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Ƚɥɚɜɚ 1. Ɉɫɧɨɜɵɬɟɨɪɢɢɪɚɫɱɟɬɚɢɡɝɢɛɚɟɦɵɯɩɥɚɫɬɢɧ
2
w
w
Q
DH
ww
yx
)1()1(
CD
2
S
3
2
SQ
coscos
YX
ba
0
803
2
bq
YX
ɉɨɤɚɠɟɦɢɡɦɟɧɟɧɢɟɢɧɬɟɧɫɢɜɧɨɫɬɢɪɚɫɩɪɟɞɟɥɟɧɧɨɣɧɚɝɪɭɡ-
ɤɢq ɜɞɨɥɶɨɫɟɣɫɢɦɦɟɬɪɢɢɩɥɚɫɬɢɧɵɇɚɨɫɢɫɢɦɦɟɬɪɢɢ x = a/2 ɩɨɥɭ
ɱɢɦ
0
3b/4; bɇɚɨɫɢɫɢɦɦɟɬɪɢɢy=bɢɦɟɟɦ
ɡɧɚɱɟɧɢɹ q ɜɵɱɢɫɥɹɟɦ ɩɪɢ y = 0; b/4; b/2;
)/3(sin
byqq S
ɡɧɚɱɟɧɢɹ
)/(sin
0
axqq S
q ɜɵɱɢɫɥɹɟɦɩɪɢ x = 0; a/4; a/2; 3a/4; aɏɚɪɚɤɬɟɪɢɡɦɟɧɟɧɢɹɩɨɩɟ
ɪɟɱɧɨɣɧɚɝɪɭɡɤɢɩɪɢɜɨɞɢɬɫɹɧɚɪɢɫ 1.11.
5. ɋɬɪɨɢɦ ɷɩɸɪɵɢɡɝɢɛɚɸɳɢɯɦɨɦɟɧɬɨɜɩɨɨɫɹɦɫɢɦɦɟɬɪɢɢ
(x = aɢy=bɷɩɸɪɵɤɪɭɬɹɳɢɯɦɨɦɟɧɬɨɜɩɨɝɪɚɧɹɦ x = ɢy=0.
ɉɨɞɫɬɚɜɥɹɹɚɛɫɰɢɫɫɭ x = a/2 ɩɪɢɷɬɨɦVLQ X=1) ɜɜɵɪɚɠɟɧɢɹ
ɞɥɹ M
ɢMy, ɚ x = 0(cosY=1) ɜɜɵɪɚɠɟɧɢɟɞɥɹH, ɩɨɥɭɱɢɦ
x
2
bq
0
S
3
y
sin
5,93
;
H
b
Ɇ
2
bq
0
286
sin
S
3
y
;
Ɇ
b
yx
bq
0
803
2
S
3
y
cos
.
b
Ɋɟɡɭɥɶɬɚɬɵɜɵɱɢɫɥɟɧɢɣɩɪɢɜɟɞɟɧɵɜɬɚɛɥɢ
Ɍɚɛɥɢɰɚ
ȼɵɱɢɫɥɟɧɢɟɨɪɞɢɧɚɬɷɩɸɪM
y VLQʌy/b)cosʌy/b) M
001001,25Â10
b/4 0,707 –0,707 –2,47 Â10–3–7,56 Â10–3–0,88 Â10
b/2 –1 0 3,5 Â10
3b/4 0,707 0,707 –2,47 Â10–3–7,56 Â10
b 0 –1 0 0 –1,25 Â10
, MyɢH ɜɫɟɱɟɧɢɹɯɩɚɪɚɥɥɟɥɶɧɵɯɨɫɢy
x
(q0b2) My(q0b2) H (q0b2)
x
–3
10,7 Â10
–3
–3
0
0,88 Â10
–3
–3
–3
–3
.coscos
ɉɨɞɫɬɚɜɥɹɹ y= b /2 (sin Y=–1) ɜɜɵɪɚɠɟɧɢɹɞɥɹ M
(cos Y= 1) ɜɜɵɪɚɠɟɧɢɟɞɥɹ H, ɩɨɥɭɱɢɦ
2
bq
0
yx
x
S
5,93
;sin
a
Ɇ
2
bq
0
286
x
S
;sin
Ɇ
a
ɗɩɸɪɵ Mx, MyɢH ɩɪɢɜɟɞɟɧɵɧɚɪɢɫ 1.11.
31
ɢMy, ɚ y= 0
x
2
bq
0
H
803
x
S
.cos
a
ȺȺɅɭɤɚɲɟɜɢɱɌɟɨɪɢɹɪɚɫɱɟɬɚɩɥɚɫɬɢɧɢɨɛɨɥɨɱɟɤ
ȼɵɱɢɫɥɟɧɢɟɨɪɞɢɧɚɬɷɩɸɪM
, MyɢH ɜɫɟɱɟɧɢɹɯɩɚɪɚɥɥɟɥɶɧɵɯɨɫɢx
x
Ɍɚɛɥɢɰɚ2
X sin(ʌx/a)cosʌx/a) M
(q0b2) My(q0b2) H (q0b2)
x
001001,25Â10
a/4 0,707 0,707 2,47 Â10
a/2 1 0 3,5 Â10
3a/4 0,707 –0,707 2,47Â10
–3
–3
–3
7,56 Â10
10,7 Â10
7,56 Â10
–3
–3
–3
a 0 –1 0 0 –1,25 Â10
q
0
0,707q
0
0,707q
0
0
7,56
0,88 1,25
b/2
0,707q
0
y
1,25 0,88
0,707q
a/2 a/2
2,47 3,5 2,47
7,56
10,7
x
0
2,47
b/2
2,47
3,5
0
(10–3q0b2) My(10–3q0b2) H (10–3q0b2)
M
x
7,56 0
7,56
0 10,7
Mx(10–3q0b2)
M
(10–3q0b2)
y
–3
q0b2)
H (10
0,88 Â10
0
–0,88 Â10
0,88
0 0,88
1,25
–3
–3
–3
–3
1,25
Ɋɢɫ Ɋɟɡɭɥɶɬɚɬɵɪɟɲɟɧɢɹɨɛɪɚɬɧɨɣɡɚɞɚɱɢɢɡɝɢɛɚɩɥɚɫɬɢɧɵ
1.3.3. Ɉɪɚɫɱɟɬɟ ɨɪɬɨɬɪɨɩɧɵɯɩɥɚɫɬɢɧɢɩɥɚɫɬɢɧ
ɧɚɭɩɪɭɝɨɦɨɫɧɨɜɚɧɢɢ
Ɉɪɬɨɬɪɨɩɧɨɣ ɩɥɚɫɬɢɧɨɣ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɚɡɵɜɚɟɬɫɹ ɩɥɚ
ɫɬɢɧɚ ɠɟɫɬɤɨɫɬɧɵɟ ɫɜɨɣɫɬɜɚ ɤɨɬɨɪɨɣ ɧɟɨɞɢɧɚɤɨɜɵ ɩɨ ɧɚɩɪɚɜɥɟ
ɧɢɹɦɤɨɨɪɞɢɧɚɬɧɵɯɨɫɟɣ x ɢ y.
