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ɩɨɥɭɱɢɦ:
mjsmj
z
,
ˆ
,
¦
s
sl
m
s
mj
msml
mC
2
. (13)
ɂɬɚɤ, ɩɨɫɤɨɥɶɤɭ ɜ ɛɚɡɢɫɟ (7) ɫ ɡɚɞɚɧɧɵɦ ɨɩɟɪɚɬɨɪ (9) ɧɟ ɢɦɟɟɬ
ɧɟɞɢɚɝɨɧɚɥɶɧɵɯ ɦɚɬɪɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɬɨ ɞɥɹ ɩɨɩɪɚɜɨɤ ɩɟɪɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ
ɤ ɭɪɨɜɧɸ ɫɟɤɭɥɹɪɧɨɟ ɭɪɚɜɧɟɧɢɟ ɧɟ ɜɨɡɧɢɤɚɟɬ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɷɬɢ
ɩɨɩɪɚɜɤɢ ɞɚɸɬɫɹ ɞɢɚɝɨɧɚɥɶɧɵɦɢ ɦɚɬɪɢɱɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɨɩɟɪɚɬɨɪɚ
ɜɨɡɦɭɳɟɧɢɹ (9):
j
)1(
H
jn
H
H
)1(
mj
mjsJmj
zz
,)
ˆ
ˆ
(, B
B
P
)(
z
sm . (14)
ȼɟɥɢɱɢɧɚ
z
s , ɜ ɩɪɢɧɰɢɩɟ, ɦɨɠɟɬ ɛɵɬɶ ɜɵɱɢɫɥɟɧɚ ɩɨ ɮɨɪɦɭɥɟ (13), ɨɞɧɚɤɨ,
ɤɚɤ ɦɨɠɧɨ ɩɨɤɚɡɚɬɶ [1], ɞɥɹ ɧɟɟ ɫɭɳɟɫɬɜɭɟɬ ɛɨɥɟɟ ɩɪɨɫɬɨɟ ɜɵɪɚɠɟɧɢɟ:
)1(2
)1()1()1(
jj
sslljj
ms
z
. (15)
ɋ ɭɱɟɬɨɦ (15) ɪɟɡɭɥɶɬɚɬ ɞɥɹ ɷɧɟɪɝɢɢ ɪɚɫɳɟɩɥɟɧɢɹ (14) ɡɚɩɢɲɟɬɫɹ ɜ ɜɢɞɟ:
H
)1(
mlj
g
B
B
P m , jjjm ...,,1, , (16)
ɝɞɟ
)1(2
)1()1()1(
1
jj
sslljj
g
(17)
ɟɫɬɶ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɦɧɨɠɢɬɟɥɶ Ʌɚɧɞɟ.
ȼ
s
-ɫɨɫɬɨɹɧɢɹɯ (0
l
) ɩɨɥɧɵɣ ɦɨɦɟɧɬ ɪɚɜɟɧ ɫɩɢɧɭ, ɢ, ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ
(17), 2
g
. ɉɪɢ 1t
l
ɞɥɹ ɫɥɭɱɚɹ 2
/
1
s
ɩɨɥɧɵɣ ɦɨɦɟɧɬ ɩɪɢɧɢɦɚɟɬ ɬɨɥɶɤɨ ɞɜɚ
ɡɧɚɱɟɧɢɹ,2
/
1r
l
j , ɢ ɮɨɪɦɭɥɚ (17) ɞɚɟɬ:
1
)12(1
r lg . (18)
ɉɨ ɚɧɚɥɨɝɢɢ ɫ ɪɟɡɭɥɶɬɚɬɨɦ (18) ɡɚɞɚɱɢ 9.4, ɜɡɹɬɭɸ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ
ɡɧɚɤɨɦ ɩɪɨɢɡɜɨɞɧɭɸ ɨɬ ɷɧɟɪɝɢɢ ɚɬɨɦɚ ɩɨ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɫɥɟɞɭɟɬ
ɢɧɬɟɪɩɪɟɬɢɪɨɜɚɬɶ ɤɚɤ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɚɬɨɦɚ.
Ⱦɢɮɮɟɪɟɧɰɢɪɭɹ ɩɨ
B
ɩɪɢɜɟɞɟɧɧɨɟ ɜɵɲɟ ɜɵɪɚɠɟɧɢɟ (16), ɧɚɣɞɟɦ, ɱɬɨ ɚɬɨɦɧɚɹ
ɫɢɫɬɟɦɚ, ɧɚɯɨɞɹɳɚɹɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɫ ɨɩɪɟɞɟɥɟɧɧɵɦ ɡɧɚɱɟɧɢɟɦ ɩɪɨɟɤɰɢɢ
ɩɨɥɧɨɝɨ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɧɚ ɧɟɤɨɬɨɪɨɟ ɧɚɩɪɚɜɥɟɧɢɟ , ɨɛɥɚɞɚɟɬ ɦɚɝɧɢɬɧɵɦ
ɦɨɦɟɧɬɨɦ
m
z
mg
Bz
P P (19)
120
ɜ ɭɤɚɡɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ.
ɛ) ȼ ɫɥɭɱɚɟ ɫɢɥɶɧɨɝɨ ɩɨɥɹ ( B
B
P
'jnjn
HH!! ) ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ ɜ
ɧɭɥɟɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɨɣ ɭɪɨɜɧɟɣ
ln
r
H , ɫɱɢɬɚɹ ɫɬɚɰɢɨɧɚɪɧɵɦɢ
ɫɨɫɬɨɹɧɢɹ
slr
msmln ,,, . (20)
ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɦɵ ɩɪɟɞɩɨɥɚɝɚɟɦ, ɱɬɨ B
B
P
lnln
rr
HH
cc
, ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
ɬɟɨɪɢɹ ɜɨɡɦɭɳɟɧɢɣ ɫ ɨɩɟɪɚɬɨɪɨɦ (6) ɜɫɟ ɟɳɟ ɩɪɢɦɟɧɢɦɚ. ȼ ɛɚɡɢɫɟ (20)
ɨɩɟɪɚɬɨɪ ɜɨɡɦɭɳɟɧɢɹ (6) ɢɦɟɟɬ ɬɨɥɶɤɨ ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ:
VB
B
P
sslrzlr
msmsmlnlmln ,,,,
ˆ
,,
B
B
P 2
lrlr
mlnmln ,,,,
szs
mssms ,
ˆ
, B
B
P )2(
sl
mm . (21)
Ɉɧɢ ɢ ɹɜɥɹɸɬɫɹ ɩɨɩɪɚɜɤɚɦɢ ɩɟɪɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɩɨ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ,
ɨɩɪɟɞɟɥɹɸɳɢɦɢ ɪɚɫɳɟɩɥɟɧɢɟ ɭɪɨɜɧɹ
ln
r
H :
H
)1(
sl
mm
B
B
P )2(
sl
mm . (22)
Ʉ ɤɚɠɞɨɦɭ ɢɡ ɧɚɣɞɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɷɧɟɪɝɢɢ
ln
r
H
)1(
sl
mm
H ɬɟɩɟɪɶ ɦɨɠɧɨ
ɞɨɛɚɜɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɨɩɪɚɜɤɭ ɩɟɪɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɩɨ ɫɩɢɧ-
