɪɟɧɤɟɥɸ
RTQe
WW
ɝɞɟ Q±ɷɧɟɪɝɢɹɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
±ɜɪɟɦɹɦɨɥɟɤɭɥɹɪɧɨɝɨɤɨɥɟɛɚɧɢɹ
IJ
0
V
ɨɬ
ɯɨɞɚ ɨɬ ɮɢɡɢɱɟɫɤɨɣ ɞɨ ɯɟɦɚɞɫɨɪɛɰɢɢ.
ɞɨ5ɫ
ɂɡɨɛɚɪɚ ɚɞɫɨɪɛɰɢɢ ɜ ɨɛɥɚɫɬɢ ɩɟɪɟ-
ȼɚɠɧɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɩɨɜɟɪɯ
T
ɧɨɫɬɧɚɹɤɨɧɰɟɧɬɪɚɰɢɹɌ = zIJɝɞɟz±ɱɢɫ
ɥɨɦɨɥɟɣɝɚɡɚɜɫɦ
ɩɨɜɟɪɯɧɨɫɬɢ
Ʌɟɧɝɦɸɪ ɜ ɫɜɨɢɯ ɪɚɛɨɬɚɯ ɪɚɫɫɦɚɬɪɢɜɚɥ ɫɤɨɪɨɫɬɢ ɢɫɩɚɪɟɧɢɹ ɢ
ɤɨɧɞɟɧɫɚɰɢɢɈɧɢɫɯɨɞɢɥɢɡɬɨɝɨɱɬɨɧɚɩɨɜɟɪɯɧɨɫɬɢɟɫɬɶɨɩɪɟɞɟɥɟɧ
ɧɨɟɱɢɫɥɨɦɟɫɬɚɛɫɨɪɛɰɢɢSɱɚɫɬɶɤɨɬɨɪɵɯɡɚɧɹɬɚɚɛɫɨɪɛɢɪɨɜɚɧɧɵɦɢ
ɦɨɥɟɤɭɥɚɦɢS
ɚɱɚɫɬɶɫɜɨɛɨɞɧɚ S0 = S – S1ɋɤɨɪɨɫɬɶɢɫɩɚɪɟɧɢɹɩɪɨ
1
ɩɨɪɰɢɨɧɚɥɶɧɚɄ1S1ɚɫɤɨɪɨɫɬɶɤɨɧɞɟɧɫɚɰɢɢɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚɫɜɨɛɨɞ
T
T
T
T
P
ɧɨɣɩɨɜɟɪɯɧɨɫɬɢɢɞɚɜɥɟɧɢɸɝɚɡɚɄ
ȼɭɫɥɨɜɢɹɯɪɚɜɧɨɜɟɫɢɹ
Ʉ
/ S = șɞɨɥɹɡɚɩɨɥɧɟɧɢɹɬɨɝɞɚ
ɝɞɟS
1
Ʉ
ɉɪɢɧɹɜɱɬɨɄ
Ɂɚɦɟɧɹɹ
K
K
2/Ʉ1
TT
P
V
ș
ɝɞɟV
V
P
= Ʉ2S0Ɋ = Ʉ2Ɋ(S – S1)
1S1
ș = Ʉ2Ɋ(1 – ș)
1
= bɩɨɥɭɱɚɟɦ
bP
±ɨɛɴɟɦɚɞɫɨɪɛɢɪɨɜɚɧɧɨɝɨɝɚɡɚɩɪɢɦɨɧɨ
m
ɫɥɨɣɧɨɦɡɚɩɨɥɧɟɧɢɢ
VbP
VbP
m
VV
m
V
ɫɬɜɨ ɚɞɫɨɪɛɢɪɨɜɚɧɧɨɝɨ ɝɚɡɚ ɩɪɨɩɨɪ
Ɋ
2S0
bP
bP
T
bPbP
bPbbP
ɉɪɢ ɧɢɡɤɨɦ ɞɚɜɥɟɧɢɢ ɤɨɥɢɱɟ
ɰɢɨɧɚɥɶɧɨɞɚɜɥɟɧɢɸ
bPVVm
ɹɯɨɧɨɫɬɪɟɦɢɬɫɹɤV
P
m
Ɍɨɝɞɚɤɚɤɩɪɢɜɵɫɨɤɢɯɞɚɜɥɟɧɢ
ɍɞɨɛɧɨɟɭɪɚɜɧɟɧɢɟɩɟɪɟɜɟɫɬɢɤɥɢɧɟɣɧɨɦɭɜɢɞɭɉɪɢɜɵɫɨɤɢɯV
V ĺ V
ɬɨɝɞɚ
