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Файл:Основы классической электродинамики. Учебное пособие
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ǛǼǴǷǺDzDZǹǴDZ 2
ɉɪɨɢɡɜɨɞɧɵɟ ɟɞɢɧɢɰɵ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɜɟɥɢɱɢɧ
Ɏɢɡɢɱɟɫɤɚɹ
ɜɟɥɢɱɢɧɚ
ɇɚɢɦɟɧɨɜɚɧɢɟ
ɟɞɢɧɢɰɵ
Ɉɛɨɡɧɚɱɟɧɢɟ Ɉɩɪɟɞɟɥɟɧɢɟ
Ʉɨɥɢɱɟɫɬɜɨ
ɷɥɟɤɬɪɢɱɟɫɬɜɚ,
ɷɥɟɤɬɪɢɱɟɫɤɢɣ
Ʉɭɥɨɧ Ʉɥ
ɡɚɪɹɞ
ɇɚɩɪɹɠɟɧɧɨɫɬɶ
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ
ȼɨɥɶɬ ɧɚ ɦɟɬɪ ȼ/ɦ
ɩɨɥɹ
ɗɥɟɤɬɪɢɱɟɫɤɨɟ
ɧɚɩɪɹɠɟɧɢɟ,
ɷɥɟɤɬɪɢɱɟɫɤɢɣ
ɩɨɬɟɧɰɢɚɥ,
ɪɚɡɧɨɫɬɶ
ȼɨɥɶɬ ȼ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ
ɩɨɬɟɧɰɢɚɥɨɜ,
ɷɥɟɤɬɪɨɞɜɢɠɭɳɚɹ
ɫɢɥɚ
ɗɥɟɤɬɪɢɱɟɫɤɚɹ
ɟɦɤɨɫɬɶ
Ɇɚɝɧɢɬɧɚɹ
ɢɧɞɭɤɰɢɹ
Ɇɚɝɧɢɬɧɵɣ
ɩɨɬɨɤ
Ɏɚɪɚɞ Ɏ
Ɍɟɫɥɚ Ɍɥ
ȼɟɛɟɪ ȼɛ
ɂɧɞɭɤɬɢɜɧɨɫɬɶ Ƚɟɧɪɢ Ƚɧ
ɗɥɟɤɬɪɢɱɟɫɤɨɟ
ɫɨɩɪɨɬɢɜɥɟɧɢɟ
Ɉɦ Ɉɦ
Ʉɭɥɨɧ ɪɚɜɟɧ ɤɨɥɢɱɟɫɬɜɭ
ɷɥɟɤɬɪɢɱɟɫɬɜɚ, ɩɪɨɯɨɞɹɳɟɝɨ ɱɟɪɟ
ɡ
ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɪɢ ɬɨɤɟ ɫɢɥɨɣ
1 Ⱥ ɡɚ ɜɪɟɦɹ 1 ɫ
ȼɨɥɶɬ ɧɚ ɦɟɬɪ ɪɚɜɟɧ ɧɚɩɪɹɠɟɧɧɨɫɬɢ
ɨɞɧɨɪɨɞɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ,
ɩɪɢ ɤɨɬɨɪɨɣ ɦɟɠɞɭ ɞɜɭɦɹ ɬɨɱɤɚɦɢ,
ɧɚɯɨɞɹɳɢɦɢɫɹ ɧɚ ɥɢɧɢɢ ɧɚɩɪɹɠɟɧɧɨɫɬɢ
ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 1 ɦ, ɫɨɡɞɚɟɬɫɹ
ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ 1 ȼ
ȼɨɥɶɬ ɪɚɜɟɧ ɷɥɟɤɬɪɢɱɟɫɤɨɦɭ
ɧɚɩɪɹɠɟɧɢɸ ɧɚ ɭɱɚɫɬɤɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɰɟɩɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɜ ɭɱɚɫɬɤɟ
ɩɪɨɯɨɞɢɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ ɫɢɥɨɣ
1 Ⱥ ɢ ɡɚɬɪɚɱɢɜɚɟɬɫɹ ɦɨɳɧɨɫɬɶ 1 ȼɬ
Ɏɚɪɚɞ ɪɚɜɟɧ ɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɟɦɤɨɫɬɢ ɤɨɧɞɟɧɫɚɬɨɪɚ, ɩɪɢ ɤɨɬɨɪɨɣ
ɡɚɪɹɞ 1 Ʉɥ ɫɨɡɞɚɟɬ ɧɚ ɤɨɧɞɟɧɫɚɬɨɪɟ
ɧɚɩɪɹɠɟɧɢɟ 1 ȼ
Ɍɟɫɥɚ ɪɚɜɟɧ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ,
ɩɪɢ ɤɨɬɨɪɨɣ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ
ɫɤɜɨɡɶ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ
ɩɥɨɳɚɞɶɸ 1 ɦ
2
ɪɚɜɟɧ 1 ȼɛ
ȼɟɛɟɪ ɪɚɜɟɧ ɦɚɝɧɢɬɧɨɦɭ ɩɨɬɨɤɭ,