ɨɪɛɢɬɚɥɶɧɨɦɭ ɜɡɚɢɦɨɞɟɣɫɬɜɢɸ. Ɍɚɤɢɟ ɩɨɩɪɚɜɤɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɫɪɟɞɧɢɟ
ɡɧɚɱɟɧɢɹ ɨɩɟɪɚɬɨɪɚ ɜ ɫɨɫɬɨɹɧɢɹɯ (20). ɉɨɫɤɨɥɶɤɭ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ
ɨɪɛɢɬɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
sl
ˆ
ˆ
)( D r
lr
mln ,, ɢɦɟɟɬ ɜɢɞ ɩɪɨɢɡɜɟɞɟɧɢɹ ɪɚɞɢɚɥɶɧɨɣ ɢ
ɭɝɥɨɜɨɣ ɱɚɫɬɟɣ,,ɬɨ ɩɪɢ ɭɫɪɟɞɧɟɧɢɢ ɨɩɟɪɚɬɨɪɚ ɩɨ
ɫɨɫɬɨɹɧɢɹɦ (20) ɢɥɢ ɩɨ ɥɸɛɵɦ ɧɨɪɦɢɪɨɜɚɧɧɵɦ ɥɢɧɟɣɧɵɦ ɤɨɦɛɢɧɚɰɢɹɦ ɬɚɤɢɯ
ɫɨɫɬɨɹɧɢɣ ɫ ɧɟɢɡɦɟɧɧɵɦɢ ɤɜɚɧɬɨɜɵɦɢ ɱɢɫɥɚɦɢ ɩɪɨɢɫɯɨɞɢɬ ɡɚɦɟɧɚ
ɮɭɧɤɰɢɢ )
),()( MT
mlln
YrR
r
sl
ˆ
ˆ
)( D r
ln
r
,
(
r
D ɧɟɤɨɬɨɪɨɣ ɩɨɫɬɨɹɧɧɨɣ
A
, ɡɚɜɢɫɹɳɟɣ ɨɬ ɤɜɚɧɬɨɜɵɯ ɱɢɫɟɥ ln
r
,:
³
f
D
0
2
2
)()( rrRrdrA
ln
r
. (23)
ɂɦɟɹ ɷɬɨ ɜɜɢɞɭ, ɦɨɠɧɨ ɡɚɩɢɫɵɜɚɬɶ ɨɩɟɪɚɬɨɪ ɫɩɢɧ-ɨɪɛɢɬɚɥɶɧɨɝɨ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɜ ɮɨɪɦɟ
xx
slAA
ˆ
ˆ
(
ˆ
ˆ
sl
yy
sl
ˆ
ˆ
)
ˆ
ˆ
zz
sl (24)
ɢ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɟɝɨ ɫɪɟɞɧɢɯ ɡɧɚɱɟɧɢɣ (ɢɥɢ ɦɚɬɪɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɨ ɥɸɛɵɦ
121
ɫɨɫɬɨɹɧɢɹɦ ɫ ɡɚɞɚɧɧɵɦɢ ɭɱɢɬɵɜɚɬɶ ɥɢɲɶ ɭɝɥɨɜɭɸ ɢ ɫɩɢɧɨɜɭɸ ɱɚɫɬɢ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɫɨɫɬɨɹɧɢɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɧɬɟɪɟɫɭɸɳɟɟ ɧɚɫ ɫɪɟɞɧɟɟ
ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɫɩɢɧ-ɨɪɛɢɬɚɥɶɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɟɫɬɶ
ln
r
,)
D
sxslxl
mssmsmllmlAr ,
ˆ
,,
ˆ
,
ˆ
ˆ
)( sl
syslyl
mssmsmllmlA ,
ˆ
,,
ˆ
,
szslzl
mssmsmllmlA ,
ˆ
,,
ˆ
, . (25)
Ʉɚɤ ɢɡɜɟɫɬɧɨ, ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ
x
- ɢ - ɩɪɨɟɤɰɢɣ ɦɨɦɟɧɬɚ ɜ ɫɨɫɬɨɹɧɢɹɯ ɫ
ɨɩɪɟɞɟɥɟɧɧɵɦ ɡɧɚɱɟɧɢɟɦ -ɩɪɨɟɤɰɢɢ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɪɚɜɧɵ ɧɭɥɸ. ɉɨɷɬɨɦɭ
ɜɵɪɚɠɟɧɢɟ (25) ɫɜɨɞɢɬɫɹ ɬɨɥɶɤɨ ɤ ɜɤɥɚɞɭ ɩɨɫɥɟɞɧɟɝɨ ɱɥɟɧɚ ɢ ɪɚɜɧɨ .
Ⱦɨɛɚɜɢɜ ɷɬɭ ɩɨɩɪɚɜɤɭ ɤ (22), ɧɚɯɨɞɢɦ ɨɤɨɧɱɚɬɟɥɶɧɨ, ɱɬɨ ɢɡɦɟɧɟɧɢɟ ɭɪɨɜɧɹ
ɷɧɟɪɝɢɢ ɜ ɫɢɥɶɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ
y
z
sl
mmA
ln
r
H
H'
ln
r
B
B
P )2(
sl
mm
sl
mmA . (26)
ȼ ɤɚɱɟɫɬɜɟ ɩɪɨɫɬɟɣɲɟɝɨ ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɷɬɭ ɮɨɪɦɭɥɭ ɜ ɩɪɢɦɟɧɟɧɢɢ
ɤ ɞɜɭɤɪɚɬɧɨ ɜɵɪɨɠɞɟɧɧɨɦɭ ɩɨ ɫɩɢɧɭ
s
-ɭɪɨɜɧɸ ɷɥɟɤɬɪɨɧɚ, ɬɨ ɟɫɬɶ – ɤ ɞɭɛɥɟɬɭ
ɫɨɫɬɨɹɧɢɣ ɫ 2
2/1
s
/
1
s
j ,0
l
. ȼ ɷɬɨɦ ɫɥɭɱɚɟ 0
l
m , ɩɪɨɟɤɰɢɹ ɩɨɥɧɨɝɨ
ɦɨɦɟɧɬɚ ɪɚɜɧɚ ɩɪɨɟɤɰɢɢ ɫɩɢɧɚ (
s
mm ), ɬɚɤ ɱɬɨ ɮɨɪɦɭɥɚ (26) ɢ ɫɨɨɬɧɨɲɟɧɢɹ
(16), (17) ɞɚɸɬ ɨɞɢɧ ɢ ɬɨɬ ɠɟ ɪɟɡɭɥɶɬɚɬ:
2/1
s : H' 2 B
B
P m , 2
/
1r m . (27)
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɧɧɵɣ
s
-ɭɪɨɜɟɧɶ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
B
ɢɫɩɵɬɵɜɚɟɬ
ɪɚɫɳɟɩɥɟɧɢɟ ɧɚ ɞɜɚ ɭɪɨɜɧɹ ɷɧɟɪɝɢɢ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɨɫɬɨɹɧɢɣ, ɨɬɞɟɥɟɧɧɵɯ ɞɪɭɝ
ɨɬ ɞɪɭɝɚ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦ ɢɧɬɟɪɜɚɥɨɦ B
B
P
HH
pn
2.Ɍɚɤɚɹ ɠɟ ɤɚɪɬɢɧɚ ɛɵɥɚ
ɩɨɥɭɱɟɧɚ ɜ ɡɚɞɚɱɟ 8.5. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɭɱɟɬɟ ɫɜɟɪɯɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɵ
-ɞɭɛɥɟɬɚ ɦɵ ɩɪɢɞɟɦ ɤ ɛɨɥɟɟ ɫɥɨɠɧɨɦɭ ɪɟɡɭɥɶɬɚɬɭ (ɫɦ. ɡɚɞɚɱɭ 9.7); ɜ ɡɚɞɚɱɟ
9.8 ɨɛɫɭɠɞɚɟɬɫɹ ɟɳɟ ɨɞɢɧ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɣ ɩɪɢɦɟɪ – ɜɥɢɹɧɢɟ ɦɚɝɧɢɬɧɨɝɨ
ɩɨɥɹ ɧɚ ɭɪɨɜɧɢ ɷɧɟɪɝɢɢ - ɢ -ɫɨɫɬɨɹɧɢɣ ɷɥɟɤɬɪɨɧɚ.