ȼ ɱɚɫɬɧɨɫɬɢ ɤ ɬɚɤɢɦ ɩɥɚɫɬɢɧɚɦ ɨɬɧɨɫɹɬɫɹ ɩɥɚɫɬɢɧɵ ɢɡɝɨ
ɬɨɜɥɟɧɧɵɟɢɡɨɪɬɨɬɪɨɩɧɨɝɨɦɚɬɟɪɢɚɥɚɩɪɢɷɬɨɦɡɚɤɨɧȽɭɤɚɜɵɪɚ
ɠɚɟɬɫɹɫɥɟɞɭɸɳɢɦɢɡɚɜɢɫɢɦɨɫɬɹɦɢ
32
Ƚɥɚɜɚ 1. Ɉɫɧɨɜɵɬɟɨɪɢɢɪɚɫɱɟɬɚɢɡɝɢɛɚɟɦɵɯɩɥɚɫɬɢɧ
W
xy
J
xy
,;;
EEEEE
x
ɝɞɟ
V
H
x
EE
Q Q
y
yxxxy
V
x
x
y
Q
y
ȿɫɥɢ ɩɨɜɬɨɪɢɬɶ ɜɫɟ ɪɚɫɫɭɠɞɟɧɢɹ ɩɪɢɜɟɞɟɧɧɵɟ
V
y
H
y
y
V
x
Q
yxxy
x
ɞɥɹ ɢɡɨɬɪɨɩɧɵɯ ɩɥɚɫɬɢɧ ɬɨ ɜɦɟɫɬɨ ɩɪɢɞɟɦ ɤ ɫɥɟɞɭɸɳɢɦ
ɫɨɨɬɧɨɲɟɧɢɹɦɞɥɹɦɨɦɟɧɬɨɜ>2, 16]:
2
§
w
w
¨
DɆ
1
2
¨
w
x
©
2
§
w
w
¨
DɆ
2
2
¨
w
y
©
2
·
w
w
Q
Q
¸
xyx
yxy
;
2
¸
w
y
¹
2
·
w
w
¸
;
2
¸
w
x
¹
2
w
w
(1.42)
DH
F
.
yx
ww
Ɂɞɟɫɶ ɜɜɟɞɟɧɵɨɛɨɡɧɚɱɟɧɢɹɠɟɫɬɤɨɫɬɟɣ
3
hE
D
1
x
;
D
2
)1(12
QQ
3
hE
y
;
D
F
)1(12
QQ
yxxyyxxy
3
hG
.
12
Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɢɡɝɢɛɚ ɚɧɚɥɨɝɢɱɧɨɟ ɭɪɚɜɧɟ
ɧɢɸɛɭɞɟɬɢɦɟɬɶɜɢɞ
4
w
w
D
2
4
y
w
(1.43)
yxq
,),(2
ɝɞɟ
4
w
w
D
1
4
x
w
4
w
w
D
3
213
yxxy
22
yx
ww
.22
Q Q DDDDD
FF
Ⱦɥɹɪɟɲɟɧɢɹɭɪɚɜɧɟɧɢɹɩɪɢɦɟɧɢɦɵɬɟɠɟɫɩɨɫɨɛɵ, ɱɬɨ
ɢɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɢɡɝɢɛɚ ɢɡɨɬɪɨɩɧɵɯ ɩɥɚɫɬɢɧ Ɍɚɤ ɩɪɢ ɡɚɞɚ
ɧɢɢɩɨɜɟɪɯɧɨɫɬɢɩɪɨɝɢɛɨɜɜɮɨɪɦɟɩɨɫɬɨɹɧɧɚɹ
q
ɋ
§
m
4
D
¨
1
4
a
©
0
4
D
2
22
nm
S
3
D
22
ba
.
4
·
n
¸
2
4
b
¹
Ɂɚɦɟɬɢɦɱɬɨɢɧɨɝɞɚɞɥɹɭɩɪɨɳɟɧɢɹɪɟɲɟɧɢɹ ɡɚɞɚɱɢɩɪɢɛɥɢ
ɠɟɧɧɨɩɪɢɧɢɦɚɸɬ
ȼɷɬɨɦɫɥɭɱɚɟɤɚɤɦɨɠɧɨɭɫɬɚɧɨ
DDD
213
ɜɢɬɶɭɪɚɜɧɟɧɢɟ ɩɪɢɜɨɞɢɬɫɹ ɤɨɛɵɱɧɨɦɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨ
ɦɭɭɪɚɜɧɟɧɢɸɞɥɹɢɡɨɬɪɨɩɧɨɣɩɥɚɫɬɢɧɵ
4
w
w
4
x
w
4
w
w
ww
4
q
w
w
4
212
y
yx
w
1
33
(1.44)
,2
D
1
ȺȺɅɭɤɚɲɟɜɢɱɌɟɨɪɢɹɪɚɫɱɟɬɚɩɥɚɫɬɢɧɢɨɛɨɥɨɱɟɤ
ɝɞɟɩɪɢɜɟɞɟɧɧɚɹ ɩɟɪɟɦɟɧɧɚɹ
4
Ɋɟɲɟɧɢɟɷɬɨɝɨɭɪɚɜɧɟ
DDyy
.
211
ɧɢɹɩɪɨɢɡɜɨɞɢɬɫɹɬɚɤɠɟɤɚɤɞɥɹɭɫɥɨɜɧɨɣ ɢɡɨɬɪɨɩɧɨɣ ɩɥɚɫɬɢɧɵ
ɭɤɨɬɨɪɨɣɜɦɟɫɬɨɞɥɢɧɵɫɬɨɪɨɧɵ b ɩɪɢɧɹɬɪɚɡɦɟɪ
4
.
DDbb
211
Ɋɚɫɫɦɨɬɪɢɦɬɟɩɟɪɶɤɨɧɫɬɪɭɤɬɢɜɧɨɨɪɬɨɬɪɨɩɧɭɸɩɥɚɫɬɢɧɭ.