ɩɪɢ ɭɛɵɜɚɧɢɢ ɤɨɬɨɪɨɝɨ ɞɨ ɧɭɥɹ
ɜ ɫɰɟɩɥɟɧɧɨɣ ɫ ɧɢɦ ɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɰɟɩɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ 1 Ɉɦ ɱɟɪɟɡ
ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɩɪɨɜɨɞɧɢɤɚ
ɩɪɨɯɨɞɢɬ ɤɨɥɢɱɟɫɬɜɨ ɷɥɟɤɬɪɢɱɟɫɬɜɚ
1 Ʉɥ
Ƚɟɧɪɢ ɪɚɜɟɧ ɢɧɞɭɤɬɢɜɧɨɫɬɢ
ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɢ, ɫ ɤɨɬɨɪɨɣ ɩɪɢ
ɫɢɥɟ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɜ ɧɟɣ 1 Ⱥ
ɫɰɟɩɥɹɟɬɫɹ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ 1 ȼɛ
Ɉɦ ɪɚɜɟɧ ɷɥɟɤɬɪɢɱɟɫɤɨɦɭ
ɫɨɩɪɨɬɢɜɥɟɧɢɸ ɭɱɚɫɬɤɚ ɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɰɟɩɢ, ɩɪɢ ɤɨɬɨɪɨɦ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ
ɫɢɥɨɣ 1 Ⱥ ɜɵɡɵɜɚɟɬ ɩɚɞɟɧɢɟ
ɧɚɩɪɹɠɟɧɢɹ 1 ȼ
191
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r
>
@
ɗɥɟɦɟɧɬɵ ɜɟɤɬɨɪ
ȼɟɤɬɨɪɧɨɟ ɩɨɥɟ
ȿɫɥɢ ɤɚɠɞɨɣ ɬɨɱɤɟ Ɇ ɫɬɚɜɢɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɟ ɜɟɤɬɨ
ɩɨɥɟ
ɦɚɝɧɢɬɧɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ). ȼ ɞɟɤɚɪɬɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ
ɝɞɟ r– ɪɚɞɢɭɫ-ɜɟɤɬɨɪ. Ʉɨɦɩɨɧɟɧɬɵ Ax, Ay, Az ɨɛɪɚɡɭɸɬ ɬɪɢ ɫɤɚɥɹɪɧɵɯ ɩɨɥɹ ɢ ɨɞɧɨɡɧɚɱɧɨ
ɫɥɟɞɭɸɳɭɸ ɩɪɨɢɡɜɨɞɧɭɸ ɩɨ ɨɛɴɟɦɭ ɩɨɥɹ ɜ ɬɨɱɤɟ
ɧɨɫɬɶ
ɜɟɤɬɨɪɧɨɟ ɩɨɥɟ
ɧɚɡɵɜɚɸɬ ɫɥɟɞɭɸɳɭɸ ɩɪɨɢɡɜɨɞɧɭɸ ɩɨ ɨɛɴɟɦɭ ɩɨɥɹ ɜ ɬɨɱɤɟ Ɇ:
)M(A (ɧɚɩɪɢɦɟɪ, ɩɨɥɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ, ɝɪɚɜɢɬɚɰɢɨɧɧɨɟ ɩɨɥɟ, ɩɨɥɟ
ɨɩɪɟɞɟɥɹɸɬ
Ⱦɢɜɟɪɝɟɧɰɢɹ ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ
Ⱦɢɜɟɪɝɟɧɰɢɟɣ ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ )M(A (ɨɛɨɡɧɚɱɚɟɬɫɹ
ȼɟɥɢɱɢɧɚ
S, ɤɨɬɨɪɚɹ ɨɤɪɭɠɚɟɬ ɬɨɱɤɭ Ɇ ɢ ɨɯɜɚɬɵɜɚɟɬ ɨɛɥɚɫɬɶ G ɫ ɨɛɴɟɦɨɦ V.
Ⱦɢɜɟɪɝɟɧɰɢɹ
, ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɢɫɬɨɱɧɢɤɚɦɢ ɩɨɥɹ, ɚ ɬɟ, ɜ ɤɨɬɨɪɵɯ
0!Adiv
Ɋɨɬɨɪ ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ
Ɋɨɬɨɪɨɦ (ɜɢɯɪɟɦ) ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ )M(A (ɨɛɨɡɧɚɱɚɟɬɫɹ
)r(A – ɜɟɤɬɨɪɧɭɸ ɮɭɧɤɰɢɸ ɜɟɤɬɨɪɧɨɝɨ ɚɪɝɭɦɟɧɬɚ.
