H
ȼɄɍ
(
x
2
, y
2
)
&
ɝɞɟ
x
2
&
y
2
ɤɨɨɪɞɢɧɚɬɵ ɜ ɩɥɨɫɤɨɫɬɢ ɜɵɯɨɞɧɨɝɨ ɢɡɨɛɪɚɠɟ
'
ɧɢɹ
"
ɧɚ ɷɤɪɚɧɟ ȼɄɍ
#(
ɋ ɞɨɫɬɚɬɨɱɧɨɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ ɮɭɧɤɰɢɹ ɪɚɫ
'
ɫɟɹɧɢɹ ɬɟɥɟɜɢɡɢɨɧɧɨɝɨ ɦɨɧɢɬɨɪɚ ɚɩɩɪɨɤɫɢɦɢɪɭɟɬɫɹ ɞɜɭɦɟɪɧɨɣ ɮɭɧɤ
'
ɰɢɟɣ Ƚɚɭɫɫɚ
H
ȼɄɍ
(
x
2
, y
2
) =
1
A
ȼɄɍ
exp
μ
a
x
2
2
+
y
2
2
2
r
2
ȼɄɍ
¶
,
(
++
)
ɝɞɟ
A
ȼɄɍ
= 2
{r
2
ȼɄɍ
ɷɮɮɟɤɬɢɜɧɚɹ ɩɥɨɳɚɞɶ ɩɹɬɧɚ ɪɚɫɫɟɹɧɢɹ
&
r
ȼɄɍ
ɷɮɮɟɤɬɢɜɧɵɣ ɪɚɞɢɭɫ ɩɹɬɧɚ ɪɚɫɫɟɹɧɢɹ ȼɄɍ
(
ɉɹɬɧɨ ɪɚɫɫɟɹɧɢɹ ɩɟɪɟɦɟɳɚɟɬɫɹ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɥɸɦɢɧɨɮɨɪɚ ɷɤɪɚ
'
ɧɚ ȼɄɍ ɫɢɧɯɪɨɧɧɨ ɢ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ ɫɤɚɧɢɪɨɜɚɧɢɹ
"+#(
ȿɫɥɢ
ɩɪɟɧɟɛɪɟɱɶ ɦɚɫɲɬɚɛɧɵɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ ɦɟɠɞɭ ɩɥɨɫɤɨɫɬɶɸ ɢɡɨɛɪɚ
'
ɠɟɧɢɹ ɨɩɬɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ Ɉɗɉ ɢ ɩɥɨɫɤɨɫɬɶɸ ɢɡɨɛɪɚɠɟɧɢɹ ɧɚ ɷɤɪɚɧɟ
ȼɄɍ
&
ɬɨ ɜɵɯɨɞɧɨɣ ɫɢɝɧɚɥ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
L
ȼɄɍ
(
x
2
, y
2
, t
) =
S
ȼɄɍ
A
ȼɄɍ
H
ȼɄɍ
(
x
2
a
x
V
, y
2
a
y
V
)
U
2
(
x
V
, y
V
)
m
1
(
x
V
, y
V
)
.
(
+,
)
ɋ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟɧɢɣ
&
ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ ɩɪɢ ɜɵɜɨɞɟ ɜɵɪɚɠɟɧɢɹ
"+*#&
ɮɨɪɦɭɥɭ
"+,#
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
&
ɛɨɥɟɟ ɭɞɨɛɧɨɦ ɞɥɹ ɞɚɥɶ
'
ɧɟɣɲɟɝɨ ɚɧɚɥɢɡɚ
4
L
ȼɄɍ
(
x
2
, y
2
, t
) =
=
S
ȼɄɍ
A
ȼɄɍ
Z
a
Z
a
Z
a
Z
a
H
ȼɄɍ
(
x
2
a
V
x
~
1
, y
2
a
V
y
~
2
)
U
2
(
V
x
~
1
, V
y
~
2
, t
)
×
×
l_]n
μ
~
1
T
1
¶
1
T
]
]ig\
μ
t
1
a
~
1
T
]
¶
l_]n
μ
t
1
T
2
¶
1
T
ɤ
]ig\
μ
t
a
t
1
T
k
¶
d~
1
dt
1
×
×
l_]n
μ
~
2
T
2
¶
1
T
]
]ig\
μ
~
2
T
]
¶
l_]n
μ
t
2
a
~
2
T
2
¶
1
T
ɤ
]ig\
μ
t
a
t
2
T
ɤ
¶
d~
2
dt
2
.
"+-#
ȿɫɥɢ ɜɵɱɢɫɥɢɬɶ ɬɪɟɯɦɟɪɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ɏɭɪɶɟ ɞɥɹ ɜɵɪɚɠɟ
'
ɧɢɹ
"+-#&
ɬɨ ɩɨɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ
'
ɜɪɟɦɟɧɧ
©i
ɝɨ ɫɩɟɤɬɪɚ ɫɢɝɧɚɥɚ ɧɚ ɜɵɯɨɞɟ Ɉɗɉ
&
ɜ ɤɨɬɨɪɨɦ ɪɟɚɥɢɡɭɟɬɫɹ
ɫɤɚɧɢɪɨɜɚɧɢɟ ɩɨ ɞɜɭɦ ɤɨɨɪɞɢɧɚɬɚɦ
4
˜
L
<
Ʉɍ
(
y
x
, y
y
, y
) =
s
]
s
ɤ
S
<
Ʉɍ
A
<
Ʉɍ
T
y
V
x
T
ɤ
˜
H
<
Ʉɍ
(
y
x
, y
y
)
×
×
X
m,n
=
a
X
p,r
=
a
sinc
μ
{T
2
μ
p
T
ɤ
a
m
T
]
¶¶
sinc
μ
{r
T
1
T
ɤ
¶
×
×
˜
U
4
μ
y
x
+
m
V
x
T
]
, y
y
+
r
V
y
T
ɤ
a
n
T
y
, y
a
p
+
r
T
ɤ
¶
,
"+.#
CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
(
ɇ
(
ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+ 3