2/1
s
2/1
p
2/3
p
ɂɡɦɟɧɟɧɢɟ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɪɨɜɧɟɣ ɚɬɨɦɚ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚɡɵɜɚɸɬ ɷɮɮɟɤɬɨɦ Ɂɟɟɦɚɧɚ. ȼ ɱɚɫɬɧɨɫɬɢ, ɬɚɤɨɣ ɬɟɪɦɢɧ
ɩɪɢɦɟɧɹɸɬ, ɝɨɜɨɪɹ ɨ ɪɚɫɳɟɩɥɟɧɢɢ ɭɪɨɜɧɟɣ, ɨɩɢɫɵɜɚɟɦɨɦ ɮɨɪɦɭɥɚɦɢ (16), (17);
ɩɪɢ ɷɬɨɦ ɜɨɡɧɢɤɚɸɳɟɟ ɜ ɫɢɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ ɨɬɤɥɨɧɟɧɢɟ
ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɫɩɟɤɬɪɚ ɨɬ ɩɪɟɞɫɤɚɡɵɜɚɟɦɨɝɨ ɮɨɪɦɭɥɚɦɢ (16), (17) ɧɚɡɵɜɚɸɬ
ɷɮɮɟɤɬɨɦ ɉɚɲɟɧɚ–Ȼɚɤɚ.
ɉɪɨɜɟɞɟɧɧɨɟ ɜɵɲɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɤɚɫɚɥɨɫɶ ɦɨɞɟɥɢ ɚɬɨɦɚ ɫ ɨɞɧɢɦ
ɷɥɟɤɬɪɨɧɨɦ, ɧɨ ɚɧɚɥɨɝɢɱɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɭɞɚɟɬɫɹ ɩɨɥɭɱɢɬɶ ɢ ɞɥɹ ɫɥɨɠɧɵɯ
122
ɚɬɨɦɨɜ, ɫɨɞɟɪɠɚɳɢɯ ɧɟɫɤɨɥɶɤɨ ɷɥɟɤɬɪɨɧɨɜ [1]. ɇɟɫɦɨɬɪɹ ɧɚ ɬɨ, ɱɬɨ ɷɥɟɤɬɪɨɧɵ
ɨɛɪɚɡɭɸɬ ɫɥɨɠɧɭɸ ɫɢɫɬɟɦɭ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɱɚɫɬɢɰ,
ɫɬɚɰɢɨɧɚɪɧɵɟ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪɨɧɨɜ ɜ ɚɬɨɦɟ ɜ ɫɢɥɭ ɫɮɟɪɢɱɟɫɤɨɣ
ɫɢɦɦɟɬɪɢɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɥɹ ɹɞɪɚ ɦɨɠɧɨ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɩɪɢɛɥɢɠɟɧɢɢ
ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɵɦ ɨɛɪɚɡɨɦ – ɫɭɦɦɚɪɧɵɦ ɨɪɛɢɬɚɥɶɧɵɦ
ɦɨɦɟɧɬɨɦ
L
, ɫɭɦɦɚɪɧɵɦ ɫɩɢɧɨɦ ɷɥɟɤɬɪɨɧɨɜ
S
ɢ ɩɨɥɧɵɦ ɦɨɦɟɧɬɨɦ ɢɦɩɭɥɶɫɚ
J
. ɇɟ ɨɫɬɚɧɚɜɥɢɜɚɹɫɶ ɧɚ ɨɛɨɫɧɨɜɚɧɢɢ ɷɬɢɯ ɭɬɜɟɪɠɞɟɧɢɣ, ɨɩɢɲɟɦ ɥɢɲɶ ɫɩɨɫɨɛ
ɨɛɨɡɧɚɱɟɧɢɹ ɚɬɨɦɧɵɯ ɭɪɨɜɧɟɣ ɷɧɟɪɝɢɢ (ɧɚɡɵɜɚɟɦɵɯ ɬɚɤɠɟ ɫɩɟɤɬɪɚɥɶɧɵɦɢ
ɬɟɪɦɚɦɢ ɚɬɨɦɚ). ɋɨɫɬɨɹɧɢɹ ɫ ɪɚɡɥɢɱɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɩɨɥɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ
ɦɨɦɟɧɬɚ ...,4,3,2,1,0
L
ɨɛɨɡɧɚɱɚɸɬɫɹ ɜ ɬɨɣ ɠɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɫɢɦɜɨɥɚɦɢ
S, P, D, F, G, …. ɋɥɟɜɚ ɜɜɟɪɯɭ ɨɤɨɥɨ ɬɚɤɨɝɨ ɫɢɦɜɨɥɚ ɭɤɚɡɵɜɚɸɬ ɱɢɫɥɨ 12
S
(ɧɚɡɵɜɚɟɦɨɟ ɦɭɥɶɬɢɩɥɟɬɧɨɫɬɶɸ ɬɟɪɦɚ ɢ ɪɚɜɧɨɟ ɱɢɫɥɭ ɫɩɢɧɨɜɵɯ ɫɨɫɬɨɹɧɢɣ
ɚɬɨɦɚ ɩɪɢ ɞɚɧɧɨɦ ɫɭɦɦɚɪɧɨɦ ɫɩɢɧɟ ɷɥɟɤɬɪɨɧɨɜ), ɚ ɫɩɪɚɜɚ ɜɧɢɡɭ – ɡɧɚɱɟɧɢɟ
ɩɨɥɧɨɝɨ ɦɨɦɟɧɬɚ
J
; ɧɚɩɪɢɦɟɪ, ɫɢɦɜɨɥɨɦ ɨɛɨɡɧɚɱɚɟɬɫɹ ɭɪɨɜɟɧɶ ɫ
2/1
2
P 1
L
,
2
/
1
S
,2
/
1
J
. Ɇɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɞɥɹ ɫɥɨɠɧɵɯ ɚɬɨɦɨɜ ɜ ɫɥɚɛɨɦ
ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɛɭɞɭɬ ɫɩɪɚɜɟɞɥɢɜɵ ɮɨɪɦɭɥɵ (16), (17), ɚ ɜ ɫɢɥɶɧɨɦ ɩɨɥɟ – (26),
ɟɫɥɢ ɜ ɷɬɢɯ ɮɨɪɦɭɥɚɯ ɡɚɦɟɧɢɬɶ «ɦɚɥɵɟ» ɛɭɤɜɵ ,j
l
,
s
ɢ
sl
mmm
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ «ɛɨɥɶɲɢɦɢ» ɛɭɤɜɚɦɢ:
J
,
L
,
S
ɢ
sl
MMM .