SdA ɟɫɬɶ ɫɤɚɥɹɪɧɵɣ ɩɨɬɨɤ ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɡɚɦɤɧɭɬɭɸ ɩɨɜɟɪɯ-
³
S
ɟɫɬɶ ɦɟɪɚ ɢɫɬɨɱɧɢɤɨɜ ɩɨɥɹ )M(A . ȿɫɥɢ ɜ ɨɛɥɚɫɬɢ G
Adiv
)M(A ɧɚɡɵɜɚɟɬɫɹ ɫɜɨɛɨɞɧɵɦ ɨɬ ɢɫɬɨɱɧɢɤɨɜ. Ɍɟ ɬɨɱɤɢ ɩɨɥɹ, ɜ ɤɨɬɨɪɵɯ
ɧɨɣ ɚɥɝɟɛɪɵ
lim)M(Adiv
V
o 0
³
S
lim)M(Arot
o
0
V
Ɇ:
³
S
ɪ A , ɬɨ ɝɨɜɨɪɹɬ ɨ ɜɟɤɬɨɪɧɨɦ
zyx
A
w
Adiv {
{
w
SdA
.
V
– ɫɬɨɤɚɦɢ ɩɨɥɹ.
0Adiv
)M(Arot {
{
Sd,A
.
V
,k)z,y,x(Aj)z,y,x(Ai)z,y,x(A)r(A)z,y,x(AA
) ɧɚɡɵɜɚɸɬ
A
w
º
ª
»
«
r
w
¼
¬
, ɬɨ
0 Adiv
>@
A,A,
)
Ɍɟɨɪɟɦɚ ɋɬɨɤɫɚ
ɐɢɪɤɭɥɹɰɢɹ ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ )M(A ɩɨ ɡɚɦɤɧɭɬɨɣ ɤɪɢɜɨɣ L ɪɚɜɧɚ ɩɨɬɨɤɭ ɪɨɬɨɪɚ
ɷɬɨɝɨ ɩɨɥɹ ɱɟɪɟɡ ɩɨɜɟɪɯɧɨɫɬɶ
Ɏɨɪɦɭɥɚ Ƚɚɭɫɫɚ – Ɉɫɬɪɨɝɪɚɞɫɤɨɝɨ
Ⱦɥɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɨɛɥɚɫɬɢ G, ɨɝɪɚɧɢɱɟɧɧɨɣ ɡɚɦɤɧɭɬɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ S,
S, ɨɩɢɪɚɸɳɭɸɫɹ ɧɚ ɤɪɢɜɭɸ L:
³³
LS
³³³ ³³
GS
192
.SdArotrdA
.SdAdVAdiv
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Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɵ ɢ ɮɨɪɦɭɥɵ ɤɥɚɫɫɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɢ
1. Ɂɚɤɨɧ Ʉɭɥɨɧɚ
1rqq
21
0
F
q
1rq
SH
0
n
¦
i
1
1
SH
0
EE
l qp E.
dlEldE
n
A
0
.
i
1
q
q
r
2
.
2
.
1
H
0
f
0
.
.
n
qdSESdE
¦
i
i
1
.
0
.
ɨ ɡɚɪɹɞɚ q
ɹɞɚ q
.
F
4
ʌİ
2. ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ
E
3. ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɬɨɱɟɱɧɨɝɨ ɡɚɪ
E
4
4. ɉɪɢɧɰɢɩ ɫɭ
ɩɟɪɩɨɡɢɰɢɢ ɩɨɥɟɣ
5. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɞɢɩɨɥɹ
6. Ɍɟɨɪɟɦɚ Ƚɚɭ
ɫɫɚ ɞɥɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ
³³
SS
n
7. ɐɢɪɤɭɥɹɰɢɹ ɜɟɤɬɨɪɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɞɨɥɶ ɡɚɦɤɧ
ɤɨɧɬɭɪɚ
L
³³
8. ɉɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ
9. ɉɨɬɟɧɰɢɚɥ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɬɨɱɟɱɧɨɝ
LL
U
M
q
0
M
4
ɭɬɨɝɨ
10. ɋɜɹɡɶ ɦɟɠɞɭ ɩɨɬɟɧɰɢɚɥɨɦ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɢ ɟɝɨ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ
M
gradE .
11. ɋɜɹɡɶ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɦɟɳ
ɟɧɢɹ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɫɬɚ-
ɬɢɱɟɫɤɨɝɨ ɩɨɥɹ
.
ED
HH
0
12. Ɍɟɨɪɟɦɚ Ƚɚɭ
13. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɟɦɤɨɫɬɶ ɭ
ɫɫɚ ɞɥɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɞɢɷɥɟɤɬɪɢɤɟ
n
qdSDSdD
.
³³
SS
¦
n
i
i
1
ɟɞɢɧɟɧɧɨɝɨ ɩɪɨɜɨɞɧɢɤɚ
q
.