m
bPVbPV
VVbV
m
P
mm
bPVVbPV
m
ȼɫɜɨɸɨɱɟɪɟɞɶVmɫɭɞɟɥɶɧɨɣɩɨɜɟɪɯɧɨɫɬɶɸȈɬɜɟɪɞɨɝɨɬɟɥɚɫɜɹ
R
ɡɚɧɨɫɨɨɬɧɨɲɟɧɢɟɦ
6
V
0
ɝɞɟ ı
±ɩɥɨɳɚɞɶɩɪɢɯɨɞɹɳɚɹɧɚɦɨɥɟɤɭɥɭɜɦɨɧɨɫɥɨɟ
±ɨɛɴɟɦɨɞɧɨɝɨɦɨɥɹɝɚɡɚɩɪɢɧɨɪɦɚɥɶɧɵɯɭɫɥɨɜɢɹɯ
V
0
VvN
m
ɉɪɢɤɨɧɤɭɪɟɧɬɧɨɣɚɞɫɨɪɛɰɢɢɧɟɫɤɨɥɶɤɢɯɚɞɫɨɪɛɟɧɬɨɜɭɪɚɜɧɟɧɢɟ
ɢɦɟɟɬɫɥɟɞɭɸɳɢɣɜɢɞ
VbP
V
i
mi i i
¦
j
bP
jj
ɉɨɫɬɨɹɧɧɚɹɫɤɨɪɨɫɬɢɄ
ɑɬɨɛɵɨɰɟɧɢɬɶɄ
0
ɩɥɨɳɚɞɶɸı
Ɍɨɝɞɚɫɤɨɪɨɫɬɶ ɚɞɫɨɪɛɰɢɢ ɦɨɠɧɨɩɪɢɪɚɜɧɹɬɶɤɱɚɫɬɨɬɟ
ɩɚɞɟɧɢɹɦɨɥɟɤɭɥɧɚɭɱɚɫɬɨɤɩɨɜɟɪɯɧɨɫɬɢı
ɬɟɨɪɢɢɝɚɡɨɜɄ
ɪɚɜɧɨ
2
ɨɛɪɚɬɧɚɜɪɟɦɟɧɢɚɞɫɨɪɛɰɢɢ
1
Q
kT
Ke
W
ɩɪɟɞɫɬɚɜɢɦɰɟɧɬɪɚɞɫɨɪɛɰɢɢɜɜɢɞɟɤɜɚɞɪɚɬɚɫ
2
N
K
S
MRT
0
ɋɨɝɥɚɫɧɨɤɢɧɟɬɢɱɟɫɤɨɣ
V
ɌɨɝɞɚɩɨɫɬɨɹɧɧɚɹɅɟɧɝɪɦɸɪɚ
NNe
K
b
KMRT
VVW
Q
MRT e
S
RT
Q
T
S
Ʉɪɨɦɟ ɬɨɝɨ ɭɞɨɛɧɨ ɡɚɩɢɫɚɬɶ ɜ ɜɢɞɟ ɱɚɫɬɨɬɧɨɝɨ ɦɧɨɠɢɬɟɥɹ
QRT
ɬɨɝɞɚ
b
VW
N
S
MRT
bbe
ȺɞɫɨɪɛɰɢɨɧɧɚɹɮɨɪɦɭɥɚȽɢɛɛɫɚ
E
D
E
A
A
ɍɞɨɛɧɨ ɫɱɢɬɚɬɶ
ɱɬɨ ɞɜɟ ɨɛɴɟɦɧɵɟ ɮɚ
ɡɵ Įɢȕ ɹɜɥɹɸɬɫɹ ɨɞ
ɧɨɪɨɞɧɵɦɢ ɜɩɥɨɬɶ ɞɨ
S
S
a
Sc
Sc
ɧɟɤɨɬɨɪɨɣ ɪɚɡɞɟɥɹɸ
ɳɟɣ ɩɨɜɟɪɯɧɨɫɬɢ S
Ɉɝɪɚɧɢɱɢɦ ɨɛɟ ɮɚɡɵ
x
xc
ɩɥɨɫɤɨɫɬɹɦɢ ɫɨɨɬɜɟɬ
ɫɬɜɭɸɳɢɦɢ ɧɭɥɟɜɵɦ
B
B
ɤɨɧɰɟɧɬɪɚɰɢɹɦ ɋ
ɋ
Ɋɚɫɫɦɨɬɪɢɦ ɫɥɭ
2
ɢ
1
ɱɚɣ ɩɪɢ ɤɨɬɨɪɨɦ ɞɚɧɧɚɹ ɫɢɫɬɟɦɚ ɧɚɯɨɞɢɬɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ ȿɫɥɢ ɩɥɨ
ɳɚɞɶɫɟɱɟɧɢɹɪɚɜɧɚɟɞɢɧɢɰɟɬɨɝɞɚ ɮɚɡɵ ɨɞɧɨɪɨɞɧɵ ɜɩɥɨɬɶɞɨSɤɨ