Ɍɚɤ ɧɚɡɵɜɚɟɬɫɹ ɢɡɨɬɪɨɩɧɚɹ ɩɥɚɫɬɢɧɚ ɭɫɢɥɟɧɧɚɹɪɟɛɪɚɦɢ ɠɟɫɬɤɨ
ɫɬɢɤɚɤɜɨɞɧɨɦɬɚɤɢɜɞɪɭɝɨɦɧɚɩɪɚɜɥɟɧɢɹɯ ɪɢɫ Ɍɚɤɚɹ
ɪɟɛɪɢɫɬɚɹɩɪɹɦɨɭɝɨɥɶɧɚɹ ɩɥɚɫɬɢɧɚɪɟɛɪɚɤɨɬɨɪɨɣɩɚɪɚɥɥɟɥɶɧɵɟɟ
ɫɬɨɪɨɧɚɦ ɩɪɨɹɜɥɹɟɬ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɪɚɡɥɢɱɧɵɟ ɠɟɫɬɤɨɫɬɧɵɟ ɯɚ
ɪɚɤɬɟɪɢɫɬɢɤɢɜɧɚɩɪɚɜɥɟɧɢɹɯx ɢy. ȿɟɪɚɫɱɟɬɦɨɠɧɨɩɪɢɛɥɢɠɟɧɧɨ
ɜɵɩɨɥɧɢɬɶ ɤɚɤ ɪɚɫɱɟɬ ɭɫɥɨɜɧɨɣ ɨɪɬɨɬɪɨɩɧɨɣ ɩɥɚɫɬɢɧɵ ɫ ɠɟɫɬɤɨ
ɫɬɹɦɢ D1, D2ɢ D
, ɜɯɨɞɹɳɢɦɢɜɭɪɚɜɧɟɧɢɟ
3
b
s
1
s
1
s
s
a
2
2
y
Ɋɢɫ Ʉɨɧɫɬɪɭɤɬɢɜɧɨɨɪɬɨɬɪɨɩɧɚɹɩɥɚɫɬɢɧɚ
x
ɉɭɫɬɶ ɞɥɹ ɪɟɛɟɪ ɩɚɪɚɥɥɟɥɶɧɵɯ ɨɫɢ x ɠɟɫɬɤɨɫɬɶ ɧɚ ɢɡɝɢɛ –
EI1ɧɚ ɤɪɭɱɟɧɢɟ – GI
ɜɟɬɫɬɜɟɧɧɨɞɥɹɪɟɛɟɪɩɚɪɚɥɥɟɥɶɧɵɯɨɫɢyɷɬɨɛɭɞɭɬEI2, GI
ɚ ɲɚɝ ɪɚɫɫɬɚɧɨɜɤɢ ɷɬɢɯ ɪɟɛɟɪ – s
ɤɪ1
ɋɨɨɬ
1
ɢs
ɤɪ2
2
ȿɫɥɢɢɡɝɢɛɚɸɳɢɟɢ ɤɪɭɬɹɳɢɟ ɦɨɦɟɧɬɵɜɨɡɧɢɤɚɸɳɢɟɜɫɟɱɟɧɢɹɯ
ɪɟɛɟɪ ɭɫɥɨɜɧɨ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɢɬɶ ɩɨ ɞɥɢɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸ
ɳɟɝɨ ɲɚɝɚ ɪɚɫɫɬɚɧɨɜɤɢ ɪɟɛɟɪ ɬɨ ɭɤɚɡɚɧɧɵɟ ɠɟɫɬɤɨɫɬɢ ɞɥɹ ɨɪɬɨ
ɬɪɨɩɧɨɣɩɥɚɫɬɢɧɵɛɭɞɭɬ
IG
IE
DD
1
1
s
2
1
IE
DD
2
;;
s
3
2
§
1
¨
DD
¨
2
s
©
IG
1
·
2ɤɪɤɪ
¸
,
¸
s
21
¹
ɝɞɟ D – ɰɢɥɢɧɞɪɢɱɟɫɤɚɹ ɠɟɫɬɤɨɫɬɶ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɫɚɦɨɣ ɢɡɨ
ɬɪɨɩɧɨɣɩɥɚɫɬɢɧɵɤɨɬɨɪɚɹɭɫɢɥɢɜɚɟɬɫɹɪɟɛɪɚɦɢ ɠɟɫɬɤɨɫɬɢ.
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɪɟɛɟɪ ɭɪɚɜɧɟɧɢɟ ɛɭɞɟɬ ɷɤɜɢɜɚɥɟɧɬɧɨ
ɭɪɚɜɧɟɧɢɸ ɚ ɩɪɢɨɬɫɭɬɫɬɜɢɢ ɫɚɦɨɣ ɩɥɚɫɬɢɧɵD ɭɪɚɜ
ɧɟɧɢɟ ɛɭɞɟɬ ɩɪɢɛɥɢɠɟɧɧɨ ɨɩɢɫɵɜɚɬɶ ɢɡɝɢɛ ɫɢɫɬɟɦɵ ɩɟɪɟ
ɤɪɟɫɬɧɵɯɛɚɥɨɤɛɚɥɨɱɧɨɣɤɥɟɬɤɢ).
.
34
Ƚɥɚɜɚ 1. Ɉɫɧɨɜɵɬɟɨɪɢɢɪɚɫɱɟɬɚɢɡɝɢɛɚɟɦɵɯɩɥɚɫɬɢɧ
Ɂɚɦɟɬɢɦɱɬɨ ɟɫɥɢɪɟɛɪɚ ɠɟɫɬɤɨɫɬɢɫɬɨɹɬ ɧɟɫɢɦɦɟɬɪɢɱɧɨɨɬ
ɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɢɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɩɥɚɫɬɢɧɵ ɪɢɫ ɬɨ ɪɚɫɱɟɬ
ɬɚɤɨɝɨɪɨɞɚɪɟɛɪɢɫɬɨɣɩɥɚɫɬɢɧɵɭɫɥɨɠɧɹɟɬɫɹɬɚɤɤɚɤɜɫɪɟɞɢɧɧɨɣ
ɩɨɜɟɪɯɧɨɫɬɢɩɨɹɜɥɹɸɬɫɹɦɟɦɛɪɚɧɧɵɟɭɫɢɥɢɹɞɚɠɟɩɪɢɦɚɥɵɯɩɪɨ
ɝɢɛɚɯ ɇɨ, ɭɩɪɨɳɚɹ ɡɚɞɚɱɭ ɧɟɪɟɞɤɨ ɭɪɚɜɧɟɧɢɟ ɩɪɢɦɟɧɹɸɬ
ɢɩɪɢɧɟɫɢɦɦɟɬɪɢɱɧɨɦɪɚɫɩɨɥɨɠɟɧɢɢɪɟɛɟɪɠɟɫɬɤɨɫɬɢ.
x
b
s
1
s
1
s
s
a
2
2
y
Ɋɢɫ 1.13. ɉɥɚɫɬɢɧɚɫɧɟɫɢɦɦɟɬɪɢɱɧɵɦ ɪɚɫɩɨɥɨɠɟɧɢɟɦ ɪɟɛɟɪ
Ɋɚɫɫɦɨɬɪɢɦ ɩɥɚɫɬɢɧɭ ɥɟɠɚɳɭɸ ɧɚ ɫɩɥɨɲɧɨɦ ɞɟɮɨɪɦɢɪɭɟ
ɦɨɦɨɫɧɨɜɚɧɢɢɪɢɫ 1.14)ȼɷɬɨɦɫɥɭɱɚɟɩɪɢɡɚɩɢɫɢɞɢɮɮɟɪɟɧɰɢ
ɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɢɡɝɢɛɚ ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɧɭɸ
ɩɨ
ɩɥɨɳɚɞɢɩɥɚɫɬɢɧɵ ɪɟɚɤɰɢɸ (ɨɬɩɨɪɨɫɧɨɜɚɧɢɹɢɧɬɟɧɫɢɜɧɨɫɬɶɸ
r = r (x, y).