C
M
193
14. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɟɦɤɨɫɬɶ ɩɥɨɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ
H
H
HSH
S
S
l
d E
,
A
S
0
C
.
d
15. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɟɦɤɨɫɬɶ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ
l
2
C
16. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɟɦɤɨɫɬɶ ɫɮɟɪɢɱɟɫɤ
C
17. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɟɦɤɨɫɬɶ ɩɚɪɚɥɥɟɥɶɧ
18. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɟɦɤɨɫɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɟɞɢ
19. ɗɧɟɪɝɢɹ ɡɚɪɹɠɟɧɧɨɝɨ ɭɟɞɢɧ
ɟɧɧɨɝɨ ɩɪɨɜɨɞɧɢɤɚ
W
0
.
)r/rln(
12
ɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ
rr
12
4
HSH
0
.
rr
12
ɨ ɫɨɟɞɢɧɟɧɧɵɯ ɤɨɧɞɟɧɫɚɬɨɪɨɜ
n
Cɋ
.
¦
i
i
1
ɧɟɧɧɵɯ ɤɨɧɞɟɧɫɚɬɨɪɨɜ
n
11
.
¦
Cɋ
i
i
1
22
MM
qqC
.
C
222
20. ɗɧɟɪɝɢɹ ɡɚɪɹɠɟɧɧɨɝɨ ɤɨɧɞɟɧɫɚɬɨɪɚ
22
M'M'
W
qqC
.
C
222
21. Ɉɛɴɟɦɧɚɹ ɩɥɨɬɧɨɫɬɶ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ
2
E
HH
W
Z
V
ED
0
.
22
22. ɋɢɥɚ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɩɪɨɜɨɞɢɦɨɫɬɢ
dq
.
I
dt
23. ɉɥɨɬɧɨɫɬɶ ɬɨɤɚ ɩɪɨɜɨɞɢɦɨɫɬɢ
dI
.
j ,vnej
d
24. ɗɥɟɤɬɪɨɞɜɢɠɭɳɚɹ ɫɢɥɚ, ɞɟɣɫɬɜ
ɭɸɳɚɹ ɜ ɰɟɩɢ,
ɫɬ.
H
q
0
H
l.
³
ɫɬ.
25. ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɞɧɨɪɨɞɧɨɝɨ ɥɢɧɟɣɧɨɝɨ ɩɪɨɜɨɞɧɢɤɚ
l
.
R
U
26. ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɵɯ ɩɪɨɜɨɞɧɢɤɨɜ
n
RR
.
¦
i
i
1
27. ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɚɪɚɥɥɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɵɯ ɩɪɨɜɨɞɧɢɤɨɜ
n
11
.
¦
RR
i
i
1
194
28. ɗɥɟɤɬɪɢɱɟɫɤɨɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɭɱɚɫɬɤɟ ɰɟɩɢ
r
R
H
knkmk
P
P
P
P
P
P
MMH
U
, l
d EEU
,
Ⱥ
A
U
ɤɭɥ.ɫɬ.
q
0
29. Ɂɚɤɨɧ Ɉɦɚ ɞɥɹ ɨɞɧɨɪɨɞɧɨɝɨ ɭɱɚɫɬ
2
³
ɫɬ.
1
ɤɚ ɰɟɩɢ
I
R
MM
U
21
.
R
2 1
30. Ɂɚɤɨɧ Ɉɦɚ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɟ
EjJ .
31. Ɇɨɳɧɨɫɬɶ ɩɨɫɬɨɹɧɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ
2
dA
P
dt
2
RIUI
U
.
R
32. Ɂɚɤɨɧ Ⱦɠɨɭɥɹ – Ʌɟɧɰɚ
2
U
33. Ɂɚɤɨɧ Ⱦɠɨɭ
2
RdtIUIdtdQ
ɥɹ – Ʌɟɧɰɚ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɟ
.
R
2
EjEJZ .
dt
34. Ɂɚɤɨɧ Ɉɦɚ ɜ ɢɧɬɟɝɪɚɥɶɧɨɣ ɮɨɪɦɟ (ɞɥɹ ɧɟɨɞɧɨɪɨɞɧɨɝɨ ɭɱɚɫɬɤɚ ɰɟɩɢ
MMH
21
.
rRI
35. Ɂɚɤɨɧ Ɉɦɚ ɞɥɹ ɡɚɦɤɧɭɬɨɝɨ ɭɱɚɫɬɤɚ ɰɟɩɢ
I
.
36. ɉɪɚɜɢɥɚ Ʉɢɪɯɝɨɮɚ
n
¦¦¦
111
37. ȼɪɚɳɚɸɳɢɣ ɦɨɦɟɧɬ, ɞɟɣɫɬɜɭ
0
ɸɳɢɣ ɧɚ ɪɚɦɤɭ ɫ ɬɨɤɨɦ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ,
>@
H
RI ;I
.
kkkk
.
D
sinBpM ,BpM
mm
38. Ɇɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɪɚɦɤɢ ɫ ɬɨɤɨɦ
nISpm .
39. ɋɜɹɡɶ ɦɟɠɞɭ ɢɧɞɭ
ɤɰɢɟɣ ɢ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
.
HB
PP
0
40. Ɂɚɤɨɧ Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ
I
0
Bd
>@
.
rld
3
r
4
S
41. ɂɧɞɭɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɪɹɦɨɝɨ ɬɨɤɚ
I
0
.
