ɝɞɟ
b
l
X
&
b
l
Y
ɨɲɢɛɤɢ ɫɱɢɫɥɟɧɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɤɨɨɪɞɢɧɚɬ ɅȺ
5
b
V
X
&
b
V
Y
ɨɲɢɛɤɢ ɫɱɢɫɥɟɧɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɜɟɤ
'
ɬɨɪɚ ɫɤɨɪɨɫɬɢ ɅȺ
5
G
ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ
5
b
G
X
&
b
G
Y
ɫɨɫɬɚɜɥɹɸɳɢɟ ɜɟɤɬɨɪɚ ɧɟɨɞɧɨɪɨɞɧɨɫɬɟɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɭɫɤɨɪɟɧɢɹ
5
U
X
&
U
Y
ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɜɟɤɬɨɪɚ ɧɟɨɞɧɨɪɨɞɧɨɫɬɟɣ
ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ
5
,
=
a
V
Y
/r
&
Y
=
a
V
X
/r
ɭɝɥɨɜɵɟ ɫɤɨɪɨɫɬɢ
ɜɪɚɳɟɧɢɹ ɦɟɫɬɧɨɣ ɜɟɪɬɢɤɚɥɢ
5
V
X
&
V
Y
ɢ
A
X
&
A
Y
ɝɨɪɢɡɨɧɬɚɥɶɧɵɟ
ɫɨɫɬɚɜɥɹɸɳɢɟ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɹ ɅȺ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
5
X
&
Y
&
Z
ɫɤɨɪɨɫɬɢ ɭɯɨɞɚ
"
ɞɪɟɣɮɚ
#
ɨɫɟɣ ɝɢɪɨɛɥɨɤɚ ɂɇɋ
5
P
X
&
P
Y
&
P
Z
ɭɝɥɵ ɪɚɫɫɨɝɥɚɫɨɜɚɧɢɹ ɨɫɟɣ ɬɪɟɯɝɪɚɧɧɢɤɚ
&
ɦɨɞɟɥɢɪɭɟɦɨɝɨ ɩɥɚɬɮɨɪɦɨɣ
ɂɇɋ
&
ɨɬɧɨɫɢɬɟɥɶɧɨ ɝɟɨɝɪɚɮɢɱɟɫɤɨɝɨ ɬɪɟɯɝɪɚɧɧɢɤɚ
4
P
X
ɢ
P
Y
ɨɲɢɛ
'
ɤɢ ɝɨɪɢɡɨɧɬɢɪɨɜɚɧɢɹ ɩɥɚɬɮɨɪɦɵ ɂɇɋ
&
P
Z
ɚɡɢɦɭɬɚɥɶɧɚɹ ɨɲɢɛɤɚ
5
w
X
&
w
Y
ɮɥɭɤɬɭɚɰɢɨɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɨɲɢɛɨɤ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ
ɚɤɫɟɥɟɪɨɦɟɬɪɨɜ
5
r
ɪɚɞɢɭɫ
'
ɜɟɤɬɨɪ ɦɟɫɬɨɩɨɥɨɠɟɧɢɹ ɅȺ
(
Ⱥɧɨɦɚɥɢɢ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɭɫɤɨɪɟɧɢɹ
G
ɨɛɵɱɧɨ ɢɡɦɟɧɹɸɬɫɹ ɦɟɞ
'
ɥɟɧɧɨ
&
ɩɪɢɱɟɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɬɢɯ ɢɡɦɟɧɟɧɢɣ ɡɚɜɢɫɹɬ ɨɬ ɤɨɨɪɞɢɧɚɬ
ɦɟɫɬɚ ɅȺ ɢ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɢ ɫɤɨɪɨɫɬɢ ɟɝɨ ɞɜɢɠɟɧɢɹ
(
ɋɤɨɪɨɫɬɢ ɫɨɛ
'
ɫɬɜɟɧɧɵɯ ɭɯɨɞɨɜ ɨɫɟɣ ɂɇɋ ɬɚɤɠɟ ɦɟɞɥɟɧɧɨ ɢɡɦɟɧɹɸɬɫɹ ɢ ɩɪɢ ɷɬɨɦ
ɫɨɞɟɪɠɚɬ ɩɨɫɬɨɹɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ
(
Ɋɟɫɬɪɢɤɬɢɜɧɚɹ ɦɨɞɟɥɶ ɜɨɡɦɭɳɟɧɢɣ ɢ ɨɲɢɛɨɤ ɂɇɋ