0
x
q (x,y)
y
a
q (x,y)
b
r (x,y)
Ɋɢɫ 1.14. ɉɥɚɫɬɢɧɚɧɚɭɩɪɭɝɨɞɟɮɨɪɦɢɪɭɟɦɨɦɨɫɧɨɜɚɧɢɢ
Ɍɨɝɞɚɭɪɚɜɧɟɧɢɟɢɡɝɢɛɚɩɥɚɫɬɢɧɵɡɚɩɢɲɟɬɫɹɬɚɤ
4
rqw
(1.45)
,
D
ɝɞɟq – ɢɧɬɟɧɫɢɜɧɨɫɬɶɜɧɟɲɧɟɣɪɚɫɩɪɟɞɟɥɟɧɧɨɣɧɚɝɪɭɡɤɢ
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɜɨɣɫɬɜ ɞɟɮɨɪɦɢɪɭɟɦɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫɜɹɡɶ
ɦɟɠɞɭɪɟɚɤɰɢɟɣɨɫɧɨɜɚɧɢɹr ɢɟɝɨɞɟɮɨɪɦɢɪɨɜɚɧɧɵɦɫɨɫɬɨɹɧɢɟɦɦɨ
ɠɟɬɛɵɬɶ ɪɚɡɥɢɱɧɨɣɇɚ ɩɪɚɤɬɢɤɟ ɨɱɟɧɶɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬɢɡɜɟɫɬɧɭɸ
35
ȺȺɅɭɤɚɲɟɜɢɱɌɟɨɪɢɹɪɚɫɱɟɬɚɩɥɚɫɬɢɧɢɨɛɨɥɨɱɟɤ
ɦɨɞɟɥɶȼɢɧɤɥɟɪɚ, ɫɨɝɥɚɫɧɨɤɨɬɨɪɨɣ r (x, y) = kɭÂ w (x, yɝɞɟ k
– ɤɨɷɮ
ɭ
ɮɢɰɢɟɧɬɠɟɫɬɤɨɫɬɢɭɩɪɭɝɨɝɨɨɫɧɨɜɚɧɢɹɤɨɷɮɮɢɰɢɟɧɬɩɨɫɬɟɥɢ).
ɉɨɞɫɬɚɜɢɜ ɡɧɚɱɟɧɢɟ r ɜ ɢ ɩɟɪɟɧɟɫɹ ɱɥɟɧ ɫɨɞɟɪɠɚɳɢɣ
ɧɟɢɡɜɟɫɬɧɭɸ ɮɭɧɤɰɢɸ w ɜ ɥɟɜɭɸ ɱɚɫɬɶ ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟɭɪɚɜɧɟɧɢɟɢɡɝɢɛɚ ɩɥɚɫɬɢɧɵɥɟɠɚɳɟɣɧɚ ɭɩɪɭ
ɝɨɦɜɢɧɤɥɟɪɨɜɫɤɨɦɨɫɧɨɜɚɧɢɢ,
k
ɭ
4
w
D
q
(1.46)
w
.
D
Ⱦɥɹ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɩɪɢɦɟɧɹɟɬɫɹ ɥɸɛɨɣ ɢɡ ɪɚɫ
ɫɦɨɬɪɟɧɧɵɯ ɪɚɧɟɟ ɫɩɨɫɨɛɨɜ ɇɚɩɪɢɦɟɪ ɞɥɹ ɲɚɪɧɢɪɧɨ ɨɩɟɪɬɨɣ ɩɨ
ɤɨɧɬɭɪɭɩɥɚɫɬɢɧɵɩɪɢɧɚɝɪɭɡɤɟɜɜɢɞɟ
q
w
0
2
22224
//
qqSS sinsin
0
xm
a
xm
kbnamD
S
a
yn
ɩɨɥɭɱɢɦ
b
yn
SS
.sinsin
b
Ʉɨɧɬɪɨɥɶɧɵɟɜɨɩɪɨɫɵ
1. Ʉɚɤɢɟ ɝɪɭɩɩɵ ɭɪɚɜɧɟɧɢɣ ɫɨɫɬɚɜɥɹɸɬ ɫɢɫɬɟɦɭ ɨɫɧɨɜɧɵɯ
ɭɪɚɜɧɟɧɢɣɬɟɨɪɢɢɭɩɪɭɝɨɫɬɢ"
2. Ʉɚɤɢɦɢ ɭɫɥɨɜɢɹɦɢ ɞɨɩɨɥɧɹɸɬɫɹ ɭɪɚɜɧɟɧɢɹɬɟɨɪɢɢɭɩɪɭɝɨ
ɫɬɢɩɪɢɪɟɲɟɧɢɢɤɨɧɤɪɟɬɧɵɯɡɚɞɚɱ"
3. ɍɤɚɠɢɬɟɨɫɧɨɜɧɵɟɫɩɨɫɨɛɵɪɟɲɟɧɢɹɡɚɞɚɱɬɟɨɪɢɢɭɩɪɭɝɨɫɬɢ
4. Ʉɚɤ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɭɱɟɧɚ ɫɢɫɬɟɦɚ ɪɚɡɪɟɲɚɸɳɢɯ ɭɪɚɜɧɟ
ɧɢɣɬɟɨɪɢɢɭɩɪɭɝɨɫɬɢɜɩɟɪɟɦɟɳɟɧɢɹɯ"
5. Ʉɚɤɢɟ ɭɪɚɜɧɟɧɢɹ ɬɪɟɛɭɟɬɫɹ ɢɧɬɟɝɪɢɪɨɜɚɬɶ ɩɪɢ ɪɟɲɟɧɢɢ
ɡɚɞɚɱɜɧɚɩɪɹɠɟɧɢɹɯ"
6. ȼ ɱɟɦ ɡɚɤɥɸɱɚɟɬɫɹ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ
ɜɫɦɟɲɚɧɧɨɣɮɨɪɦɟ"
7. Ʉɚɤɚɹ ɡɚɞɚɱɚ ɧɚɡɵɜɚɟɬɫɹ ɩɪɹɦɨɣ ɡɚɞɚɱɟɣ ɬɟɨɪɢɢ ɭɩɪɭɝɨ
ɫɬɢ"
8. Ʉɚɤɨɟɬɟɥɨɧɚɡɵɜɚɟɬɫɹɩɥɚɫɬɢɧɨɣɱɬɨɩɨɧɢɦɚɟɬɫɹɩɨɞɫɪɟ
ɞɢɧɧɨɣɩɥɨɫɤɨɫɬɶɸ?