B
a
S
2
42. ɂɧɞɭɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɰɟɧɬɪɟ ɤɪɭ
B
ɝɨɜɨɝɨ ɜɢɬɤɚ ɫ ɬɨɤɨɦ
I
0
.
2
R
)
195
43. ɋɢɥɚ Ʌɨɪɟɧɰɚ
>
@
)
t
(
,
LCdtq d
M
Z
>@
D
sinqvBF ,BvqF .
44. Ɂɚɤɨɧ Ⱥɦɩɟɪɚ
sinIBdldF ,BldIFd .
45. ɐɢɪɤɭɥɹɰɢɹ ɜɟɤɬɨɪɚ ɢɧɞɭ
L (ɡɚɤɨɧ ɩɨɥɧɨɝɨ ɬɨɤɚ)
ɬɭɪɚ
46. Ɍɟɨɪɟɦɚ Ƚɚɭ
ɫɫɚ ɞɥɹ ɩɨɬɨɤɚ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
47. Ɂɚɤɨɧ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭ
48. ɗȾɋ ɫɚɦɨɢɧɞɭ
ɤɰɢɢ
49. ɂɧɞɭɤɬɢɜɧɨɫɬɶ ɞɥɢɧɧɨɝɨ ɫɨɥɟɧɨɢ
ɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ ɜɞɨɥɶ ɡɚɦɤɧɭɬɨɝɨ ɤɨɧ-
n
IdlBldB
P
³³
LL
n
³³
SS
0
dSBSdB 0.
n
¦
1
k
ɤɰɢɢ
dɎ
.
H
i
dt
dI
.
L
H
s
dt
ɞɚ
2
SN
PP
.
L
0
l
50. ɗɧɟɪɝɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɫɜɹɡɚɧɧɨɝɨ ɫ ɤɨɧɬɭɪɨɦ
2
LI
W
.
2
51. Ɉɛɴɟɦɧɚɹ ɩɥɨɬɧɨɫɬɶ ɷɧɟɪɝɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
2
PP
H
W
Z
0
V
BH
22
D
.
k
,
.
52. ɉɨɥɧɚɹ ɫɢɫɬɟɦɚ ɭ
ɪɚɜɧɟɧɢɣ Ɇɚɤɫɜɟɥɥɚ ɜ ɢɧɬɟɝɪɚɥɶɧɨɣ ɮɨɪɦɟ
w
B
ldE
³³
LS
³³
LS
³³
SV
³
S
;Sd
w
t
§
¨
¨
©
0
·
w
D
¸
jldH
U
;Sd
¸
w
t
¹
;dVSdD
,SdB
ɝɞɟ
.Ej ,HB ,ED
JPPHH
53. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭ
00
ɪɚɜɧɟɧɢɟ ɫɜɨɛɨɞɧɵɯ ɧɟɡɚɬɭɯɚɸɳɢɯ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨ-
ɥɟɛɚɧɢɣ ɢ ɟɝɨ ɪɟɲɟɧɢɟ
2
1
2
0
q q
q
cos
m
0
196
54. Ɏɨɪɦɭɥɚ Ɍɨɦɫɨɧɚ
Z
C
Z
).t
(
A
, t
L U
LCdt
L Rdtq d
MZZ
Z GGZ Z
L /UA ,
LCT
S
2 .
55. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭ
ɪɚɜɧɟɧɢɟ ɫɜɨɛɨɞɧɵɯ ɡɚɬɭɯɚɸɳɢɯ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟ-
ɛɚɧɢɣ ɢ ɟɝɨ ɪɟɲɟɧɢɟ
2
qd
2
dt
56. Ʌɨɝɚɪɢɮɦɢɱɟɫɤɢɣ ɞɟɤ
R
1
0
LCdtdqL
t
G
m
)tcos(eqq ,q
MZ
.
ɪɟɦɟɧɬ ɡɚɬɭɯɚɧɢɹ ɤɨɥɟɛɚɧɢɣ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɤɨɥɟɛɚɬɟɥɶ-
ɧɨɦ ɤɨɧɬɭɪɟ
57. Ⱦɨɛɪɨɬɧɨɫɬɶ ɤɨɥɟɛɚɬɟɥ
R
T
GT
2
ɶɧɨɝɨ ɤɨɧɬɭɪɚ
S
Q
G
2
S
L
1
LC
1
|
.
2
R
2
L
4
.
CLRT
58. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɜɵɧɭɠɞɟɧɧɵɯ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ
ɢ ɟɝɨ ɪɟɲɟɧɢɟ ɞɥɹ ɭɫɬɚɧɨɜɢɜɲɢɯɫɹ ɤɨɥɟɛɚɧɢɣ
2
dq
2
1
m
cos
q
cos
q
59. Ⱥɦɩɥɢɬɭɞɚ ɜɵɧɭ
ɠɞɟɧɧɵɯ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ
U
A
L
m
2
22
0
.
