ВУЗ:
Составители:
23
()i
:
'
R
, ɨɩɪɟɞɟɥɹɸɬ ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɜɥ. ɫ. ɢ ɜ ɫɢɫɬɟɦɟ
ɤɨɨɪɞɢɧɚɬ
i -ɝɨ ɮɪɚɝɦɟɧɬɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɬɪɭɤɬɭɪɚ
ɩɨɬɟɧɰɢɚɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɬɨɥɶɤɨ
ɤ ɩɨɹɜɥɟɧɢɸ ɦɟɯɚɧɢɡɦɚ ɨɞɧɨɜɪɟɦɟɧɧɨɣ «ɨɪɢɟɧɬɚɰɢɨɧɧɨɣ ɧɚɤɚɱɤɢ»
ɫɩɢɧɨɜ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ.
ɉɨɫɤɨɥɶɤɭ ɩɨɬɟɧɰɢɚɥ
12
,,V
ZZ
R ɹɜɥɹɟɬɫɹ ɫɤɚɥɹɪɨɦ, ɬɨ
ɧɟɫɮɟɪɢɱɟɫɤɢɟ ɱɥɟɧɵ ɷɬɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɟɥɢɱɢɧɚɦɢ
()i
N , ɧɟ
ɦɟɧɹɸɬ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɣɫɹ ɫɢɫɬɟɦɵ J ɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɡɚɤɨɧɭ
ɫɨɯɪɚɧɟɧɢɹ
(35), ɧɨ ɦɨɝɭɬ ɢɡɦɟɧɢɬɶ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ
L ɢ ɫɩɢɧɵ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ
i
J ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɹɦ
ɢ ɪɚɜɧɵɟ ɩɨ ɚɛɫɨɥɸɬɧɵɦ ɡɧɚɱɟɧɢɹɦ ɜɟɥɢɱɢɧɵ. ɉɪɢ ɷɬɨɦ ɧɟɫɮɟɪɢɱɟɫɤɢɟ
ɱɥɟɧɵ ɩɨɬɟɧɰɢɚɥɚ
12
,,V
ZZ
R ɢɡɦɟɧɹɸɬ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ
ɦɨɦɟɧɬ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɵ
'L , ɢɦɟɸɳɢɟ
ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɱɟɬɧɨɫɬɶ, ɩɨɫɤɨɥɶɤɭ ɜ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧ
()i
N ɜɯɨɞɹɬ
ɫɮɟɪɢɱɟɫɤɢɟ ɮɭɧɤɰɢɢ ɫɨ ɡɧɚɱɟɧɢɟɦ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ 2
L
.
Ɉɞɧɨɜɪɟɦɟɧɧɨ ɜɟɥɢɱɢɧɵ
()i
N ɧɟ ɦɟɧɹɸɬ ɩɪɨɟɤɰɢɢ
i
K
ɫɩɢɧɚ ɮɪɚɝɦɟɧɬɚ
ɞɟɥɟɧɢɹ
i
J ɧɚ ɟɝɨ ɨɫɶ ɫɢɦɦɟɬɪɢɢ, ɬɚɤ ɤɚɤ ɭɤɚɡɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɡɚɜɢɫɹɬ ɨɬ
D
– ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ
2*
0
mi
D
Z
ɫ ɧɭɥɟɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɩɪɨɟɤɰɢɣ.
ɍɱɢɬɵɜɚɹ, ɱɬɨ ɜ ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɮɪɚɝɦɟɧɬɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɨɫɶɸ
ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ (
12
ZZ Z
), ɩɨɬɟɧɰɢɚɥ
12
,,V
Z
Z
R ɦɨɠɧɨ
ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
,, ,'VVR
ZZ T
R , ɝɞɟ '
T
– ɭɝɨɥ ɦɟɠɞɭ
ɧɚɩɪɚɜɥɟɧɢɟɦ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɢ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ȼ
ɩɨɬɟɧɰɢɚɥɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ
,'VR
T
ɢɡ-ɡɚ ɫɥɨɠɟɧɢɹ ɹɞɟɪɧɨɝɨ
ɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɩɨɹɜɥɹɟɬɫɹ ɤɭɥɨɧɨɜɫɤɢɣ ɛɚɪɶɟɪ ɩɪɢ ɡɧɚɱɟɧɢɹɯ
ɪɚɞɢɭɫɚ
12
12
00
20 20
22
'1 ' 1 '
BA A
R
RYR Ys
TET ET
, ɝɞɟ
ɜɟɥɢɱɢɧɚ
s
ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɩɨɪɹɞɤɚ ɪɚɞɢɭɫɚ ɹɞɟɪɧɵɯ ɫɢɥ 2
s
| ɮɦ, ɚ
ɪɚɞɢɭɫ ɹɞɪɚ
1
3
0
1.4
i
A
i
R
A ɮɦ. Ⱦɥɹ ɦɚɥɵɯ ɭɝɥɨɜ '
T
ɜɟɥɢɱɢɧɚ ɦɚɤɫɢɦɭɦɚ
ɤɭɥɨɧɨɜɫɤɨɝɨ ɛɚɪɶɟɪɚ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ:
2
'
'0 ,
2
C
BB
T
T
(36)
ɝɞɟ ɤɨɧɫɬɚɧɬɵ
0B ɢ ɋ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɚɦɢ ɞɟɮɨɪɦɚɰɢɢ
2
i
E
ɢ
ɪɚɞɢɭɫɚɦɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ
0
i
A
R
.
ɍɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ ɞɥɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ. ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɞɥɹ ɦɚɥɵɯ ɭɝɥɨɜ '
T
ɜ
:'R(i ) , ɨɩɪɟɞɟɥɹɸɬ ɧɚɩɪɚɜɥɟɧɢɟ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɜ ɥ. ɫ. ɢ ɜ ɫɢɫɬɟɦɟ
ɤɨɨɪɞɢɧɚɬ i -ɝɨ ɮɪɚɝɦɟɧɬɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɫɬɪɭɤɬɭɪɚ
ɩɨɬɟɧɰɢɚɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɦɨɠɟɬ ɩɪɢɜɨɞɢɬɶ ɬɨɥɶɤɨ
ɤ ɩɨɹɜɥɟɧɢɸ ɦɟɯɚɧɢɡɦɚ ɨɞɧɨɜɪɟɦɟɧɧɨɣ «ɨɪɢɟɧɬɚɰɢɨɧɧɨɣ ɧɚɤɚɱɤɢ»
ɫɩɢɧɨɜ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɨɪɛɢɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ.
ɉɨɫɤɨɥɶɤɭ ɩɨɬɟɧɰɢɚɥ V R, Z1, Z2 ɹɜɥɹɟɬɫɹ ɫɤɚɥɹɪɨɦ, ɬɨ
ɧɟɫɮɟɪɢɱɟɫɤɢɟ ɱɥɟɧɵ ɷɬɨɝɨ ɩɨɬɟɧɰɢɚɥɚ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɟɥɢɱɢɧɚɦɢ N (i ) , ɧɟ
ɦɟɧɹɸɬ ɩɨɥɧɨɝɨ ɫɩɢɧɚ ɞɟɥɹɳɟɣɫɹ ɫɢɫɬɟɦɵ J ɢ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɡɚɤɨɧɭ
ɫɨɯɪɚɧɟɧɢɹ (35), ɧɨ ɦɨɝɭɬ ɢɡɦɟɧɢɬɶ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ
L ɢ ɫɩɢɧɵ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ J i ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɩɨ ɧɚɩɪɚɜɥɟɧɢɹɦ
ɢ ɪɚɜɧɵɟ ɩɨ ɚɛɫɨɥɸɬɧɵɦ ɡɧɚɱɟɧɢɹɦ ɜɟɥɢɱɢɧɵ. ɉɪɢ ɷɬɨɦ ɧɟɫɮɟɪɢɱɟɫɤɢɟ
ɱɥɟɧɵ ɩɨɬɟɧɰɢɚɥɚ V R, Z1, Z2 ɢɡɦɟɧɹɸɬ ɨɬɧɨɫɢɬɟɥɶɧɵɣ ɨɪɛɢɬɚɥɶɧɵɣ
ɦɨɦɟɧɬ L ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɧɚ ɜɟɥɢɱɢɧɵ 'L , ɢɦɟɸɳɢɟ
ɩɨɥɨɠɢɬɟɥɶɧɭɸ ɱɟɬɧɨɫɬɶ, ɩɨɫɤɨɥɶɤɭ ɜ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧ N (i ) ɜɯɨɞɹɬ
ɫɮɟɪɢɱɟɫɤɢɟ ɮɭɧɤɰɢɢ ɫɨ ɡɧɚɱɟɧɢɟɦ ɨɪɛɢɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ L 2 .