9. ɑɬɨ ɧɚɡɵɜɚɟɬɫɹ ɫɪɟɞɢɧɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ ɢɡɨɝɧɭɬɨɣ ɩɥɚ
ɫɬɢɧɵɢɟɟɩɪɨɝɢɛɨɦ"
10. ɉɪɢɜɟɞɢɬɟ ɤɥɚɫɫɢɮɢɤɚɰɢɸ ɩɥɚɫɬɢɧ ɩɨ ɨɬɧɨɲɟɧɢɸ ɢɯ
ɬɨɥɳɢɧɵɤɯɚɪɚɤɬɟɪɧɨɦɭɪɚɡɦɟɪɭ
36
Ƚɥɚɜɚ 1. Ɉɫɧɨɜɵɬɟɨɪɢɢɪɚɫɱɟɬɚɢɡɝɢɛɚɟɦɵɯɩɥɚɫɬɢɧ
11. Ʉɚɤɪɚɡɞɟɥɹɸɬɫɹ ɬɨɧɤɢɟ ɩɥɚɫɬɢɧɵ ɩɨ ɨɬɧɨɲɟɧɢɸ ɦɚɤɫɢ
ɦɚɥɶɧɨɝɨɩɪɨɝɢɛɚɤɢɯ ɬɨɥɳɢɧɟ"
12. ɉɪɢɤɚɤɢɯɬɨɥɳɢɧɚɯ ɢɩɪɨɝɢɛɚɯ ɩɥɚɫɬɢɧɚ ɫɱɢɬɚɟɬɫɹ ɬɨɧ
ɤɨɣɢɠɟɫɬɤɨɣ"
13. ɉɟɪɟɱɢɫɥɢɬɟɝɢɩɨɬɟɡɵɄɢɪɯɝɨɮɚ ɢɫɩɨɥɶɡɭɟɦɵɟɜ ɬɟɨɪɢɢ
ɪɚɫɱɟɬɚɬɨɧɤɢɯɩɥɚɫɬɢɧ
14. ɂɡɥɨɠɢɬɟɝɢɩɨɬɟɡɭɩɪɹɦɨɣɧɨɪɦɚɥɢ. ɑɬɨɢɡɧɟɟɫɥɟɞɭɟɬ?
15. ɉɪɢɜɟɞɢɬɟɝɢɩɨɬɟɡɭɨɧɟɞɟɮɨɪɦɢɪɭɟɦɨɫɬɢɫɪɟɞɢɧɧɨɣɩɨ
ɜɟɪɯɧɨɫɬɢɜɟɟɩɥɨɫɤɨɫɬɢ
16. ɋɮɨɪɦɭɥɢɪɭɣɬɟɝɢɩɨɬɟɡɭɨ ɧɟɧɚɞɚɜɥɢɜɚɧɢɢɫɥɨɟɜ. ɑɬɨɢɡ
ɧɟɟɫɥɟɞɭɟɬ"
17. Ʉɚɤɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɭɫɥɨɜɢɹ ɩɪɢɧɹɬɵ ɜ ɬɟɯɧɢɱɟɫɤɨɣ
ɬɟɨɪɢɢɢɡɝɢɛɚɩɥɚɫɬɢɧ"
18. Ʉɚɤɢɟɩɟɪɟɦɟɳɟɧɢɹɢɞɟɮɨɪɦɚɰɢɢɭɱɢɬɵɜɚɸɬɫɹɩɪɢɪɚɫ
ɱɟɬɟɬɨɧɤɢɯɩɥɚɫɬɢɧ"
19. Ʉɚɤɢɟɜɟɥɢɱɢɧɵɢɤɚɤɨɣɡɚɜɢɫɢɦɨɫɬɶɸɫɜɹɡɵɜɚɸɬɭɪɚɜ
ɧɟɧɢɹɄɨɲɢɜɩɥɚɫɬɢɧɟ"
20. ɑɬɨɬɚɤɨɟɤɪɢɜɢɡɧɵɫɪɟɞɢɧɧɨɣɩɨɜɟɪɯɧɨɫɬɢɩɥɚɫɬɢɧɵ"
21. Ʉɚɤɢɟɤɨɦɩɨɧɟɧɬɵɧɚɩɪɹɠɟɧɢɣɭɱɢɬɵɜɚɸɬɫɹɩɪɢ ɪɚɫɱɟɬɟ
ɬɨɧɤɢɯɩɥɚɫɬɢɧ"
22. Ʉɚɤɢɟ ɜɧɭɬɪɟɧɧɢɟ ɭɫɢɥɢɹ ɭɱɢɬɵɜɚɸɬɫɹ ɩɪɢ ɪɚɫɱɟɬɟ ɬɨɧ
ɤɢɯɩɥɚɫɬɢɧ? Ʉɚɤɨɟɭɧɢɯɩɪɚɜɢɥɨɡɧɚɤɨɜ"
23. Ɂɚɩɢɲɢɬɟɜɵɪɚɠɟɧɢɹ ɞɥɹ ɦɨɦɟɧɬɨɜɜ ɫɟɱɟɧɢɹɯɩɥɚɫɬɢɧɵ
ɱɟɪɟɡɮɭɧɤɰɢɸɩɪɨɝɢɛɨɜ
24. ɉɪɢɜɟɞɢɬɟ ɮɨɪɦɭɥɭ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɠɟɫɬɤɨɫɬɢ ɩɥɚɫɬɢ
ɧɵ. ɑɬɨɨɧɚɯɚɪɚɤɬɟɪɢɡɭɟɬ"
25. Ɂɚɩɢɲɢɬɟ ɮɨɪɦɭɥɵ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɜ ɫɟɱɟ
ɧɢɹɯɩɥɚɫɬɢɧɵ
26. ɂɡɤɚɤɢɯɭɫɥɨɜɢɣɦɨɠɟɬɛɵɬɶɩɨɥɭɱɟɧɨɭɪɚɜɧɟɧɢɟɋɨɮɢ
ɀɟɪɦɟɧ– Ʌɚɝɪɚɧɠɚ"
27. ɉɪɢɜɟɞɢɬɟɭɪɚɜɧɟɧɢɟɋɨɮɢɀɟɪɦɟɧ– Ʌɚɝɪɚɧɠɚ. Ʉɚɤɨɧɨ
ɟɳɟɧɚɡɵɜɚɟɬɫɹ"
28. Ʉɚɤɢɟ ɭɫɥɨɜɢɹ ɞɥɹ ɩɥɚɫɬɢɧɵ ɧɚɡɵɜɚɸɬɫɹ ɝɪɚɧɢɱɧɵɦɢ?