22
4
ZGZZ
60. Ɋɟɡɨɧɚɧɫɧɚɹ ɰɢɤɥɢɱɟɫɤɚɹ ɱɚɫɬɨɬɚ ɢ ɪɟɡɨɧɚɧɫɧɚɹ ɚɦɩɥɢɬ
2
0
61. ɂɧɞɭɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬɭ
62. ȿɦɤɨɫɬɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɤɨɧɬ
ɭɪɚ
x
2 2
ɪɚ
L
C
ɪɟɡ.ɪɟɡ.
Lx
.
1
m
G
2
0
.
63. ɉɨɥɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ
2
1
§
2
Z
¨
©
·
LRZ
.
¸
C
Z
¹
64. ɋɞɜɢɝ ɮɚɡ ɤɨɥɟɛɚɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɢ ɫɢɥɵ ɬɨɤɚ
1
Z
L
Z
M
tg
C
R
UU
CL
.
U
R
65. Ɂɚɤɨɧ Ɉɦɚ ɞɥɹ ɰɟɩɢ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ
U
I
Z
U
m
.
I ,
m
Z
197
ɭɞɚ
.
2 2
66. ɋɪɟɞɧɹɹ ɦɨɳɧɨɫɬɶ, ɪɚɡɜɢɜɚɟɦɚɹ ɜ ɰɟɩɢ ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɬɨɤɚ
H
I
P
¹
ᬩ
§
C L R
R
Z Z
M
)
t
(
H H )
t
(EE
MZM
Z
M
.
cos
U
67. Ʉɨɷɮɮɢɰɢɟɧɬ ɦɨɳɧɨɫɬɢ
cos
2
2
1
¸
68. Ɏɚɡɨɜɚɹ ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɜɨ
c
11
.
HPHPPH
2
11
H
w
v
.
2
22
t
w
69. ȼɨɥɧɨɜɵɟ ɭ
v
00
ɪɚɜɧɟɧɢɹ ɞɥɹ ɜɟɤɬɨɪɨɜ E ɢ
2
w
E
2
''
w
tEv
H ,
70. ɍɪɚɜɧɟɧɢɹ ɩɥɨɫɤɨɣ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɜɨɥɧɵ
cos
m
cos
m
;
kx
.kx
71. Ɉɛɴɟɦɧɚɹ ɩɥɨɬɧɨɫɬɶ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
HES .
2
HE
PPHH
0
22
72. ȼɟɤɬɨɪ ɍɦɨɜɚ –
Z
.
2
0
ɉɨɣɧɬɢɧɝɚ (ɜɟɤɬɨɪ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ)
>@
ɥɧ
198
ǛǼǴǷǺDzDZǹǴDZ 5
ɇɟɤɨɬɨɪɵɟ ɡɧɚɦɟɧɚɬɟɥɶɧɵɟ ɫɨɛɵɬɢɹ
ɢɫɬɨɪɢɢ ɪɚɡɜɢɬɢɹ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɢ
ɜ
Ƚɨɞ ɋɨɛɵɬɢɟ ɍɱɟɧɵɣ
1780
1785 Ɉɬɤɪɵɬ ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɷɥɟɤɬɪɨɫɬɚɬɢɤɢ ɒ. Ʉɭɥɨɧ
1799
1802 Ɉɬɤɪɵɬɨ ɹɜɥɟɧɢɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɞɭɝɢ ȼ. ȼ. ɉɟɬɪɨɜ
1820 Ɉɛɧɚɪɭɠɟɧɨ ɦɚɝɧɢɬɧɨɟ ɞɟɣɫɬɜɢɟ ɬɨɤɚ ɏ. ɗɪɫɬɟɞ
1820
1827 Ɉɬɤɪɵɬ ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɰɟɩɢ Ƚ. Ɉɦ
1831 Ɉɬɤɪɵɬ ɡɚɤɨɧ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ Ɇ. Ɏɚɪɚɞɟɣ
1832 Ɉɬɤɪɵɬɨ ɹɜɥɟɧɢɟ ɫɚɦɨɢɧɞɭɤɰɢɢ Ⱦ. Ƚɟɧɪɢ
1833
1841–1842
1842
1843 Ɉɬɤɪɵɬ ɡɚɤɨɧ ɷɥɟɤɬɪɨɥɢɡɚ Ɇ. Ɏɚɪɚɞɟɣ
1853
1860–1865 ɋɨɡɞɚɧɚ ɬɟɨɪɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Ⱦ. Ɇɚɤɫɜɟɥɥ
1865
1883 Ɉɬɤɪɵɬɨ ɹɜɥɟɧɢɟ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ Ɍ. ɗɞɢɫɨɧ
1887
1895
1897 Ɉɬɤɪɵɬ ɷɥɟɤɬɪɨɧ Ⱦ. Ɍɨɦɫɨɧ
1908
1911
1911 Ɉɬɤɪɵɬɨ ɹɜɥɟɧɢɟ ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ
1986
ɇɚɱɚɬɵ ɨɩɵɬɵ, ɩɪɢɜɟɞɲɢɟ ɤ ɨɬɤɪɵɬɢɸ
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ (ɨɩɵɬɵ ɨɩɢɫɚɧɵ ɜ 1791 ɝ.)