ɋɭɳɟɫɬɜɟɧɧɨ ɧɨɜɵɣ ɞɥɹ ɧɚɫ ɚɫɩɟɤɬ ɡɞɟɫɶ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɫɥɨɠɧɵɣ
ɚɬɨɦ ɦɨɠɟɬ ɢɦɟɬɶ ɫɨɫɬɨɹɧɢɟ ɫ ɪɚɜɧɵɦ ɧɭɥɸ ɫɭɦɦɚɪɧɵɦ ɫɩɢɧɨɦ.
ɉɪɢ 0,0 z
L
S
ɦɧɨɠɢɬɟɥɶ Ʌɚɧɞɟ
g
ɪɚɜɟɧ ɟɞɢɧɢɰɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɪɚɫɳɟɩɥɟɧɢɟ ɭɪɨɜɧɹ ɷɧɟɪɝɢɢ ɚɬɨɦɚ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɧɚɡɵɜɚɸɬ ɧɨɪɦɚɥɶɧɵɦ
ɷɮɮɟɤɬɨɦ Ɂɟɟɦɚɧɚ. ɉɪɢ ɨɬɥɢɱɧɨɦ ɨɬ ɟɞɢɧɢɰɵ ɦɧɨɠɢɬɟɥɟ Ʌɚɧɞɟ ɪɚɫɳɟɩɥɟɧɢɟ,
ɨɩɢɫɵɜɚɟɦɨɟ ɮɨɪɦɭɥɚɦɢ (16), (17), ɧɚɡɵɜɚɸɬ ɚɧɨɦɚɥɶɧɵɦ ɷɮɮɟɤɬɨɦ Ɂɟɟɦɚɧɚ;
ɬɚɤɨɟ ɧɚɡɜɚɧɢɟ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɞɨ ɨɬɤɪɵɬɢɹ ɫɩɢɧɚ ɷɥɟɤɬɪɨɧɚ ɧɚɛɥɸɞɚɟɦɵɣ ɜ
ɨɩɵɬɚɯ ɷɮɮɟɤɬ Ɂɟɟɦɚɧɚ ɫ 1z
g
ɧɟ ɭɞɚɜɚɥɨɫɶ ɨɛɴɹɫɧɢɬɶ.
ɋɥɨɠɧɵɣ ɚɬɨɦ ɦɨɠɟɬ ɧɟ ɢɦɟɬɶ ɧɢ ɫɩɢɧɚ (0
S
), ɧɢ ɨɪɛɢɬɚɥɶɧɨɝɨ
ɦɨɦɟɧɬɚ (0
L
), ɬɚɤ ɱɬɨ ɢ ɩɨɥɧɵɣ ɦɨɦɟɧɬ ɨɛɪɚɳɚɟɬɫɹ ɜ ɧɭɥɶ (0
J
). Ɍɨɝɞɚ
ɥɢɧɟɣɧɵɣ ɩɨ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɨɩɟɪɚɬɨɪ ), ɨɱɟɜɢɞɧɨ, ɧɟ ɞɚɟɬ
ɫɦɟɳɟɧɢɹ ɭɪɨɜɧɟɣ ɧɢ ɜ ɤɚɤɨɦ ɩɨɪɹɞɤɟ ɬɟɨɪɢɢ ɜɨɡɦɭɳɟɧɢɣ, ɩɨɫɤɨɥɶɤɭ ɜɫɟ ɟɝɨ
ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɢɫɱɟɡɚɸɬ. Ⱦɥɹ ɬɚɤɨɝɨ ɫɨɫɬɨɹɧɢɹ ɚɬɨɦɚ ɫɦɟɳɟɧɢɟ
ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɭɪɨɜɧɹ ɜ ɩɟɪɜɨɦ ɧɟɢɫɱɟɡɚɸɳɟɦ ɩɪɢɛɥɢɠɟɧɢɢ ɪɚɜɧɨ ɫɪɟɞɧɟɦɭ
ɡɧɚɱɟɧɢɸ ɤɜɚɞɪɚɬɢɱɧɨɝɨ ɩɨ ɩɨɥɸ ɜɨɡɦɭɳɟɧɢɹ, ɤɨɬɨɪɨɟ ɢɦɟɟɬ ɜɢɞ ɫɭɦɦɵ
ɜɤɥɚɞɨɜ ɨɬ ɜɫɟɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɚɬɨɦɟ (ɢɧɞɟɤɫ i ɧɭɦɟɪɭɟɬ ɷɥɟɤɬɪɨɧɵ):
ˆ
2
ˆ
(
zzB
SLB P
¦
H'
i
ii
yxH
mc
e
222
2
2
8
. (28)
Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɡɞɟɫɶ ɨɛɨɡɧɚɱɟɧɨ ɩɨɫɪɟɞɫɬɜɨɦ
H
. ɉɨɫɤɨɥɶɤɭ ɭɫɪɟɞɧɟɧɢɟ
ɨɩɟɪɚɬɨɪɨɜ ɤɨɨɪɞɢɧɚɬ ɷɥɟɤɬɪɨɧɨɜ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩɪɨɜɨɞɢɬɫɹ ɜ ɫɮɟɪɢɱɟɫɤɢ
123
ɫɢɦɦɟɬɪɢɱɧɨɦ ɫɨɫɬɨɹɧɢɢ ɚɬɨɦɚ, ɬɨ
222
3
2
iii
ryx . ȼɵɱɢɫɥɢɜ ɦɚɝɧɢɬɧɵɣ
ɦɨɦɟɧɬ ɚɬɨɦɚ ɩɨ ɮɨɪɦɭɥɟ
H
z
wH'w P /,ɩɨɥɭɱɢɦ H
z
F P , ɝɞɟ
ɤɨɷɮɮɢɰɢɟɧɬ , ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɦɚɝɧɢɬɧɭɸ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɚɬɨɦɚ ɜ
ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɨɫɬɨɹɧɢɢ, ɤɚɤ ɜɢɞɧɨ ɢɡ (28), ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ
ɫɨɨɬɧɨɲɟɧɢɟɦ, ɧɚɡɵɜɚɟɦɵɦ ɮɨɪɦɭɥɨɣ Ʌɚɧɠɟɜɟɧɚ:
F
¦
F
i
i
r
mc
e
2
2
2
6
. (29)
ɋɨɝɥɚɫɧɨ (29) ɜɟɥɢɱɢɧɚ ɨɬɪɢɰɚɬɟɥɶɧɚ, ɬɨ ɟɫɬɶ ɚɬɨɦɵ ɫF 0
S
L
ɞɢɚɦɚɝɧɢɬɧɵ [1].