Ɉɞɧɨɜɪɟɦɟɧɧɨ ɜɟɥɢɱɢɧɵ N (i ) ɧɟ ɦɟɧɹɸɬ ɩɪɨɟɤɰɢɢ Ki ɫɩɢɧɚ ɮɪɚɝɦɟɧɬɚ
ɞɟɥɟɧɢɹ J i ɧɚ ɟɝɨ ɨɫɶ ɫɢɦɦɟɬɪɢɢ, ɬɚɤ ɤɚɤ ɭɤɚɡɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɡɚɜɢɫɹɬ ɨɬ
D – ɮɭɧɤɰɢɣ ȼɢɝɧɟɪɚ Dm2*0 Zi ɫ ɧɭɥɟɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ
ɩɪɨɟɤɰɢɣ.
ɍɱɢɬɵɜɚɹ, ɱɬɨ ɜ ɨɛɥɚɫɬɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɭɝɥɨɜɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɩɟɪɜɢɱɧɵɯ ɮɪɚɝɦɟɧɬɨɜ ɨɫɢ ɫɢɦɦɟɬɪɢɢ ɮɪɚɝɦɟɧɬɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɨɫɶɸ
ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ( Z Z1 Z2 ), ɩɨɬɟɧɰɢɚɥ V R, Z1, Z2 ɦɨɠɧɨ
ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ V R, Z , Z V R,T ' , ɝɞɟ T ' – ɭɝɨɥ ɦɟɠɞɭ
ɧɚɩɪɚɜɥɟɧɢɟɦ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ R ɢ ɨɫɶɸ ɫɢɦɦɟɬɪɢɢ ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ. ȼ
ɩɨɬɟɧɰɢɚɥɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɮɪɚɝɦɟɧɬɨɜ V R,T ' ɢɡ-ɡɚ ɫɥɨɠɟɧɢɹ ɹɞɟɪɧɨɝɨ
ɢ ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ ɩɨɹɜɥɹɟɬɫɹ ɤɭɥɨɧɨɜɫɤɢɣ ɛɚɪɶɟɪ ɩɪɢ ɡɧɚɱɟɧɢɹɯ
1 2
ɪɚɞɢɭɫɚ RB T ' RA01 1 E 2 Y20 T ' RA02 1 E 2 Y20 T ' s , ɝɞɟ
ɜɟɥɢɱɢɧɚ s ɢɦɟɟɬ ɡɧɚɱɟɧɢɟ ɩɨɪɹɞɤɚ ɪɚɞɢɭɫɚ ɹɞɟɪɧɵɯ ɫɢɥ s | 2 ɮɦ, ɚ
1
ɪɚɞɢɭɫ ɹɞɪɚ RA0i 1.4 Ai 3 ɮɦ. Ⱦɥɹ ɦɚɥɵɯ ɭɝɥɨɜ T ' ɜɟɥɢɱɢɧɚ ɦɚɤɫɢɦɭɦɚ
ɤɭɥɨɧɨɜɫɤɨɝɨ ɛɚɪɶɟɪɚ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ:
2
C T'
B T' B 0 , (36)
2
i
ɝɞɟ ɤɨɧɫɬɚɧɬɵ B 0 ɢ ɋ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɚɦɢ ɞɟɮɨɪɦɚɰɢɢ E 2 ɢ
ɪɚɞɢɭɫɚɦɢ ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ RA0i .
ɍɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ ɞɥɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɨɪɛɢɬɚɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ
ɮɪɚɝɦɟɧɬɨɜ ɞɟɥɟɧɢɹ ɜɨ ɜ. ɫ. ɞɟɥɹɳɟɝɨɫɹ ɹɞɪɚ ɞɥɹ ɦɚɥɵɯ ɭɝɥɨɜ T ' ɜ
23
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