"
!
ˆX
(
t
)
!x
ɬ
#
R
=
= [1 0
. . .
0]
R
11
R
12
. . . R
1
n
R
21
R
22
. . . R
2
n
. . . . . . . . . . . . . . . . . . .
R
n
1
R
n
2
. . . R
nn
= [
R
11
R
12
. . . R
1
n
]
.
"+-#
Ɉɤɨɧɱɚɬɟɥɶɧɵɣ ɨɛɳɢɣ ɜɢɞ ɚɥɝɨɪɢɬɦɚ ɪɚɛɨɬɵ ɫɢɧɯɪɨɧɢɡɚɬɨɪɚ ɯɚɨ
'
ɬɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ
&
ɩɨɥɭɱɟɧɧɨɝɨ ɧɚ ɨɫɧɨɜɟ ɊɎɄ
&
ɞɥɹ ɫɥɭɱɚɹ
&
ɤɨɝɞɚ ɩɟ
'
ɪɟɞɚɟɬɫɹ ɬɨɥɶɤɨ ɨɞɧɚ ɤɨɦɩɨɧɟɧɬɚ ɯɚɨɬɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ
&
ɩɨɥɭɱɢɦ ɩɪɢ
ɩɨɞɫɬɚɧɨɜɤɟ ɜɵɪɚɠɟɧɢɣ
"++#"+-#
ɜ ɭɪɚɜɧɟɧɢɹ
"0#& "1#
ɫ ɭɱɟɬɨɦ ɫɢɦɦɟ
'
ɬɪɢɢ ɦɚɬɪɢɰɵ
R
&
R
ij
=
R
ji
4
d
ˆX
(
t
)
dt
=
g
(
t,
ˆX
(
t
)) +
2
N
0
[
R
11
R
12
. . . R
1
n
]
ɬ
(
z
(
t
)
a
ˆ
x
1
(
t
))
,
(
+.
)
d
R
dt
=
"
!
g
(
t,
ˆX
)
!x
ɬ
#
R
+
R
"
!
g
(
t,
ˆX
)
!x
ɬ
#
ɬ
a
a
2
N
0
[
R
11
R
12
. . . R
1
n
]
ɬ
[
R
11
R
12
. . . R
1
n
]
.
"+/#
ȼɵɪɚɠɟɧɢɹ
"+.#
ɢ
"+/#
ɨɛɨɛɳɚɸɬɫɹ ɞɥɹ ɫɥɭɱɚɹ
&
ɤɨɝɞɚ ɢɡ
n
ɯɚɨɬɢ
'
ɱɟɫɤɢɯ ɫɢɝɧɚɥɨɜ ɩɟɪɟɞɚɟɬɫɹ
i
'
ɣ ɫɢɝɧɚɥ
(
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜ ɷɬɢɯ ɜɵɪɚɠɟ
'
ɧɢɹɯ ɫɥɟɞɭɟɬ ɩɪɨɢɡɜɟɫɬɢ ɩɨɞɫɬɚɧɨɜɤɭ
4
ɜɦɟɫɬɨ
z
(
t
)
a
x
i
(
t
)
ɩɨɞɫɬɚɜɢɦ
z
(
t
)
a
x
1
(
t
)
&
ɜɦɟɫɬɨ
[
R
i
1
R
i
2
. . . R
in
]
ɩɨɞɫɬɚɜɢɦ
[
R
11
R
12
. . . R
1
n
]
(
Ⱦɚɥɟɟ ɪɚɫɫɦɨɬɪɢɦ ɫɢɫɬɟɦɭ ɫɜɹɡɢ ɞɥɹ ɫɥɭɱɚɹ
&
ɤɨɝɞɚ ɜ ɤɚɱɟɫɬɜɟ ɝɟɧɟ
'
ɪɚɬɨɪɚ ɯɚɨɬɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɨɞɟɥɶ Ʌɨɪɟɧɰɚ
(
=
ɢɫɬɟɦɚ Ʌɨɪɟɧɰɚ
(
ɋɢɫɬɟɦɚ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɢɦɟ
'
ɟɬ ɜɢɞ
dx
dt
=
p
(
y
a
x
)
,
dy
dt
=
rx
a
y
a
xz,
dz
dt
=
xy
a
bz,
(
+0
)
ɝɞɟ
x
&
y
&
z
ɩɟɪɟɦɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ
5
r
&
p
&
b
ɩɚɪɚɦɟɬɪɵ
(
Ⱦɢɧɚɦɢɱɟɫɤɚɹ
ɫɢɫɬɟɦɚ
"+0#
ɨɩɢɫɵɜɚɟɬ ɤɨɧɜɟɤɬɢɜɧɨɟ ɞɜɢɠɟɧɢɟ ɠɢɞɤɨɫɬɢ
&
ɩɨɦɟɳɟɧ
'
ɧɨɣ ɦɟɠɞɭ ɞɜɭɦɹ ɧɚɝɪɟɬɵɦɢ ɩɥɚɫɬɢɧɚɦɢ
(
ɍɪɚɜɧɟɧɢɹ
"+0#
ɛɵɥɢ ɜɵɜɟ
'
ɞɟɧɵ ɗ
(
ɇ
(
Ʌɨɪɟɧɰɟɦ
U+/W(
ɉɨɫɤɨɥɶɤɭ ɷɬɢ ɭɪɚɜɧɟɧɢɹ ɢɦɟɸɬ ɞɨɫɬɚɬɨɱɧɨ
ɩɪɨɫɬɨɣ ɜɢɞ
&
ɚ ɧɟɥɢɧɟɣɧɨɫɬɶ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɩɟɪɚɰɢɹɯ ɩɟɪɟɦɧɨɠɟɧɢɹ
CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
(
ɇ
(
ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+ +*/