9.7. ɉɪɢ ɜɵɛɨɪɟ ɨɫɢ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
ɨɩɟɪɚɬɨɪ ɷɧɟɪɝɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɷɥɟɤɬɪɨɧɚ ɢ
ɩɪɨɬɨɧɚ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɢ ɫ ɜɧɟɲɧɢɦ ɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ ɢɦɟɟɬ ɜɢɞ
z B
V
ˆ
C
2
ˆ
1
ˆ
ıı B
ze 1
ˆ
VP B
zp 2
ˆ
VP , (1)
ɝɞɟ ɦɚɬɪɢɰɵ ɉɚɭɥɢ ɫ ɧɨɦɟɪɚɦɢ 1 ɢ 2 ɞɟɣɫɬɜɭɸɬ ɧɚ ɫɩɢɧɨɜɵɟ ɫɨɫɬɨɹɧɢɹ
ɷɥɟɤɬɪɨɧɚ ɢ ɩɪɨɬɨɧɚ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ;0!C – ɩɨɫɬɨɹɧɧɚɹ, ɨɩɪɟɞɟɥɹɸɳɚɹ
ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɦɚɫɲɬɚɛ ɫɜɟɪɯɬɨɧɤɨɣ ɫɬɪɭɤɬɭɪɵ
s
1-ɭɪɨɜɧɹ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ (ɫɦ.
ɡɚɞɚɱɭ 8.8).
ɉɨɫɬɪɨɢɦ ɦɚɬɪɢɰɭ ɨɩɟɪɚɬɨɪɚ (1) ɩɨ ɫɩɢɧɨɜɵɦ ɫɨɫɬɨɹɧɢɹɦ ɫ
ɨɩɪɟɞɟɥɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ -ɩɪɨɟɤɰɢɢ ɫɩɢɧɚ ɨɛɟɢɯ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɱɚɫɬɢɰ:
z
21
1 pn ,
21
2 np ,
21
3 nn ,
21
4 pp . (2)
ȼ ɛɚɡɢɫɟ (2) ɜɬɨɪɨɟ ɢ ɬɪɟɬɶɟ ɫɥɚɝɚɟɦɵɟ ɨɩɟɪɚɬɨɪɚ (1) ɨɛɥɚɞɚɸɬ ɥɢɲɶ
ɞɢɚɝɨɧɚɥɶɧɵɦɢ ɦɚɬɪɢɱɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ, ɚ ɦɚɬɪɢɰɚ ɢɦɟɟɬ ɭɠɟ
ɢɡɜɟɫɬɧɵɣ ɧɚɦ ɛɥɨɱɧɨ-ɞɢɚɝɨɧɚɥɶɧɵɣ ɜɢɞ (ɫɦ. ɮɨɪɦɭɥɭ (8) ɜ ɡɚɞɚɱɟ 8.6).
Ɉɛɨɡɧɚɱɢɜ
2
ˆ
1
ˆ
ıı
pe
a PP ,
pe
b P
P , (3)
ɩɨɥɭɱɚɟɦ
V
ˆ
¸
¸
¸
¸
¸
¹
·
¨
¨
¨
¨
¨
©
§
bBC
bBC
aBCC
CaBC
000
000
002
002
. (4)
124
ȼ ɩɪɟɧɟɛɪɟɠɟɧɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ, ɨɩɢɫɵɜɚɟɦɵɦ ɨɩɟɪɚɬɨɪɨɦ (1),
ɫɨɫɬɨɹɧɢɹ (2) ɨɛɥɚɞɚɸɬ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɷɧɟɪɝɢɟɣ, ɬɨ ɟɫɬɶ ɜ ɬɚɤɨɦ ɩɪɢɛɥɢɠɟɧɢɢ
s
1-ɭɪɨɜɟɧɶ ɷɧɟɪɝɢɢ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ ɱɟɬɵɪɟɯɤɪɚɬɧɨ ɜɵɪɨɠɞɟɧ ɩɨ ɫɩɢɧɨɜɵɦ
ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɚɦ (ɩɨ -ɩɪɨɟɤɰɢɹɦ ɫɩɢɧɚ) ɷɥɟɤɬɪɨɧɚ ɢ ɩɪɨɬɨɧɚ. ɉɨɥɚɝɚɹ, ɱɬɨ
ɩɪɢɥɨɠɟɧɧɨɟ ɢɡɜɧɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ
z
B
ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɚɛɵɦ, ɛɭɞɟɦ
ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɨɩɟɪɚɬɨɪ (1) ɜ ɤɚɱɟɫɬɜɟ ɜɨɡɦɭɳɟɧɢɹ. Ɍɨɝɞɚ ɨɩɪɟɞɟɥɹɟɦɵɟ ɢɦ
ɩɨɩɪɚɜɤɢ ɩɟɪɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɤ
s
1-ɭɪɨɜɧɸ ɷɧɟɪɝɢɢ ɫɥɟɞɭɟɬ ɧɚɣɬɢ ɤɚɤ ɤɨɪɧɢ
ɫɟɤɭɥɹɪɧɨɝɨ ɭɪɚɜɧɟɧɢɹ
)1(
H
0)(det
)1(
GH
cc
kkkk
V ,
ɝɞɟ – ɷɥɟɦɟɧɬɵ ɦɚɬɪɢɰɵ (4). ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɢɦɟɟɬ ɱɟɬɵɪɟ ɤɨɪɧɹ:
kk
V
c
222
)1(
1
4 BaCC H ,
222
)1(
2
4 BaCC H ,
bBC H
)1(
3
, . (5) bBC H
)1(
4
Ɋɢɫ. 9.1
–
3C
C
0
)1(
H
)1(
1
H
)1(
3
H
B
)1(
2
H
)1(
4
H
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɨ ɜɧɟɲɧɟɦ ɦɚɝɧɢɬɧɨɦ
ɩɨɥɟ, ɜɥɢɹɧɢɟ ɤɨɬɨɪɨɝɨ ɭɱɢɬɵɜɚɟɬɫɹ
ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɦɟɠɞɭ
ɦɚɝɧɢɬɧɵɦɢ ɦɨɦɟɧɬɚɦɢ ɷɥɟɤɬɪɨɧɚ ɢ ɹɞɪɚ
ɚɬɨɦɚ, ɭɤɚɡɚɧɧɨɟ ɜɵɲɟ ɜɵɪɨɠɞɟɧɢɟ
s
1-
ɭɪɨɜɧɹ ɷɧɟɪɝɢɢ ɩɨɥɧɨɫɬɶɸ ɫɧɢɦɚɟɬɫɹ.
ȼɨɡɧɢɤɚɸɳɟɟ ɩɪɢ ɷɬɨɦ ɪɚɫɳɟɩɥɟɧɢɟ
ɭɪɨɜɧɹ ɫɯɟɦɚɬɢɱɟɫɤɢ ɢɡɨɛɪɚɠɟɧɨ ɧɚ
ɪɢɫ. 9.1. ȼ ɤɨɥɢɱɟɫɬɜɟɧɧɵɯ ɨɰɟɧɤɚɯ
ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ
pBe
P!!P|P ɢ
Bp
ba P|P 2.