(
Ɉɛɵɱɧɨ ɛɵ
'
ɫɬɪɨ ɢɡɦɟɧɹɸɳɢɟɫɹ ɲɭɦɨɜɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɫɨɛɫɬɜɟɧɧɵɯ ɨɲɢɛɨɤ ɧɚ
'
ɜɢɝɚɰɢɨɧɧɵɯ ɢɡɦɟɪɟɧɢɣ ɫɱɢɬɚɸɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ ɛɟɥɵɦɢ ɝɚɭɫɫɨɜɫɤɢ
'
ɦɢ ɲɭɦɚɦɢ ɫ ɧɭɥɟɜɵɦɢ ɫɪɟɞɧɢɦɢ ɢ ɢɡɜɟɫɬɧɵɦɢ ɫɩɟɤɬɪɚɥɶɧɵɦɢ ɩɥɨɬ
'
ɧɨɫɬɹɦɢ ɦɨɳɧɨɫɬɢ
U.W(
Ɍɚɤɚɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɫɬɨɯɚɫɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ
ɨɛɴɹɫɧɹɟɬɫɹ ɮɥɭɤɬɭɚɰɢɹɦɢ ɫɨɛɫɬɜɟɧɧɵɯ ɨɲɢɛɨɤ ɢɡɦɟɪɟɧɢɣ
(
ɉɪɢ ɨɩɢɫɚɧɢɢ ɧɟɪɟɝɭɥɹɪɧɵɯ ɦɟɞɥɟɧɧɨ ɢɡɦɟɧɹɸɳɢɯɫɹ ɫɨɫɬɚɜɥɹɸ
'
ɳɢɯ ɨɲɢɛɨɤ ɚɤɫɟɥɟɪɨɦɟɬɪɨɜ ɂɇɋ ɢ ɧɚɜɢɝɚɰɢɨɧɧɵɯ ɤɨɪɪɟɤɬɨɪɨɜ ɧɚɢ
'
ɛɨɥɶɲɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɩɨɥɭɱɢɥɚ ɦɚɪɤɨɜɫɤɚɹ ɞɢɮɮɭɡɢɨɧɧɚɹ ɦɨɞɟɥɶ
U.W&
ɜɵɪɚɠɚɟɦɚɹ ɫɬɨɯɚɫɬɢɱɟɫɤɢɦɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦɢ ɭɪɚɜɧɟɧɢɹɦɢ
(
ɂɡɦɟɧɹɸɳɢɟɫɹ ɩɪɢ ɞɜɢɠɟɧɢɢ ɅȺ ɫɨɫɬɚɜɥɹɸɳɢɟ ɜɟɤɬɨɪɚ
b
G
ɧɟ
'
ɨɞɧɨɪɨɞɧɨɫɬɟɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɨɥɹ ɜ ɫɬɨɯɚɫɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɨɩɢɫɵ
'
ɜɚɸɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ ɦɚɪɤɨɜɫɤɢɦɢ ɫɥɭɱɚɣɧɵɦɢ ɩɪɨɰɟɫɫɚɦɢ
&
ɫɨɨɬɜɟɬ
'
ɫɬɜɭɸɳɢɦɢ ɫɬɨɯɚɫɬɢɱɟɫɤɢɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɹɦ
b @
G
X
=
a
V
R
G
b
G
X
+
W
GX
,
b @
G
Y
=
a
V
R
G
b
G
Y
+
W
GY
,
(
,
)
ɝɞɟ
V
ɫɤɨɪɨɫɬɶ ɅȺ
5
R
G
ɪɚɞɢɭɫ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɤɨɪɪɟɥɹɰɢɢ ɧɟ
'
ɨɞɧɨɪɨɞɧɨɫɬɟɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɨɥɹ
"
ɩɨɥɟ ɫɬɚɬɢɫɬɢɱɟɫɤɢ ɨɞɧɨɪɨɞɧɨ
#5
W
GX
&
W
GY
ɧɟɡɚɜɢɫɢɦɵɟ ɛɟɥɵɟ ɝɚɭɫɫɨɜɫɤɢɟ ɩɪɨɰɟɫɫɵ
&
ɩɨɪɨɠɞɚɸ
'
ɳɢɟ ɧɟɨɞɧɨɪɨɞɧɨɫɬɢ ɢ ɢɦɟɸɳɢɟ ɪɚɜɧɵɟ ɧɭɥɸ ɫɪɟɞɧɢɟ
(
0. CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
(
ɇ
(
ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+
