Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Электрические машины и микромашины. Задачи. Учебное пособие
.pdf
'
F
F
kF ,
aq q aq
F'
ɝɞɟ
ɦɚɲɢɧɵ
ɥɸɫɧɨɣɦɚɲɢɧɵ
k
±ɚɦɩɥɢɬɭɞɚɆȾɋ ɩɨɩɟɪɟɱɧɨɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɹɜɧɨɩɨɥɸɫɧɨɣ
aq
F
±ɚɦɩɥɢɬɭɞɚɆȾɋ ɩɨɩɟɪɟɱɧɨɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɧɟɹɜɧɨɩɨ
aq
k
± ɤɨɷɮɮɢɰɢɟɧɬɩɨɩɟɪɟɱɧɨɣɪɟɚɤɰɢɢɹɤɨɪɹɈɛɵɱɧɨ
q
·
q
ȼ ɹɜɧɨɩɨɥɸɫɧɨɣ ɦɚɲɢɧɟ ɧɟɛɨɥɶɲɨɣ ɩɪɨɜɚɥ ɜɤɪɢɜɨɣ ɢɧɞɭɤɰɢɢ
ɩɨɹɜɥɹɟɬɫɹ ɢɩɨ ɩɪɨɞɨɥɶɧɨɣ ɨɫɢɄɚɤ ɢ ɜɩɪɟɞɵɞɭɳɟɦ ɫɥɭɱɚɟ ɦɨɠɧɨ
ɡɚɩɢɫɚɬɶ
'
kF ,
ad d ad
ɝɞɟ F'ad±ɚɦɩɥɢɬɭɞɚɆȾɋ ɩɪɨɞɨɥɶɧɨɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɹɜɧɨɩɨɥɸɫɧɨɣ
ɦɚɲɢɧɵ
ɞɨɥɶɧɨɣɪɟɚɤɰɢɢɹɤɨɪɹɈɛɵɱɧɨ
F
±ɫɨɨɬɜɟɬɫɬɜɟɧɧɨɧɟɹɜɧɨɩɨɥɸɫɧɨɣkd±ɤɨɷɮɮɢɰɢɟɧɬɩɪɨ
ad
k
·
d
Ɇɟɬɨɞ ɞɜ
ɭɯ ɪɟɚɤɰɢɣ ɜ ɬɨɦ ɢ ɡɚɤɥɸɱɚɟɬɫɹ, ɱɬɨ ɩɨɥɟ ɪɟɚɤɰɢɢ ɹɤɨ-
ɪɹ ɪɚɫɤɥɚɞɵɜɚɸɬ ɧɚ ɫɨɫɬɚɜɥɹɸɳɢɟ ɩɨ ɩɪɨɞɨɥɶɧɨɣ d ɢ ɩɨɩɟɪɟɱɧɨɣ q
ɨɫɹɦ.
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ ɜɜɨɞɹɬ ɩɨɧɹɬɢɹ ɬɨɤɚ
Ɏ
ɢɎ
ad
, ɗȾɋ E
aq
ad
ɢE
,ɢɧɞɭɤɬɢɜɧɵɯɫɨɩɪɨɬɢɜɥɟɧɢɣ x
aq
ɞɨɥɶɧɨɣɢ ɩɨɩɟɪɟɱɧɨɣɨɫɹɦ ɉɪɢ ɷɬɨɦ
ɭɝɨɥɦɟɠɞɭɬɨɤɨɦɹɤɨɪɹɢ
ɗȾɋ ȿ0.