ɉɨɥɭɱɟɧɧɵɣ ɪɟɡɭɥɶɬɚɬ ɦɨɠɧɨ ɩɨɹɫɧɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. ȼ
ɨɬɫɭɬɫɬɜɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɟ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɫɩɢɧ
ɷɥɟɤɬɪɨɧɚ ɢ ɫɩɢɧ ɹɞɪɚ ɨɛɪɚɡɭɸɬ ɟɞɢɧɭɸ ɫɩɢɧɨɜɭɸ ɩɨɞɫɢɫɬɟɦɭ ɚɬɨɦɚ, ɤɨɬɨɪɚɹ
ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɫɢɧɝɥɟɬɧɨɦ ɫɨɫɬɨɹɧɢɢ (ɫ ɪɚɜɧɵɦ ɧɭɥɸ ɫɭɦɦɚɪɧɵɦ ɫɩɢɧɨɦ
ɢ ɷɧɟɪɝɢɟɣ C3 ) ɢɥɢ ɜ ɨɞɧɨɦ ɢɡ ɜɵɪɨɠɞɟɧɧɵɯ ɬɪɢɩɥɟɬɧɵɯ ɫɨɫɬɨɹɧɢɣ (ɫ
ɪɚɜɧɵɦ ɟɞɢɧɢɰɟ ɫɭɦɦɚɪɧɵɦ ɫɩɢɧɨɦ ɢ ɷɧɟɪɝɢɟɣ C ). ȼ ɫɥɚɛɨɦ ɜɧɟɲɧɟɦ ɩɨɥɟ,
ɩɪɢ , ɜɨɡɧɢɤɚɟɬ ɥɢɧɟɣɧɨɟ ɩɨ ɩɨɥɸ ɪɚɫɳɟɩɥɟɧɢɟ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ
ɭɪɨɜɧɹ ɫɩɢɧɨɜɨɝɨ ɬɪɢɩɥɟɬɚ, ɚ ɷɧɟɪɝɢɹ ɫɢɧɝɥɟɬɧɨɝɨ ɫɩɢɧɨɜɨɝɨ ɫɨɫɬɨɹɧɢɹ ɩɨɱɬɢ
ɧɟ ɢɡɦɟɧɹɟɬɫɹ:
CB
B
P
ɬɪɢɩɥɟɬ:
°
°
¯
°
°
®
H
H
H
,
,
,
)1(
4
)1(
1
)1(
3
bBC
C
bBC
125
ɫɢɧɝɥɟɬ: , C3
)1(
2
H CB
B
P . (6)
ɋ ɭɜɟɥɢɱɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɩɪɢ CB
B
!!P , ɫɜɹɡɶ ɷɥɟɤɬɪɨɧɧɨɝɨ ɢ ɹɞɟɪɧɨɝɨ
ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɨɜ ɩɪɚɤɬɢɱɟɫɤɢ ɪɚɡɪɵɜɚɟɬɫɹ ɢ ɪɨɥɶ ɫɬɚɰɢɨɧɚɪɧɵɯ ɫɨɫɬɨɹɧɢɣ
ɩɟɪɟɯɨɞɢɬ ɤ ɫɨɫɬɨɹɧɢɹɦ (2), ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦɫɹ ɨɬɫɭɬɫɬɜɢɟɦ ɤɨɪɪɟɥɹɰɢɢ
ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɧɵɦ ɢ ɹɞɟɪɧɵɦ ɫɩɢɧɚɦɢ. ɗɬɢɦ ɫɨɫɬɨɹɧɢɹɦ ɨɬɜɟɱɚɸɬ ɱɟɬɵɪɟ
ɭɪɨɜɧɹ ɷɧɟɪɝɢɢ, B
pe
)(2
21
VPVP , ɝɞɟ
1
V
ɢ
2
V – ɩɪɨɟɤɰɢɢ ɫɩɢɧɨɜ ɷɥɟɤɬɪɨɧɚ
ɢ ɩɪɨɬɨɧɚ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɧɟɡɚɜɢɫɢɦɨ ɞɪɭɝ ɨɬ ɞɪɭɝɚ
ɩɪɢɧɢɦɚɸɳɢɟ ɡɧɚɱɟɧɢɹ 2
/
1r . Ʉ ɤɚɠɞɨɦɭ ɢɡ ɷɬɢɯ ɭɪɨɜɧɟɣ ɞɨɛɚɜɥɹɟɬɫɹ
ɩɨɩɪɚɜɤɚ (ɟɟ ɞɨɫɬɚɬɨɱɧɨ ɜɡɹɬɶ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ), ɨɛɭɫɥɨɜɥɟɧɧɚɹ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɷɥɟɤɬɪɨɧɚ ɢ ɩɪɨɬɨɧɚ. Ɍɚɤɚɹ ɩɨɩɪɚɜɤɚ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɞɢɚɝɨɧɚɥɶɧɵɣ ɦɚɬɪɢɱɧɵɣ ɷɥɟɦɟɧɬ ɨɩɟɪɚɬɨɪɚ
C
2
ˆ
1
ˆ
ıı ɜ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɦ ɫɨɫɬɨɹɧɢɢ (2) ɢ ɪɚɜɧɚ ɩɪɨɫɬɨ
21
4 VVC . Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ
ɢɦɟɧɧɨ ɭɤɚɡɚɧɧɵɟ ɱɟɬɵɪɟ ɡɧɚɱɟɧɢɹ ɷɧɟɪɝɢɢ ɢ ɞɚɸɬ ɮɨɪɦɭɥɵ (5) ɩɪɢ
:CB
B
!!P
aBC H
)1(
1
, ,,.(7)aBC H
)1(
2
bBC H
)1(
3
bBC H
)1(
4
9.8. Ʉɚɤ ɩɨɤɚɡɚɧɨ ɜ ɡɚɞɚɱɟ 9.6, ɩɪɢ ɜɵɛɨɪɟ ɨɫɢ ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ
ɩɪɢɥɨɠɟɧɧɨɝɨ ɢɡɜɧɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɩɟɪɚɬɨɪ ɜɨɡɦɭɳɟɧɢɹ, ɥɢɧɟɣɧɵɣ ɩɨ
ɩɨɥɸ ɢ ɜɤɥɸɱɚɸɳɢɣ ɫɩɢɧ-ɨɪɛɢɬɚɥɶɧɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ, ɢɦɟɟɬ ɜɢɞ:
z
B
V
ˆ
sl
ˆ
ˆ
A P )
ˆ
2
ˆ
(
zzB
slB sl
ˆ
ˆ
A )
ˆ
ˆ
(
zzB
sJB P . (1)
ɋɨɫɬɨɹɧɢɹ ɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɮɨɪɦɟ ɥɢɧɟɣɧɵɯ
ɤɨɦɛɢɧɚɰɢɣ ɛɚɡɢɫɧɵɯ ɜɟɤɬɨɪɨɜ ɫɨɫɬɨɹɧɢɹ ɜɢɞɚ
2/1
p
2/3
p
sl
msml ,, :
¦
s
sl
m
sl
mj
msml
msmlCmj ,,, , (2)
ɝɞɟ 2
/
1
s
– ɫɩɢɧ ɷɥɟɤɬɪɨɧɚ,1
l
– ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ ɷɥɟɤɬɪɨɧɚ ɜ
p
-
ɫɨɫɬɨɹɧɢɹɯ,
sl
mmm – ɩɪɨɟɤɰɢɹ ɫɭɦɦɚɪɧɨɝɨ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɷɥɟɤɬɪɨɧɚ.