ɥɢɱɟɫɬɜɨiɤɨɦɩɨɧɟɧɬɚɜɩɨɜɟɪɯɧɨɫɬɧɨɦɫɥɨɟɪɚɜɧɨ
ED
cxaxc
ii
ɉɪɢɷɬɨɦɨɛɳɟɟɤɨɥɢɱɟɫɬɜɨiɤɨɦɩɨɧɟɧɬɚɦɟɠɞɭɩɥɨɫɤɨɫɬɹɦɢȺɢ
ȼɪɚɜɧɨ
DEV
xc a x c Ƚ
ȿɫɥɢɮɚɡɚȕ± ɝɚɡɨɨɛɪɚɡɧɚ ɬɨɜɟɥɢɱɢɧɨɣ
iii
c
ɦɨɠɧɨɩɪɟɧɟɛɪɟɱɶ
i
ɬɨɝɞɚ
DV
xc Ƚ
ȿɫɥɢɩɪɨɢɡɜɨɥɶɧɨɜɵɛɪɚɬɶɞɪɭɝɭɸɩɨɜɟɪɯɧɨɫɬɶ S
1
ɨɬSɬɨɨɱɟɜɢɞɧɨɱɬɨ
ɯ
DV DV
xc Ƚ xc Ƚ
ii ii
ii
1
ɧɚɪɚɫɫɬɨɹɧɢɢ
Ƚ
E
DV
ȽȽcxx
iii
ɢɥɢ
VV VV
ȽȽ ȽȽ
cc
ɂɥɢɜɨɛɳɟɦɫɥɭɱɚɟ
VV
ȽȽ
ii
NN
ij
VV
N Ƚ Nconst
ij jj
VV
ȽȽ
jj
ɝɞɟ N±ɦɨɥɶɧɚɹɞɨɥɹ
ɉɪɢ ɧɟɛɨɥɶɲɨɦ ɨɛɪɚɬɢɦɨɦ ɢɡɦɟɧɟɧɢɢ ɷɬɨɣ ɫɢɫɬɟɦɵ ɢɡɦɟɧɟɧɢɟ
ɷɧɟɪɝɢɢdEɦɨɠɧɨɩɪɟɞɫɬɚɜɢɬɶɤɚɤɫɭɦɦɭ
dE dE dE dE dS dn P dV dS dn
DEV D DDD E E
7 7
EE V V
dV TdS dn dA
PP
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ii i i
PJ
¦
ii
Ɉɬɫɸɞɚɫɥɟɞɭɟɬɱɬɨ
DVV
7 dAdndSdE
JP
¦
ii
ɂɧɬɟɝɪɢɪɭɹɷɬɨɜɵɪɚɠɟɧɢɟɩɨɥɭɱɚɟɦ
VVV
AnTSE
ɉɨɫɥɟɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɹdE
S
¦
S
¦
S
ɪɚɜɧɨ
JP
ii
VV
AnTSE
JP
ii
VVVV
iiii
JJPP
AddAdndndTSTdSdE
66
ɋɪɚɜɧɢɜɚɹɫɩɪɟɞɵɞɭɳɢɦɜɵɪɚɠɟɧɢɟɦɩɨɥɭɱɢɦ
VV
AddndTS
ii
6
6
VV
dndTSAd
PJ
ii
ȼɩɟɪɟɫɱɟɬɟɧɚɟɞɢɧɢɰɭɩɨɜɟɪɯɧɨɫɬɢ
Ƚ
J
Ƚ
J
J
P
J
P
P
P
VV
dndTSd
PJ
6
ii
ɉɪɢɌ = constɬɨɟɫɬɶɩɪɢɢɡɨɬɟɪɦɢɱɟɫɤɨɦɩɪɨɰɟɫɫɟ
V
dnd
PJ
6
ii
Ⱦɥɹɞɜɭɯɤɨɦɩɨɧɟɧɬɧɨɣɫɢɫɬɟɦɵɦɨɠɧɨɡɚɩɢɫɚɬɶ
d
VV
d Ƚ d
PP
i
Ɋɚɡɞɟɥɹɸɳɭɸɩɨɜɟɪɯɧɨɫɬɶɦɨɠɧɨɜɵɛɪɚɬɶɬɚɤɨɣ ɱɬɨɛɵ
