ɝɞɟ
x
0
&
y
0
ɤɨɨɪɞɢɧɚɬɵ ɜ ɩɥɨɫɤɨɫɬɢ ɢɡɨɛɪɚɠɟɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
5
}
0
A
0
ɡɚɞɧɢɣ ɚɩɟɪɬɭɪɧɵɣ ɭɝɨɥ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
5
~
i
(
w
)
ɢ
~
ɚ
(
w
)
ɫɩɟɤɬɪɚɥɶɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɨɩɭɫɤɚɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɢ ɚɬ
'
ɦɨɫɮɟɪɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
5
s
ɨɬɧ
(
w
)
ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɩɟɤɬɪɚɥɶɧɚɹ ɱɭɜ
'
ɫɬɜɢɬɟɥɶɧɨɫɬɶ ɉɂ
5
n
ɥɢɧɟɣɧɨɟ ɭɜɟɥɢɱɟɧɢɟ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
5
H
w
o
ɫɩɟɤɬɪɚɥɶɧɵɣ ɢɦɩɭɥɶɫɧɵɣ ɨɬɤɥɢɤ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
(
ȿɫɥɢ ɜɜɟɫɬɢ ɩɨɧɹɬɢɟ ɩɨɥɢɯɪɨɦɚɬɢɱɟɫɤɨɣ ɮɭɧɤɰɢɢ ɪɚɫɫɟɹɧɢɹ ɢ ɢɫ
'
ɩɨɥɶɡɨɜɚɬɶ ɦɨɞɟɥɶɧɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɉɂ ɜ ɜɢɞɟ ɤɨɦɩɨɡɢɰɢɢ ɩɪɨɫɬɪɚɧ
'
ɫɬɜɟɧɧɨɝɨ ɮɢɥɶɬɪɚ ɫ ɢɦɩɭɥɶɫɧɵɦ ɨɬɤɥɢɤɨɦ
H
ɉɂ
(
x
V
, y
V
)
ɢ ɜɪɟɦɟɧɧ
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ɝɨ
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H
0
ɉɂ
(
t
)
U1W&
ɬɨ ɫɢɝɧɚɥ ɧɚ
ɜɵɯɨɞɟ ɥɢɧɟɣɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɪɚɤɬɚ
&
ɥɢɧɟɣɧɵɟ ɢɫɤɚɠɟɧɢɹ ɤɨɬɨɪɨɝɨ
ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɢɦɩɭɥɶɫɧɵɦ ɨɬɤɥɢɤɨɦ
H
ɷ
(
t
)
&
ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜ ɜɢɞɟ
U
2
(
x
V
, y
V
, t
) =
U
1
(
x
V
, y
V
, t
)
k
1
V
x
H
0
ɉɂ
μ
x
V
V
x
¶
k
1
V
x
H
ɷ
μ
x
V
V
x
¶
; (4)
ɡɞɟɫɶ
U
1
(
x
V
, y
V
, t
) =
k
1
b
E
ɧ
(
x
V
, y
V
, t
)
d
H
ɉɂ
(
x
V
, y
V
)
(
/
)
ɫɢɝɧɚɥ ɧɚ ɜɵɯɨɞɟ ɉɂ
"
ɩɨɡ
(
/
ɧɚ ɪɢɫ
( -#5
b
E
ɧ
(
x
0
, y
0
, t
) =
L
ɧ
μ
x
0
n
,
y
0
n
, t
¶
k
H
N
(
x
0
, y
0
)
(
0
)
ɧɨɪɦɢɪɨɜɚɧɧɚɹ ɨɫɜɟɳɟɧɧɨɫɬɶ ɜ ɩɥɨɫɤɨɫɬɢ ɢɡɨɛɪɚɠɟɧɢɹ ɨɩɬɢɱɟɫɤɨɣ
ɫɢɫɬɟɦɵ
5
H
N
(
x
0