Ȼɟɡ ɭɱɟɬɚ ɜɨɡɦɭɳɟɧɢɹ (1) ɩɟɪɟɱɢɫɥɟɧɧɵɟ ɛɚɡɢɫɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢ ɥɸɛɵɟ ɢɯ
ɥɢɧɟɣɧɵɟ ɤɨɦɛɢɧɚɰɢɢ ɩɪɢɧɚɞɥɟɠɚɬ ɨɞɧɨɦɭ ɢ ɬɨɦɭ ɠɟ ɲɟɫɬɢɤɪɚɬɧɨ
ɜɵɪɨɠɞɟɧɧɨɦɭ (ɩɨ ɢ )
l
m
s
m
p
-ɭɪɨɜɧɸ ɷɧɟɪɝɢɢ. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɧɚɣɬɢ
ɩɨɩɪɚɜɤɢ ɩɟɪɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɜɨɡɦɭɳɟɧɢɟɦ (1), ɫɥɟɞɭɟɬ
ɪɟɲɢɬɶ ɫɟɤɭɥɹɪɧɨɟ ɭɪɚɜɧɟɧɢɟ
)1(
H
0)(det
)1(
GH
cc
kkkk
V , (3)
126
ɝɞɟ – ɦɚɬɪɢɰɚ 6, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɨɩɟɪɚɬɨɪɭ ɜɨɡɦɭɳɟɧɢɹ (1). ɗɬɭ
ɦɚɬɪɢɰɭ ɦɨɠɧɨ ɜɡɹɬɶ ɤɚɤ ɜ «-ɩɪɟɞɫɬɚɜɥɟɧɢɢ» (ɫ ɛɚɡɢɫɨɦ
kk
V
c
6 u
sl
msml
sl
msml ,, ), ɬɚɤ ɢ ɜ «
s
l
mj -ɩɪɟɞɫɬɚɜɥɟɧɢɢ» (ɫ ɛɚɡɢɫɨɦ (2)). ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ
ɜ ɧɟɞɢɚɝɨɧɚɥɶɧɭɸ ɱɚɫɬɶ ɦɚɬɪɢɰɵ V ɞɚɟɬ ɜɤɥɚɞ ɥɢɲɶ ɱɥɟɧ , ɚ ɜɨ ɜɬɨɪɨɦ –
, ɩɨɫɤɨɥɶɤɭ ɦɚɬɪɢɰɵ ɢ , ɤɚɤ ɧɚɦ ɢɡɜɟɫɬɧɨ, ɞɢɚɝɨɧɚɥɶɧɵ ɜ ɛɚɡɢɫɟ
(2). ȼɵɛɟɪɟɦ, ɧɚɩɪɢɦɟɪ, ɜɬɨɪɨɣ ɜɚɪɢɚɧɬ.
ˆ
sl
ˆ
ˆ
A
zB
sB
ˆ
P sl
ˆ
ˆ
z
J
ˆ
əɜɧɵɣ ɜɢɞ ɫɨɫɬɨɹɧɢɣ (2) ɥɟɝɤɨ ɩɨɥɭɱɢɬɶ ɫ ɩɨɦɨɳɶɸ ɡɚɤɨɧɚ ɫɥɨɠɟɧɢɹ
ɦɨɦɟɧɬɨɜ, ɩɪɢɜɥɟɤɚɹ ɮɨɪɦɭɥɵ, ɤɨɬɨɪɵɦɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɟɣɫɬɜɢɟ ɨɩɟɪɚɬɨɪɨɜ
rrr
slJ
ˆ
ˆ
ˆ
. (4)
Ɍɚɤ, ɫɨɝɥɚɫɧɨ ɩɪɚɜɢɥɭ ɫɥɨɠɟɧɢɹ ɦɨɦɟɧɬɨɜ, ɜ ɫɨɫɬɨɹɧɢɟ ɫ ɫɭɦɦɚɪɧɨɣ ɩɪɨɟɤɰɢɟɣ
ɦɨɦɟɧɬɚ 2
/
3 m ɜɤɥɚɞ ɦɨɠɟɬ ɞɚɬɶ ɥɢɲɶ 2/1,2/11,1
sl
msml ɢ,
ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
2/3,2/3 mj 2/1,2/11,1
sl
msml . (5)
ɉɪɢɦɟɧɢɜ ɤ ɨɛɟɢɦ ɫɬɨɪɨɧɚɦ ɪɚɜɟɧɫɬɜɚ (5) ɨɩɟɪɚɬɨɪ , ɧɚɣɞɟɦ
ɫɨɫɬɨɹɧɢɟ
slJ
ˆ
ˆ
ˆ
2/1,2/3 mj , ɚ ɡɚɬɟɦ, ɩɨɜɬɨɪɹɹ ɩɨɞɨɛɧɭɸ ɩɪɨɰɟɞɭɪɭ, ɩɨɥɭɱɢɦ ɢ
ɨɫɬɚɥɶɧɵɟ ɱɥɟɧɵ ɤɜɚɪɬɟɬɚ . ɋɨɫɬɨɹɧɢɟ
2/3
p 2/1,2/1 mj , ɤɚɤ ɢ
2/1,2/3 mj , ɞɨɥɠɧɨ ɢɦɟɬɶ ɜɢɞ ɥɢɧɟɣɧɨɣ ɤɨɦɛɢɧɚɰɢɢ ɫɨɫɬɨɹɧɢɣ ɫ
ɢ 22/1,0
sl
mm /1,1
sl
mm , ɬɚɤ ɱɬɨ ɨɧɨ ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɹɟɬɫɹ
ɭɫɥɨɜɢɹɦɢ ɧɨɪɦɢɪɨɜɤɢ ɢ ɨɪɬɨɝɨɧɚɥɶɧɨɫɬɢ ɤ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɧɚɣɞɟɧɧɨɦɭ
ɫɨɫɬɨɹɧɢɸ
2/1,2/3 mj :
2/1,2/1
3
2
2/10
3
1
sl
mm 2/11
sl
mm . (6)
ȼɬɨɪɨɟ ɫɨɫɬɨɹɧɢɟ ɞɭɛɥɟɬɚ ɩɨɥɭɱɚɟɦ ɢɡ (6) ɫ ɩɨɦɨɳɶɸ ɩɨɧɢɠɚɸɳɟɝɨ
ɨɩɟɪɚɬɨɪɚ .
