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ȿɫɥɢ ɮɭɧɤɰɢɹ y = M(x) ɢɦɟɟɬ ɤɭɫɨɱɧɨ-ɥɨɦɚɧɵɣ ɜɢɞ, ɬɨ ɞɚɧɧɭɸ ɡɚɞɚɱɭ ɦɨɠ-
ɧɨ ɪɟɲɚɬɶ ɢ ɝɪɚɮɢɱɟɫɤɢ.
6. ɋɅɍɑȺɃɇɕȿ ɉɊɈɐȿɋɋɕ (ɎɍɇɄɐɂɂ)
6.1. Ɉɛɳɢɟ ɩɨɧɹɬɢɹ
ɋɜɟɞɟɧɢɹ ɨ ɫɥɭɱɚɣɧɵɯ ɩɪɨɰɟɫɫɚɯ, ɢɯ ɨɫɨɛɟɧɧɨɫɬɹɯ, ɦɟɬɨɞɚɯ ɨɩɢɫɚɧɢɹ, ɩɚ-
ɪɚɦɟɬɪɚɯ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ [5, ɪɚɡɞ. 1].
6.2.ɍɡɤɨɩɨɥɨɫɧɵɟ ɫɥɭɱɚɣɧɵɟ ɩɪɨɰɟɫɫɵ (ɍɋɉ)
ȼɚɠɧɨɫɬɶ ɷɬɢɯ ɩɪɨɰɟɫɫɨɜ ɞɥɹ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɪɚɞɢɨɬɟɯɧɢɤɢ ɬɪɟɛɭɟɬ ɛɨɥɟɟ
ɩɨɞɪɨɛɧɨɝɨ ɢɯ ɪɚɫɫɦɨɬɪɟɧɢɹ.
Ⱦɥɹ ɛɨɥɟɟ ɩɨɞɪɨɛɧɨɝɨ ɚɧɚɥɢɡɚ ɨɩɪɟɞɟɥɢɦ ɨɝɢɛɚɸɳɭɸ U
m
(t) ɢ ɮɚɡɭ M(t)
ɍɋɉ. ɑɚɫɬɨ ɨɝɢɛɚɸɳɭɸ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ
U
m
(t)=[u
2
(t)+u
1
2
(t)]
1/2
, (6.1)
ɝɞɟ u
1
(t) - ɫɨɩɪɹɠɟɧɧɵɣ ɩɨ Ƚɢɥɶɛɟɪɬɭ ɩɪɨɰɟɫɫ. ɉɪɢɦɟɧɹɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ƚɢɥɶ-
ɛɟɪɬɚ ɤ ɢɫɯɨɞɧɨɦɭ ɜɵɪɚɠɟɧɢɸ, ɩɨɥɭɱɚɟɦ u
1
(t)=-U
m
(t)sin[Z
0
t--M(t)]. Ɍɨɱɧɨɫɬɶ
ɜɵɪɚɠɟɧɢɹ ɞɥɹ U
m
(t) ɢɧɨɝɞɚ ɦɨɠɟɬ ɜɵɡɵɜɚɬɶ ɫɨɦɧɟɧɢɟ, ɩɨɫɤɨɥɶɤɭ ɬɨɥɶɤɨ ɞɥɹ
ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɪɚɜɟɧɫɬɜɨ (6.1) ɧɟɫɨɦɧɟɧɧɨ. Ɉɩɪɟɞɟɥɢɦ, ɧɚɫɤɨɥɶɤɨ
ɩɚɪɚɦɟɬɪɵ ɍɋɉ ɜɥɢɹɸɬ ɧɚ ɬɨɱɧɨɫɬɶ ɷɬɨɣ ɮɨɪɦɭɥɵ.
ɂɫɩɨɥɶɡɭɹ ɢɡɜɟɫɬɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɫɨɫɬɚɜɥɹɸɳɢɯ ɤɨɦɩɥɟɤɫɧɨɣ ɚɦɩɥɢ-
ɬɭɞɵ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɫɢɝɧɚɥɚ z(t), ɩɨɥɭɱɢɦ
U
c
(t)=U
m
(t)cosM(t) ɢ U
s
(t)=U
m
(t)sinM(t).
ɉɪɢɦɟɧɹɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ƚɢɥɶɛɟɪɬɚ ɤ ɢɫɯɨɞɧɨɦɭ ɜɵɪɚɠɟɧɢɸ ɞɥɹ ɍɋɉ ɢ
ɢɫɩɨɥɶɡɭɹ ɫɨɫɬɚɜɥɹɸɳɢɟ ɤɨɦɩɥɟɤɫɧɨɣ ɨɝɢɛɚɸɳɟɣ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ
ttU
xt
dx
ttU
xt
dx
tu
sc 001
sin
1
cos
1
Z
S
Z
S
³³
f
f
f
f
.
Ɋɚɡɥɨɠɢɦ ɮɭɧɤɰɢɢ U
c
(t) ɢ U
s
(t) ɜ ɩɨɞɵɧɬɟɝɪɚɥɶɧɵɯ ɜɵɪɚɠɟɧɢɹɯ ɜ ɪɹɞ Ɍɟɣ-
ɥɨɪɚ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ x = t ɢ ɩɨɱɥɟɧɧɨ ɩɪɨɢɧɬɟɝɪɢɪɭɟɦ. ɉɨɥɭɱɢɦ
»
¼
º
«
¬
ª
cc
c
³
f
f
...
!2
1
cos
1
01
tUtUtxtUx
xt
dx
tu
ccc
Z
S
»
¼
º
«
¬
ª
cc
c
³
f
f
...
!2
1
sin
1
0
tUtUtxtUx
xt
dx
sss
Z
S
= U
c
(t)sinZ
0
t +U
s
(t)cosZ
0
t +Q(t), (6.2)
ɝɞɟ Q(t) - ɨɫɬɚɬɨɱɧɨɟ ɫɥɚɝɚɟɦɨɟ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɟ ɨɬɛɪɨɲɟɧɧɭɸ ɱɚɫɬɶ ɫɭɦɦɵ.
ɉɨɞɫɬɚɜɢɜ ɜ ɜɵɪɚɠɟɧɢɟ (6.2) U
c
(t) ɢ U
s
(t), ɩɨɥɭɱɢɦ
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