ɋɨɡɞɚɧ ɩɟɪɜɵɣ ɢɫɬɨɱɧɢɤ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ –
ɝɚɥɶɜɚɧɢɱɟɫɤɢɣ ɷɥɟɦɟɧɬ ɢ ɛɚɬɚɪɟɹ ɷɥɟɦɟɧɬɨɜ
(«ɜɨɥɶɬɨɜ ɫɬɨɥɛ»)
Ɉɬɤɪɵɬ ɡɚɤɨɧ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɬɨɤɨɜ,
ɫɨɡɞɚɧɚ ɩɟɪɜɚɹ ɬɟɨɪɢɹ ɦɚɝɧɟɬɢɡɦɚ, ɨɫɧɨɜɚɧɧɚɹ ɧɚ
ɝɢɩɨɬɟɡɟ ɦɨɥɟɤɭɥɹɪɧɵɯ ɬɨɤɨɜ
ɋɮɨɪɦɭɥɢɪɨɜɚɧɨ ɩɪɚɜɢɥɨ, ɨɩɪɟɞɟɥɹɸɳɟɟ
ɧɚɩɪɚɜɥɟɧɢɟ ɢɧɞɭɤɰɢɨɧɧɨɝɨ ɬɨɤɚ
Ɉɬɤɪɵɬ ɡɚɤɨɧ ɬɟɩɥɨɜɨɝɨ ɞɟɣɫɬɜɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ
ɬɨɤɚ
ɍɫɬɚɧɨɜɥɟɧ ɤɨɥɟɛɚɬɟɥɶɧɵɣ ɯɚɪɚɤɬɟɪ ɪɚɡɪɹɞɚ
ɤɨɧɞɟɧɫɚɬɨɪɚ
ȼɵɜɟɞɟɧɚ ɮɨɪɦɭɥɚ ɞɥɹ ɩɟɪɢɨɞɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ
ɤɨɥɟɛɚɧɢɣ
ȼɵɞɜɢɧɭɬɚ ɢɞɟɹ ɨɛ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɩɪɢɪɨɞɟ
ɫɜɟɬɚ, ɩɨɫɬɭɥɢɪɨɜɚɧɨ ɫɭɳɟɫɬɜɨɜɚɧɢɟ
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɜɨɥɧ
ɋɨɡɞɚɧ ɜɢɛɪɚɬɨɪ ɞɥɹ ɜɨɡɛɭɠɞɟɧɢɹ
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ
ɉɟɪɜɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɜɨɥɧ
ɞɥɹ ɛɟɫɩɪɨɜɨɥɨɱɧɨɣ ɫɜɹɡɢ
ɋɨɡɞɚɧ ɩɪɢɛɨɪ ɞɥɹ ɪɟɝɢɫɬɪɚɰɢɢ ɡɚɪɹɠɟɧɧɵɯ
ɱɚɫɬɢɰ
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɞɨɤɚɡɚɧɚ ɞɢɫɤɪɟɬɧɨɫɬɶ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɡɚɪɹɞɨɜ
Ɉɬɤɪɵɬɨ ɹɜɥɟɧɢɟ ɜɵɫɨɤɨɬɟɦɩɟɪɚɬɭɪɧɨɣ
ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ
Ʌ. Ƚɚɥɶɜɚɧɢ
Ⱥ. ȼɨɥɶɬɚ
Ⱥ. Ⱥɦɩɟɪ
ɗ. ɏ. Ʌɟɧɰ
Ⱦ. Ⱦɠɨɭɥɶ,
ɗ. ɏ. Ʌɟɧɰ
Ⱦ. Ƚɟɧɪɢ
ɍ. Ɍɨɦɫɨɧ
Ⱦ. Ɇɚɤɫɜɟɥɥ
Ƚ. Ƚɟɪɰ
Ⱥ. ɉɨɩɨɜ
Ƚ. Ƚɟɣɝɟɪ,
ɗ. Ɋɟɡɟɪɮɨɪɞ
Ɋ. Ɇɢɥɥɢɤɟɧ
Ƚ. Ʉɚɦɟɪɥɢɧɝ-
Ɉɧɧɟɫ
Ʉ. Ɇɸɥɥɟɪ,
Ƚ. Ȼɟɞɧɨɪɰ
199
ǛǜǑǐǔǝǗǚǎǔǑ
ǎǎǑǐǑǙǔǑ
1. ǩǗǑǖǞǜǔǣǑǝǖǚǑ ǛǚǗǑ
2. ǛǚǝǞǚǫǙǙǧǕ ǩǗǑǖǞǜǔǣǑǝǖǔǕ Ǟǚǖ
3. ǘnjǏǙǔǞǙǚǑ ǛǚǗǑ
ǝǚǐǑǜǒnjǙǔǑ
............................................................................................................................ 3
Ʉɪɚɬɤɢɟ ɜɵɜɨɞɵ………………………………………………………… ................................ 35
ȼɨɩɪɨɫɵ ɞɥɹ ɫɚɦɨɤɨɧɬɪɨɥɹ ɢ ɩɨɜɬɨɪɟɧɢɹ……………………………. ................................. 38
ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ.......................................................................... ................................. 38
Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ………………………………. .................................. 42
Ʉɪɚɬɤɢɟ ɜɵɜɨɞɵ ........................................................................................................................ 59
ȼɨɩɪɨɫɵ ɞɥɹ ɫɚɦɨɤɨɧɬɪɨɥɹ ɢ ɩɨɜɬɨɪɟɧɢɹ .............................................................................. 61
ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ........................................................................................................... 62
Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ
.................................................................................................................................... 4
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1.1. ɂɫɯɨɞɧɵɟ ɩɨɥɨɠɟɧɢɹ. Ɉɫɧɨɜɧɵɟ ɩɨɧɹɬɢɹ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ....................................... 7
1.2. Ɉɫɧɨɜɧɨɣ ɡɚɤɨɧ ɷɥɟɤɬɪɨɫɬɚɬɢɤɢ…………………………….. .................................... 9
1.3. ɗɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ. ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ………... ...................................... 10
1.4. ɐɢɪɤɭɥɹɰɢɹ ɜɟɤɬɨɪɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ.
ɉɨɬɟɧɰɢɚɥ ɩɨɥɹ ........................................................................................................... 14