2/1
p
slJ
ˆ
ˆ
ˆ
ȼɵɩɢɲɟɦ ɨɩɪɟɞɟɥɹɟɦɵɟ ɭɤɚɡɚɧɧɵɦ ɨɛɪɚɡɨɦ ɜɟɤɬɨɪɵ ɫɨɫɬɨɹɧɢɣ (2),
ɨɛɨɡɧɚɱɚɹ ɞɥɹ ɤɪɚɬɤɨɫɬɢ ɫɨɫɬɨɹɧɢɹ
sl
msml ,2/1,1
ɤɚɤ
sl
mm , ɝɞɟ
,,ɢ ɩɪɢɫɜɚɢɜɚɹ ɫɨɫɬɨɹɧɢɹɦ (2) ɧɨɦɟɪɚ1,0,1
l
m p n,
s
mk, ɤɨɬɨɪɵɟ ɧɢɠɟ
ɛɭɞɭɬ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɧɭɦɟɪɚɰɢɢ ɦɚɬɪɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ :
kk
V
c
127
2/3
p :
°
°
°
°
¯
°
°
°
°
®
p
pn
pn
n
612/3,2/3
30
3
2
1
3
1
2/1,2/3
11
3
1
0
3
2
2/1,2/3
512/3,2/3
(7)
2/1
p :
°
°
¯
°
°
®
pn
pn
40
3
1
1
3
2
2/1,2/1
21
3
2
0
3
1
2/1,2/1
(8)
ȼ ɷɬɨɦ ɛɚɡɢɫɟ ɨɩɟɪɚɬɨɪ
ɞɢɚɝɨɧɚɥɟɧ, ɩɪɢɱɟɦ ɟɝɨ ɞɢɚɝɨɧɚɥɶɧɵɟ ɷɥɟɦɟɧɬɵ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɮɨɪɦɭɥɨɣ (ɫɦ. ɬɚɤɠɟ (5) ɜ ɡɚɞɚɱɟ 8.7)
sl
ˆ
ˆ
A
¯
®
.2/1,
;2/3,2/
)1()1()1(
2
2/1,1
jA
jA
sslljj
A
sl
Ɉɩɟɪɚɬɨɪ ɬɚɤɠɟ ɞɢɚɝɨɧɚɥɟɧ, ɟɝɨ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɢɦɟɸɬ ɜɢɞ
zB
JB
ˆ
P
P
zB
JB
ˆ
mB
B
P , jjjm
...,,1, .
Ⱦɢɚɝɨɧɚɥɶɧɵɟ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɨɩɟɪɚɬɨɪɚ , ɩɪɟɞɫɬɚɜɥɹɸɳɢɟ ɫɨɛɨɣ
ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ ɞɥɹ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɜɵɲɟ ɫɨɫɬɨɹɧɢɣ
z
s
ˆ
k , ɧɚɯɨɞɢɦ ɫ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɚɜɟɧɫɬɜ (7), (8):
6/11
ˆ
1
z
s , 6/12
ˆ
2
z
s , 6/13
ˆ
3
z
s ,
6/14
ˆ
4
z
s , 2/15
ˆ
5
z
s , 2/16
ˆ
6
z
s . (9)
Ɍɚɤɢɟ ɠɟ ɡɧɚɱɟɧɢɹ
z
s ɞɚɟɬ ɢ ɮɨɪɦɭɥɚ (15) ɡɚɞɚɱɢ 9.6 (ɷɬɚ ɮɨɪɦɭɥɚ ɜ ɧɚɲɟɦ
ɢɡɥɨɠɟɧɢɢ ɨɫɬɚɟɬɫɹ ɧɟɞɨɤɚɡɚɧɧɨɣ). ɇɚɤɨɧɟɰ, ɡɚɦɟɱɚɟɦ, ɱɬɨ ɛɭɞɭɬ ɧɟ ɪɚɜɧɵ
ɧɭɥɸ ɥɢɲɶ ɬɟ ɧɟɞɢɚɝɨɧɚɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɨɩɟɪɚɬɨɪɚ , ɤɨɬɨɪɵɟ ɫɜɹɡɵɜɚɸɬ
ɫɨɫɬɨɹɧɢɹ
z
s
ˆ
k ɫ ɪɚɡɥɢɱɧɵɦɢ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ m :j
2
ˆ
1
z
s 1
ˆ
2
z
s 4
ˆ
3
z
s 3/23
ˆ
4
z
s .
128
ɋɨɛɪɚɜ ɜɫɟ ɜɦɟɫɬɟ ɢ ɨɛɨɡɧɚɱɢɜ H P B
B
, ɩɨɥɭɱɚɟɦ
¸
¸
¸
¸
¸
¸
¸
¸
¹
·
¨
¨
¨
¨
¨
¨
¨
¨
©
§
H
H
HH
HH
HH
HH
22/0
022/
00
00
00
00
00
00
3/3/2
3/23/22/
00
00
00
00
00
00
3/3/2
3/23/22/
ˆ
A
A
A
A
A
A
V
ɇɚɣɞɟɧɧɚɹ ɦɚɬɪɢɰɚ ɢɦɟɟɬ ɛɥɨɱɧɨ-ɞɢɚɝɨɧɚɥɶɧɨɟ ɫɬɪɨɟɧɢɟ. ȼɢɞɧɨ, ɱɬɨ
ɟɟ ɞɢɚɝɨɧɚɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɢ ɭɠɟ ɹɜɥɹɸɬɫɹ ɤɨɪɧɹɦɢ (ɞɜɭɦɹ ɢɡ ɲɟɫɬɢ)
ɫɟɤɭɥɹɪɧɨɝɨ ɭɪɚɜɧɟɧɢɹ (3), ɚ ɨɫɬɚɥɶɧɵɟ ɱɟɬɵɪɟ ɤɨɪɧɹ
V
ˆ
55
V
66
V
)1(
H ɨɩɪɟɞɟɥɹɸɬɫɹ ɢɡ
ɞɜɭɯ ɧɟ ɫɜɹɡɚɧɧɵɯ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɭɪɚɜɧɟɧɢɣ ɜɬɨɪɨɣ ɫɬɟɩɟɧɢ:
09/2)3/()3/22/(
2)1()1(
HHHHH AA ,
09/2)3/()3/22/(
2)1()1(
HHHHH AA .
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɢɫɤɨɦɵɟ ɩɨɩɪɚɜɤɢ ɤ ɲɟɫɬɢɤɪɚɬɧɨ ɜɵɪɨɠɞɟɧɧɨɦɭ ɭɪɨɜɧɸ
ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɧɵɯ
p
-ɫɨɫɬɨɹɧɢɣ ɢɦɟɸɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
¸
¹
·
¨
©
§
PPP H
22
)1(
1
)(4/9
22
1
BABAB
A
BBB
,
¸
¹
·
¨
©
§
PPP H
22
)1(
2
)(4/9
22
1
BABAB
A
BBB
,
¸
¹
·
¨
©
§
PPP H
22
)1(
3
)(4/9
22
1
BABAB
A
BBB
,
¸
¹
·
¨
©
§
PPP H
22
)1(
4
)(4/9
22
1
BABAB
A
BBB
,
BA
B
P H 22/
)1(
5
,
BA
B
P H 22/
)1(
6
. (10)
Ɉɬɜɟɱɚɸɳɚɹ ɫɨɨɬɧɨɲɟɧɢɹɦ (10) ɤɚɪɬɢɧɚ ɪɚɫɳɟɩɥɟɧɢɹ
p
-ɭɪɨɜɧɹ ɫɯɟɦɚɬɢɱɧɨ
ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 9.2.
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɷɮɮɟɤɬɚ Ɂɟɟɦɚɧɚ ɜ ɫɥɚɛɨɦ ɩɨɥɟ ( AB
B
P ) ɮɨɪɦɭɥɵ
(10) ɩɪɢɜɨɞɹɬ ɤ ɬɟɦ ɠɟ ɪɟɡɭɥɶɬɚɬɚɦ, ɱɬɨ ɢ ɫɨɨɬɧɨɲɟɧɢɹ (16), (17) ɡɚɞɚɱɢ 9.6 ɫɨ
129