ȽV
ɬɨɝɞɚ
w
ɦɨɥɶɫɦ
Ƚ
Ƚ
Â
ɝɞɟ
P
w
P
a
w
w
RT a
T
ɬɨɝɞɚ
P
OQ aRT
ɫɱɢɬɚɹ ɱɬɨ
RT
da
w
a
w
P/Pq
Ƚ
ɩɨɥɨɠɢɬɟɥɶɧɚɢɨɡɧɚɱɚɟɬɱɬɨɫɭɳɟɫɬɜɭɟɬɢɡɛɵɬɨɤɚɞɫɨɪɛɢɪɭɟɦɨɝɨ
ȿɫɥɢ
ɤɨɦɩɨɧɟɧɬɚɜɩɨɜɟɪɯɧɨɫɬɧɨɦɫɥɨɟɂɫɩɨɥɶɡɭɹɭɪɚɜɧɟɧɢɟȽɢɛɫɚȾɸɝɟ
Nd
6
ɦɚ
ii
ɦɨɠɧɨɡɚɩɢɫɚɬɶ
ɨɬɪɢɰɚɬɟɥɶɧɚɬɨɝɞɚ
a
w
N
PP
i
dNdN
d
d
N
ɉɨɞɫɬɚɜɥɹɹɩɨɫɥɟɞɧɟɟɜɵɪɚɠɟɧɢɟɜɮɨɪɦɭɥɭɞɥɹɨɩɪɟɞɟɥɟɧɢɹdȖ
ɩɨɥɭɱɚɟɦ
NN
VV VV
d Ƚ d Ƚ ddȽȽ
JPPP
NN
ɂɡɨɬɟɪɦɵɚɞɫɨɪɛɰɢɢɝɚɡɨɜɜɵɪɚɠɚɸɬɬɚɤɠɟɨɬɞɚɜɥɟɧɢɹ
ªº
«»
¬¼
ȽɨɬɊ
ɩɪɢ ɷɬɨɦ ɭɪɚɜɧɟɧɢɟ Ƚɢɛɛɫɚ ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɫɜɹɡɶ ɦɟɠɞɭ ɢɡɨɬɟɪɦɚɦɢ
ɚɞɫɨɪɛɰɢɢɢɞɜɭɯɦɟɪɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ ɫɨɫɬɨɹɧɢɹ
ɦɚɚɞɫɨɪɛɰɢɨɧɧɨɝɨɭɪɚɜɧɟɧɢɹɅɟɧɝɦɸɪɚɝɞɟ
aɢb-const
Ƚ
ɮɨɪ
bc
ac
Ɍɟɩɥɨɬɚɚɞɫɨɪɛɰɢɢ
ɂɧɬɟɪɟɫɧɨ ɪɚɫɫɦɨɬɪɟɬɶ ɞɜɚ ɚɞɫɨɪɛɰɢɨɧɧɵɯ ɩɪɨɰɟɫɫɚ ȼ ɩɟɪɜɨɦ
ɯ
ɫɥɭɱɚɟɩɪɨɚɧɚɥɢɡɢɪɭɟɦɚɞɫɨɪɛɰɢɸɜɟɳɟɫɬɜɚ
g
xn
ɝɚɡɨɨɛɪɚɡɧɵɣɚɞɫɨɪɛɚɬɩɪɢ Ɋ
S
xn
Ɍ
S
xn
ɚɞɫɨɪɛɟɧɬɩɪɢɌ
S
xn
ɝɚɡɚɞɫɨɪɛɢɪɨɜɚɧɧɵɣɧɚ
ȿɫɥɢɬɚɤɨɣɩɪɨɰɟɫɫɩɪɨɬɟɤɚɟɬɩɪɢ
ɥɨɬɚ
qE '
Q
ɪɚɜɧɚ ɢɡɦɟɧɟɧɢɸ
i
ɨɡɧɚɱɚɟɬɦɨɥɶɧɚɹɷɧɟɝɢɹ
i
E'
ɜ ɪɚɫɱɟɬɟ ɧɚ ɦɨɥɶ ɚɞɫɨɪɛɟɧɬɚ
PLQ
ȼɨɜɬɨɪɨɦɫɥɭɱɚɟɚɞɫɨɪɛɢɪɨɜɚɧɧɵɣɩɪɨɰɟɫɫɢɞɟɬɩɨɫɯɟɦɟ
S
ɝɚɡ
S
n
S
n
Ɋ Ɍ
xn
ɝɚɡ ɚɞɫɨɪɛɢɪɨɜɚɧɧɵɣ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɬɧɨɲɟɧɢɢ
ɧɚɚɞɫɨɪɛɟɧɬɟɯ1