, y
0
)
ɧɨɪɦɢɪɨɜɚɧɧɚɹ ɩɨɥɢɯɪɨɦɚɬɢɱɟɫɤɚɹ ɮɭɧɤɰɢɹ
ɪɚɫɫɟɹɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ
5
k
1
=
{
sin
2
}
0
A
0
A
ɉɂ
s
w
max
Z
0
b
L
w
(
w
)
~
[
(
w
)
~
i
(
w
)
s
ɨɬɧ
(
w
)
dw
(
1
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ɤɨɷɮɮɢɰɢɟɧɬ
&
ɱɢɫɥɟɧɧɨ ɪɚɜɧɵɣ ɚɦɩɥɢɬɭɞɟ
b
U
max
ɩɨɥɟɡɧɨɝɨ ɫɢɝɧɚ
'
ɥɚ ɨɬ ɨɛɴɟɤɬɚ ɛɟɡ ɭɱɟɬɚ ɥɢɧɟɣɧɵɯ ɢɫɤɚɠɟɧɢɣ
&
ɤɨɬɨɪɵɟ ɜɧɨɫɹɬ ɡɜɟɧɶɹ
ɬɪɚɤɬɚ Ɉɗɉ
5
A
ɉɂ
ɩɥɨɳɚɞɶ ɱɭɜɫɬɜɢɬɟɥɶɧɨɝɨ ɷɥɟɦɟɧɬɚ
5
s
w
max
ɦɚɤ
'
ɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɫɩɟɤɬɪɚɥɶɧɨɣ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ ɷɥɟɦɟɧɬɚ
5
d
ɢɧ
'
ɬɟɝɪɚɥɶɧɚɹ ɨɩɟɪɚɰɢɹ ɜɡɚɢɦɧɨɣ ɤɨɜɚɪɢɚɰɢɢ
(
ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɫɢɝɧɚɥɚ ɧɚ ɜɵɯɨɞɟ ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɪɚɤɬɚ ɮɭɧɤɰɢɟɣ
ɬɪɟɯ ɩɟɪɟɦɟɧɧɵɯ
x
V
&
y
V
ɢ
t
ɩɨɡɜɨɥɹɟɬ ɭɱɟɫɬɶ ɫɭɳɟɫɬɜɭɸɳɭɸ ɩɪɢ ɫɤɚ
'
ɧɢɪɨɜɚɧɢɢ ɜɡɚɢɦɨɫɜɹɡɶ ɦɟɠɞɭ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦɢ ɢ ɜɪɟɦɟɧɧ
©
ɵɦɢ ɤɨ
'
ɨɪɞɢɧɚɬɚɦɢ
&
ɬɚɤ ɤɚɤ
x
V
ɢ
y
V
ɹɜɥɹɸɬɫɹ ɮɭɧɤɰɢɹɦɢ ɜɪɟɦɟɧɢ
t
(
Ɉɞɧɚɤɨ
ɚɧɚɥɢɡ ɫɢɝɧɚɥɚ
&
ɨɩɢɫɵɜɚɟɦɨɝɨ ɮɭɧɤɰɢɟɣ ɬɚɤɢɯ ɫɥɨɠɧɵɯ ɚɪɝɭɦɟɧɬɨɜ
&
ɤɚɤɢɦɢ ɹɜɥɹɸɬɫɹ
x
V
ɢ
y
V
&
ɤɪɚɣɧɟ ɡɚɬɪɭɞɧɟɧ
(
ɉɨɷɬɨɦɭ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ
ɚɧɚɥɢɡɟ ɩɪɟɞɥɚɝɚɟɬɫɹ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɬɟɦ
&
ɱɬɨ ɜ ɩɪɨɰɟɫɫɟ ɫɤɚɧɢɪɨɜɚ
'
ɧɢɹ ɫɢɝɧɚɥ ɦɨɞɭɥɢɪɭɟɬɫɹ ɩɨ ɚɦɩɥɢɬɭɞɟ
(
Ⱥɦɩɥɢɬɭɞɧɚɹ ɦɨɞɭɥɹɰɢɹ ɨɫɭ
'
ɳɟɫɬɜɥɹɟɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ
&
ɱɬɨ ɨɬɥɢɱɧɵɣ ɨɬ ɧɭɥɹ ɫɢɝɧɚɥ ɮɨɪɦɢɪɭɟɬɫɹ
CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
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ɇ
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ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+ 1