Ʉɚɤɨɝɨɬɢɩɚɨɧɢɛɵɜɚɸɬ"
29. ɉɟɪɟɱɢɫɥɢɬɟ ɨɫɧɨɜɧɵɟ ɬɢɩɵ ɡɚɤɪɟɩɥɟɧɢɹ ɤɪɚɟɜ ɩɪɹɦɨ
ɭɝɨɥɶɧɨɣɩɥɚɫɬɢɧɵ
30. Ɂɚɩɢɲɢɬɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɡɚɞɟɥɚɧɧɨɝɨ ɤɪɚɹ ɩɥɚ
ɫɬɢɧɵ. Ʉɚɤɨɝɨɬɢɩɚɷɬɢɭɫɥɨɜɢɹ"
37
ȺȺɅɭɤɚɲɟɜɢɱɌɟɨɪɢɹɪɚɫɱɟɬɚɩɥɚɫɬɢɧɢɨɛɨɥɨɱɟɤ
31. ɉɪɢɜɟɞɢɬɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɲɚɪɧɢɪɧɨ ɨɩɟɪɬɨɝɨ
ɤɪɚɹ. Ʉɚɤɨɝɨɬɢɩɚɷɬɢɭɫɥɨɜɢɹ"
32. ɋɮɨɪɦɭɥɢɪɭɣɬɟ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɫɜɨɛɨɞɧɨɝɨ ɤɪɚɹ
ɩɪɹɦɨɭɝɨɥɶɧɨɣɩɥɚɫɬɢɧɵ
33. Ʉɚɤɨɝɨɜɢɞɚɡɚɞɚɱɚɧɚɡɵɜɚɟɬɫɹɤɪɚɟɜɨɣɡɚɞɚɱɟɣ"
34. ɉɪɢ ɤɚɤɢɯ ɭɫɥɨɜɢɹɯ ɜɨɡɧɢɤɚɟɬ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɢɡɝɢɛ
ɩɥɚɫɬɢɧɵ"
35. ɉɪɢɤɚɤɢɯ ɭɫɥɨɜɢɹɯɜɨɡɧɢɤɚɟɬɱɢɫɬɵɣɢɡɝɢɛɩɪɹɦɨɭɝɨɥɶ
ɧɨɣɩɥɚɫɬɢɧɵ"
36. ɋɮɨɪɦɭɥɢɪɭɣɬɟɩɪɹɦɭɸɡɚɞɚɱɭɢɡɝɢɛɚɩɥɚɫɬɢɧɵ.
37. ɉɪɢɜɟɞɢɬɟɩɨɫɬɚɧɨɜɤɭɨɛɪɚɬɧɨɣɡɚɞɚɱɢɢɡɝɢɛɚɩɥɚɫɬɢɧɵ
38. Ʉɚɤɚɹ ɩɥɚɫɬɢɧɚ ɧɚɡɵɜɚɟɬɫɹ ɨɪɬɨɬɪɨɩɧɨɣ ɤɨɧɫɬɪɭɤɬɢɜɧɨ
ɨɪɬɨɬɪɨɩɧɨɣ"
39. Ɂɚɩɢɲɢɬɟɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɢɡɝɢɛɚɞɥɹ ɨɪɬɨ
ɬɪɨɩɧɨɣɩɥɚɫɬɢɧɵ
40. ɉɪɢɜɟɞɢɬɟɭɪɚɜɧɟɧɢɟ ɋɨɮɢ ɀɟɪɦɟɧɞɥɹ ɩɥɚɫɬɢɧɵ ɥɟɠɚ
ɳɟɣɧɚɭɩɪɭɝɨɦɨɫɧɨɜɚɧɢɢ
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Ƚɥɚɜɚ 1. Ɉɫɧɨɜɵɬɟɨɪɢɢɪɚɫɱɟɬɚɢɡɝɢɛɚɟɦɵɯɩɥɚɫɬɢɧ
Ƚɥɚɜɚ 2. ɆȿɌɈȾɕɉɊɂȻɅɂɀȿɇɇɈȽɈ Ɋȿɒȿɇɂə
ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɈȽɈɍɊȺȼɇȿɇɂəɂɁȽɂȻȺ
Ʉɚɤ ɭɠɟ ɨɬɦɟɱɚɥɨɫɶ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɢɡɝɢɛɚ ɩɥɚɫɬɢɧɵ
(1.29) ɜ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɮɨɪɦɟɜɨɡɦɨɠɧɨ ɥɢɲɶɜ ɧɟɤɨɬɨɪɵɯ ɱɚɫɬ
ɧɵɯ ɫɥɭɱɚɹɯ ɡɚɞɚɧɢɹ ɧɚɝɪɭɡɤɢ ɢ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜɢɣ Ɍɨɱɧɨɝɨ ɪɟ
ɲɟɧɢɹɞɥɹɛɨɥɶɲɢɧɫɬɜɚɩɪɚɤɬɢɱɟɫɤɢɯ ɡɚɞɚɱɢɡɝɢɛɚɩɥɚɫɬɢɧɞɨɫɢɯ
ɩɨɪ ɧɟ ɩɨɥɭɱɟɧɨ ɩɨɫɤɨɥɶɤɭ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ
ɭɪɚɜɧɟɧɢɣɤɤɨɬɨɪɵɦɨɧɢɩɪɢɜɨɞɹɬɫɹɩɪɟɞɫɬɚɜɥɹɟɬɛɨɥɶɲɢɟɦɚ
ɬɟɦɚɬɢɱɟɫɤɢɟ ɬɪɭɞɧɨɫɬɢ ɉɨɷɬɨɦɭ ɜɚɠɧɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɢɧɠɟɧɟɪ
ɧɨɣɩɪɚɤɬɢɤɢɢɦɟɸɬɩɪɢɛɥɢɠɟɧɧɵɟɧɨɞɨɫɬɚɬɨɱɧɨɨɛɳɢɟɦɟɬɨɞɵ
ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɩɪɢɤɥɚɞɧɨɣ ɦɟɯɚɧɢɤɢ ɞɟɮɨɪɦɢɪɭɟɦɨɝɨ ɬɟɥɚ
ȼ ɞɚɧɧɨɦ ɩɨɫɨɛɢɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ ɯɚ
ɪɚɤɬɟɪɧɵɟɞɥɹɡɚɞɚɱ ɢɡɝɢɛɚ ɩɥɚɫɬɢɧɧɨɫ ɬɚɤɢɦɠɟɭɫɩɟɯɨɦɩɪɢɦɟ