2
v = constɬɨɜɵɞɟɥɹɟɦɚɹɬɟɩ
g
nx
Ɍɟɩɥɨɬɚɜɵɞɟɥɹɸɳɚɹɫɹɜɩɪɨɰɟɫɫɟɚɞɫɨɪɛɰɢɢɬɚɤɨɝɨɬɢɩɚɧɚɡɵ
ɜɚɟɬɫɹɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣɬɟɩɥɨɬɨɣ
Qɩɪɢv = constȼɪɚɫɱɟɬɟɧɚɦɨɥɶ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɬɟɩɥɨɬɚ ɚɞɫɨɪɛɰɢɢ ɪɚɜɧɚ
qE '
d
ɢɡɦɟɧɟɧɢɟ
ɦɨɥɹɪɧɨɣɩɚɪɰɢɚɥɶɧɨɣɷɧɟɪɝɢɢɢɟɟɦɨɠɧɨɩɪɟɞɫɬɚɜɢɬɶɜɫɥɟɞɭɸɳɟɦ
ɜɢɞɟ
Q
w
i
qV
dT
S
n
w
Ⱥɞɫɨɪɛɰɢɸɦɨɠɧɨɪɚɫɫɦɚɬɪɢɜɚɬɶɤɚɤɜɡɚɢɦɨɞɟɣɫɬɜɢɟɞɜɭɯɮɚɡɫ
ɨɛɪɚɡɨɜɚɧɢɟɦɤɨɦɩɥɟɤɫɚɚɞɫɨɪɛɟɧɬɚɞɫɨɪɛɚɬ
Ɍɨɝɞɚɫɜɨɛɨɞɧɚɹɷɧɟɪɝɢɹɪɚɜɧɚ
S
S
SS
S
S
S
S
dnGdnGdG
S
S
GnGnG
ɉɪɢɧɢɦɚɹ ɱɬɨ ɚɞɫɨɪɛɟɧɬ ɢɧɟɪɬɧɵɣ ɬɨɝɞɚ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɫɜɨ
ɛɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɷɧɟɪɝɢɢ ɢ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɷɧɬɚɥɶɩɢɢ ɢɦɟɟɬ
ɫɥɟɞɭɸɳɢɣɜɢɞ
SSS
dndATdSdH
PS
SSS
dndATdSdE
PS
SSS
nATSE
PS
SSS
nATSH
PS
ɋɜɨɛɨɞɧɵɟɷɧɟɪɝɢɢȽɟɥɶɦɝɨɥɶɰɚɢȽɢɛɛɫɚɢɦɟɟɬɜɢɞ
PS
SSS
dndATdSdHdG
SSS
dndATdSdEdA
PS
SS
nAA
PS
SS
nAG
PS
ȼ ɬɟɪɦɨɞɢɧɚɦɢɤɟ ɚɞɫɨɪɛɰɢɢ ɜɜɨɞɹɬ ɧɟɤɨɬɨɪɵɟ ɫɩɟɰɢɚɥɶɧɵɟ
ɨɛɨɡɧɚɱɟɧɢɹ
PS
ɝɞɟ
ʌɩɨɜɟɪɯɧɨɫɬɧɨɟɞɚɜɥɟɧɢɟɢɨɧɨɪɚɜɧɨ
ɧɚɬɹɠɟɧɢɟ
SSS
dnAdTdSdH
SSS
dnAddTSdG
PS
P
³
SSS
nTSH
P
SS
nG
JS
ɩɨɜɟɪɯɧɨɫɬɧɨɟ
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