1.5. ɋɜɹɡɶ ɦɟɠɞɭ ɫɢɥɨɜɨɣ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ
ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ .......................................................................................... 17
1.6. Ɍɟɨɪɟɦɚ Ƚɚɭɫɫɚ ɞɥɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ ...................................... 19
1.7. Ⱦɢɷɥɟɤɬɪɢɤɢ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ. Ɍɟɨɪɟɦɚ Ƚɚɭɫɫɚ
ɞɥɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɞɢɷɥɟɤɬɪɢɤɟ .......................................................... 21
1.8.
ɉɪɨɜɨɞɧɢɤɢ ɜ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɦ ɩɨɥɟ. Ʉɨɧɞɟɧɫɚɬɨɪɵ .......................................
1.9. ɗɧɟɪɝɢɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ……………………….... ................................... 33
......................... ...................................................... 45
2.1. ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɢ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ………………... ..................................... 45
2.2. Ɂɚɤɨɧ Ɉɦɚ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɮɨɪɦɟ………………….. ..................................... 47
2.3. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɢ ɩɚɪɚɥɥɟɥɶɧɨɟ ɫɨɟɞɢɧɟɧɢɟ ɩɪɨɜɨɞɧɢɤɨɜ.
ɗɥɟɤɬɪɨɢɡɦɟɪɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ. ............................................................................. 50
2.4. Ɋɚɛɨɬɚ ɢ ɦɨɳɧɨɫɬɶ ɬɨɤɚ. Ɂɚɤɨɧ Ⱦɠɨɭɥɹ – Ʌɟɧɰɚ .................................................... 54
2.5. Ɂɚɤɨɧ Ɉɦɚ ɜ ɢɧɬɟɝɪɚɥɶɧɨɣ ɮɨɪɦɟ ............................................................................. 56
2.6. Ɋɚɫɱɟɬ ɪɚɡɜɟɬɜɥɟɧɧɵɯ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ....................................................... 57
ɪɟɲɟɧɢɹ ...................................................................................
28
65
3.1. Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɢ ɟɝɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ..................................................................... 69
3.2. Ɂɚɤɨɧ Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ .................................................................................. 72
3.3. Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɞɜɢɠɭɳɟɝɨɫɹ ɡɚɪɹɞɚ. ɋɢɥɚ Ʌɨɪɟɧɰɚ............................................. 74
3.4. ɉɪɨɜɨɞɧɢɤ ɫ ɬɨɤɨɦ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ. Ɂɚɤɨɧ Ⱥɦɩɟɪɚ.. .......................................... 76
3.5. ɐɢɪɤɭɥɹɰɢɹ ɜɟɤɬɨɪɚ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ.. ................................ 78
3.6. Ɍɟɨɪɟɦɚ Ƚɚɭɫɫɚ ɞɥɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ ..................................................... 79
3.7. Ɇɚɝɧɢɬɧɵɟ ɫɜɨɣɫɬɜɚ ɜɟɳɟɫɬɜɚ .................................................................................. 81
Ʉɪɚɬɤɢɟ ɜɵɜɨɞɵ ........................................................................................................................ 85
ȼɨɩɪɨɫɵ ɞɥɹ ɫɚɦɨɤɨɧɬɪɨɥɹ ɢ ɩɨɜɬɨɪɟɧɢɹ
ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ...........................................................................................................
Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ ................................................................................... 90
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