ɧɹɟɦɵɟɞɥɹɪɚɫɱɟɬɚɨɛɨɥɨɱɟɤɢɞɪɭɝɢɯɬɨɧɤɨɫɬɟɧɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ
ȼɡɚɜɢɫɢɦɨɫɬɢɨɬɩɨɞɯɨɞɨɜɤɪɟɲɟɧɢɸɡɚɞɚɱɦɨɠɧɨɜɵɞɟɥɢɬɶ
ɨɫɧɨɜɧɵɟɤɥɚɫɫɢɮɢɤɚɰɢɢɩɪɢɛɥɢɠɟɧɧɵɯɦɟɬɨɞɨɜ
ɉɨ ɬɢɩɭ ɪɚɡɪɟɲɚɸɳɢɯ ɭɪɚɜɧɟɧɢɣ ɩɪɢɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ
ɦɨɠɧɨɪɚɡɞɟɥɢɬɶɧɚɞɜɟ ɝɪɭɩɩɵɉɟɪɜɭɸɫɨɫɬɚɜɥɹɸɬ ɬɚɤɧɚɡɵɜɚɟ
ɦɵɟɦɟɬɨɞɵɪɟɲɟɧɢɹɤɪɚɟɜɵɯɡɚɞɚɱɞɥɹɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯɭɪɚɜ
ɧɟɧɢɣɂɡ ɱɢɫɥɚ ɷɬɢɯɦɟɬɨɞɨɜ ɡɞɟɫɶɛɭɞɭɬ ɪɚɫɫɦɨɬɪɟɧɵ ɦɟɬɨɞɤɨ
ɧɟɱɧɵɯɪɚɡɧɨɫɬɟɣɆɄɊɢɦɟɬɨɞȻɭɛɧɨɜɚ – Ƚɚɥɺɪɤɢɧɚ ɆȻȽ
ȼɬɨɪɭɸ ɝɪɭɩɩɭ ɫɨɫɬɚɜɥɹɸɬ ɩɪɹɦɵɟ ɜɚɪɢɚɰɢɨɧɧɵɟ ɦɟɬɨɞɵ ɨɫɧɨ
ɜɚɧɧɵɟ ɧɚ ɜɚɪɢɚɰɢɨɧɧɵɯ ɩɪɢɧɰɢɩɚɯ ɦɟɯɚɧɢɤɢ ɩɪɟɠɞɟ ɜɫɟɝɨ ɧɚ
ɩɪɢɧɰɢɩɟ ɦɢɧɢɦɭɦɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ Ʌɚɝɪɚɧɠɚ ɢ ɩɪɢɧ
ɰɢɩɟɦɢɧɢɦɭɦɚɞɨɩɨɥɧɢɬɟɥɶɧɨɣɪɚɛɨɬɵɄɚɫɬɢɥɶɹɧɨɄɷɬɢɦ ɦɟ
ɬɨɞɚɦ ɜ ɱɚɫɬɧɨɫɬɢ ɨɬɧɨɫɹɬɫɹ ɦɟɬɨɞ Ɋɢɬɰɚ – Ɍɢɦɨɲɟɧɤɨ ɆɊɌ
ɜɚɪɢɚɰɢɨɧɧɨ-ɪɚɡɧɨɫɬɧɵɣ ɦɟɬɨɞ ȼɊɆ ɚ ɬɚɤɠɟ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨ
ɫɬɪɚɧɟɧɧɵɣɜɧɚɫɬɨɹɳɟɟɜɪɟɦɹɦɟɬɨɞɤɨɧɟɱɧɵɯɷɥɟɦɟɧɬɨɜɆɄɗ
ɉɨ ɫɯɟɦɟ ɩɨɫɬɪɨɟɧɢɹ ɩɪɢɛɥɢɠɟɧɧɨɝɨɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɪɚɡɥɢ
ɱɚɸɬ ɪɚɡɧɨɫɬɧɵɟ ɢ ɩɪɨɟɤɰɢɨɧɧɵɟ ɦɟɬɨɞɵ ȼ ɪɚɡɧɨɫɬɧɵɯ ɦɟɬɨɞɚɯ
ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɨɣ ɮɨɪɦɟ
ɆɄɊ ȼɊɆ ɚ ɜ ɩɪɨɟɤɰɢɨɧɧɵɯ ɡɚɦɟɧɹɟɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦ ɤɨɧɟɱ
ɧɨɦɟɪɧɵɦɭɪɚɜɧɟɧɢɟɦ ɪɟɲɟɧɢɟɤɨɬɨɪɨɝɨ ɢɳɟɬɫɹ ɩɪɢ ɩɨɦɨɳɢ ɬɚɤ
ɧɚɡɵɜɚɟɦɵɯɤɨɨɪɞɢɧɚɬɧɵɯ (ɛɚɡɢɫɧɵɯ) ɮɭɧɤɰɢɣ ɆȻȽɆɊɌɆɄɗ.
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ȺȺɅɭɤɚɲɟɜɢɱɌɟɨɪɢɹɪɚɫɱɟɬɚɩɥɚɫɬɢɧɢɨɛɨɥɨɱɟɤ
y
y
ɂ ɧɚɤɨɧɟɰ ɩɨ ɜɢɞɭ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɢɫɤɨɦɨɝɨ ɪɟɲɟɧɢɹ ɩɪɢ
ɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ ɪɚɡɞɟɥɹɸɬɫɹ ɧɚ ɱɢɫɥɟɧɧɨ-ɚɧɚɥɢɬɢɱɟɫɤɢɟ (ɩɨ
ɥɭɚɧɚɥɢɬɢɱɟɫɤɢɟɢɱɢɫɥɟɧɧɵɟ (ɫɟɬɨɱɧɵɟȼɩɟɪɜɵɯɢɡɧɢɯɪɟɲɟ
ɧɢɟ ɡɚɞɚɱɢ ɢɳɟɬɫɹ ɜ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɮɨɪɦɟ ɫ ɩɨɞɥɟɠɚɳɢɦɢ ɨɩɪɟ
ɞɟɥɟɧɢɸ ɱɢɫɥɨɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɧɟɢɡɜɟɫɬɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
ɆȻȽ ɆɊɌ ȼ ɫɟɬɨɱɧɵɯ ɦɟɬɨɞɚɯ ɆɄɊ ȼɊɆ ɆɄɗ ɪɟɲɟɧɢɟ
ɢɳɟɬɫɹ ɜ ɜɢɞɟ ɱɢɫɥɨɜɵɯ ɡɧɚɱɟɧɢɣ ɢɫɤɨɦɨɣ ɮɭɧɤɰɢɢ ɜ ɧɟɤɨɬɨɪɨɣ
ɞɢɫɤɪɟɬɧɨɣɫɨɜɨɤɭɩɧɨɫɬɢɬɨɱɟɤɭɡɥɚɯɫɟɬɤɢ).
Ʉɪɨɦɟ ɬɨɝɨ ɩɪɢɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ ɦɨɝɭɬ ɪɟɚɥɢɡɨɜɵɜɚɬɶɫɹ
ɤɚɤ ɜ ɮɨɪɦɟ ɦɟɬɨɞɚ ɩɟɪɟɦɟɳɟɧɢɣ ɨɫɧɨɜɧɵɦɢ ɧɟɢɡɜɟɫɬɧɵɦɢ
ɡɞɟɫɶɹɜɥɹɸɬɫɹɩɟɪɟɦɟɳɟɧɢɹ – ɜ ɜɢɞɟɢɫɤɨɦɵɯ ɮɭɧɤɰɢɣɢɥɢ ɱɢɫ
ɥɨɜɵɯɡɧɚɱɟɧɢɹɜɭɡɥɚɯ ɫɟɬɤɢ ɬɚɤɢɜɮɨɪɦɟɦɟɬɨɞɚɫɢɥ ɨɫɧɨɜ
ɧɵɦɢ ɧɟɢɡɜɟɫɬɧɵɦɢ ɹɜɥɹɸɬɫɹ ɭɫɢɥɢɹ ɢɥɢ ɧɚɩɪɹɠɟɧɢɹ ɉɪɢ ɪɚɫ
ɱɟɬɟɫɥɨɠɧɵɯɬɨɧɤɨɫɬɟɧɧɵɯɤɨɧɫɬɪɭɤɰɢɣ ɜ ɱɚɫɬɧɨɫɬɢ ɨɛɨɥɨɱɟɤ
ɧɟɪɟɞɤɨɩɪɢɛɥɢɠɟɧɧɨɟ ɪɟɲɟɧɢɟ ɢɳɟɬɫɹ ɜ ɫɦɟɲɚɧɧɨɣ ɮɨɪɦɟ ɨɫ
ɧɨɜɧɵɦɢɧɟɢɡɜɟɫɬɧɵɦɢɡɞɟɫɶɹɜɥɹɸɬɫɹɢɩɟɪɟɦɟɳɟɧɢɹɢɭɫɢɥɢɹ
2Ɋɚɫɱɟɬɩɥɚɫɬɢɧɦɟɬɨɞɨɦɤɨɧɟɱɧɵɯɪɚɡɧɨɫɬɟɣ
Ɇɟɬɨɞɤɨɧɟɱɧɵɯ ɪɚɡɧɨɫɬɟɣ ɢɥɢ, ɤɚɤɟɝɨ ɟɳɟ ɧɚɡɵɜɚɸɬ, ɦɟ
ɬɨɞ ɫɟɬɨɤ ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ ɞɨɫɬɚɬɨɱɧɨ ɷɮɮɟɤɬɢɜɧɵɯ ɱɢɫɥɟɧ
ɧɵɯɦɟɬɨɞɨɜɪɟɲɟɧɢɹɤɪɚɟɜɵɯɡɚɞɚɱɞɥɹɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯɭɪɚɜ
ɧɟɧɢɣɋɨɝɥɚɫɧɨ ɷɬɨɦɭ ɦɟɬɨɞɭɜɫɹ ɨɛɥɚɫɬɶɪɟɲɟɧɢɹɤɪɚɟɜɨɣ ɡɚɞɚ
ɱɢɫɪɟɞɢɧɧɚɹ ɩɥɨɫɤɨɫɬɶɩɥɚɫɬɢɧɵ ɩɨɜɟɪɯɧɨɫɬɶ ɨɛɨɥɨɱɤɢ ɢ ɬ ɩ
ɩɨɤɪɵɜɚɟɬɫɹɫɟɬɤɨɣɥɢɧɢɣɬɨɱɤɢɩɟɪɟɫɟɱɟɧɢɹɤɨɬɨɪɵɯ ɧɚɡɵɜɚɸɬ
ɫɹɭɡɥɚɦɢ Ɂɚɧɟɢɡɜɟɫɬɧɵɟ ɜ ɡɚɞɚɱɟ ɩɪɢɧɢɦɚɸɬɫɹ ɱɢɫɥɨɜɵɟ ɡɧɚɱɟ
ɧɢɹ ɢɫɤɨɦɨɣ ɮɭɧɤɰɢɢ ɜ ɭɡɥɚɯ ɫɟɬɤɢ ɭɡɥɨɜɵɟ ɧɟɢɡɜɟɫɬɧɵɟ ɉɪɢ
ɷɬɨɦ ɩɪɨɢɡɜɨɞɧɵɟ ɜɯɨɞɹɳɢɟ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɡɚ
ɦɟɧɹɸɬɫɹ ɩɪɢɛɥɢɠɟɧɧɵɦɢ ɜɵɪɚɠɟɧɢɹɦɢ ɜɜɢɞɟ ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɵɯ ɨɬɧɨɲɟɧɢɣ ɦɟɠɞɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɭɡɥɨɜɵɦɢ ɧɟɢɡɜɟɫɬɧɵ
ɦɢɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɵɦɢɨɩɟɪɚɬɨɪɚɦɢ ɩɪɨɢɡɜɨɞɧɵɯɉɨɞɫɬɚɜɢɜ
ɷɬɢ ɤɨɧɟɱɧɵɟ ɪɚɡɧɨɫɬɢ ɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɩɨɥɭɱɢɜ
ɬɟɦ ɫɚɦɵɦ ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɵɣ ɨɩɟɪɚɬɨɪ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ
ɭɪɚɜɧɟɧɢɹɬɪɟɛɭɟɦɟɝɨɜɵɩɨɥɧɟɧɢɹ ɜɤɚɠɞɨɦɭɡɥɟɫɟɬɤɢ
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɤɪɚɟɜɨɣ ɡɚɞɚɱɢ ɬɚɤɠɟ ɡɚɩɢɫɵɜɚɸɬ ɱɟɪɟɡ
ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɵɟɨɩɟɪɚɬɨɪɵ, ɫɜɹɡɵɜɚɹ ɜɫɜɨɸɨɱɟɪɟɞɶ ɪɚɡɧɨɫɬ
ɧɵɦɢ ɨɬɧɨɲɟɧɢɹɦɢ ɧɟɢɡɜɟɫɬɧɵɟ ɜ ɩɪɢɝɪɚɧɢɱɧɵɯ ɭɡɥɚɯ ɫɟɬɤɢ
ȼ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ ɡɚɞɚɱɚ ɪɟɲɟɧɢɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɭɪɚɜɧɟɧɢɹ
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