I
ɢ I
, ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ
d
q
ɢxaqɩɨ ɩɪɨ
ad
Iq = Iɚcos<, Id = Iɚsin<, ɝɞɟ
<
±
ɍɪɚɜɧɟɧɢɹɧɚɩɪɹɠɟɧɢɹ
ȼɟɤɬɨɪɧɵɟɞɢɚɝɪɚɦɦɵɫɢɧɯɪɨɧɧɵɯɦɚɲɢɧ
ɋɢɧɯɪɨɧɧɵɣɝɟɧɟɪɚɬɨɪ ɍɪɚɜɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹɹɜɧɨɩɨɥɸɫɧɨɝɨ
ɫɢɧɯɪɨɧɧɨɝɨɝɟɧɟɪɚɬɨɪɚɦɨɠɧɨɡɚɩɢɫɚɬɶɜɫɥɟɞɭɸɳɟɦɜɢɞɟ
UE E E E Ir E jIx jIx jIx Ir,
0adaqs1a10 dad qaq a1a1
xad, x
ɝɞɟ
ɪɟɚɤɰɢɢɹɤɨɪɹ
ɩɨɬɨɤ ɹɤɨɪɹ ɧɚ ɩɪɨɞɨɥɶɧɭɸ ɢ ɩɨɩɟɪɟɱɧɭɸ ɫɨɫɬɚɜɥɹɸɳɢɟ ɩɨɷɬɨɦɭ
ɭɪɚɜɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹɜɵɝɥɹɞɢɬɬɚɤ
± ɢɧɞɭɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɨɞɨɥɶɧɨɣ ɢ ɩɨɩɟɪɟɱɧɨɣ
aq
ȼ ɧɟɹɜɧɨɩɨɥɸɫɧɨɦ ɝɟɧɟɪɚɬɨɪɟ ɧɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɚɫɤɥɚɞɵɜɚɬɶ
U
M
d
U
M
<
U
M
<
1
ɪ
r
0
UE E E Ir E jIx jIx Ir,
0as1a10 ɚ aa1a1
ɝɞɟ
x
±ɢɧɞɭɤɬɢɜɧɨɟɫɨɩɪɨɬɢɜɥɟɧɢɟɹɤɨɪɹ
a
ȼɟɥɢɱɢɧɭ
xa + x1 = x
ɩɪɨɬɢɜɥɟɧɢɟɦ ɹɤɨɪɹ
ɉɨɷɬɨɦɭ ɩɨɫɥɟɞɧɟɟ ɭɪɚɜɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹɦɨɠɟɬ
ɧɚɡɵɜɚɸɬ ɫɢɧɯɪɨɧɧɵɦ ɢɧɞɭɤɬɢɜɧɵɦ ɫɨ-
c
ɛɵɬɶɩɪɟɞɫɬɚɜɥɟɧɨɜɫɥɟɞɭɸɳɟɦɜɢɞɟ
UE jIx Ir.
0 ɚɫ a1
ȿɫɥɢɭɱɟɫɬɶɱɬɨɜɦɚɲɢɧɚɯɫɪɟɞɧɟɣɢɛɨɥɶɲɨɣɦɨɳɧɨɫɬɢr
ɬɨɚɤɬɢɜɧɵɦɫɨɩɪɨɬɢɜɥɟɧɢɟɦɫɬɚɬɨɪɚ
UE jIx.
r
ɦɨɠɧɨɩɪɟɧɟɛɪɟɱɶɌɨɝɞɚ
1
0 ɚɫ
ɇɚɪɢɫɩɨɫɬɪɨɟɧɵɜɟɤɬɨɪɧɵɟɞɢɚɝɪɚɦɦɵɫɢɧɯɪɨɧɧɵɯɝɟɧɟɪɚ
ɬɨɪɨɜ
ɚ
xdIj
a
E
o
Ij
aqxq
Ij
1xa
I
1ra
T
I
ɚ
I
q
I
d
ɛ
Ij
ɚxa
E
o
xaIj
I
1ra
T
I
ɚ
ɜ
E
Ij
o
T
<
Ɋɢɫȼɟɤɬɨɪɧɵɟɞɢɚɝɪɚɦɦɵɫɢɧɯɪɨɧɧɵɯɝɟɧɟɪɚɬɨɪɨɜ
ɹɜɧɨɩɨɥɸɫɧɨɝɨɚɧɟɹɜɧɨɩɨɥɸɫɧɨɝɨɩɪɢ
ɋɢɧɯɪɨɧɧɵɣɞɜɢɝɚɬɟɥɶ
ɞɜɢɝɚɬɟɥɹ
ɧɟɹɜɧɨɩɨɥɸɫɧɨɝɨɩ
ɍɪɚɜɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹɹɜɧɨɩɨɥɸɫɧɨɝɨ
ɢ
=
1
r1 # 0ɛ
ɜ
<<x
1
c
ɫxa
I
ɚ
U E E E E I r E jI x jI x jI x I r .
0adaqs1a1 0 dad qaq a1a1
Ⱦɥɹɧɟɹɜɧɨɩɨɥɸɫɧɨɝɨɞɜɢɝɚɬɟɥɹɩɪɢr
UEjIx.
ȼɟɤɬɨɪɧɵɟɞɢɚ
ɝɪɚɦɦɵɞɜɢɝɚɬɟɥɹɩɨɤɚɡɚɧɵɧɚɪɢɫ
= 0ɭɪɚɜɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹ
1
0 ɚɫ
8
ɚ
I
1ra
U
Ij
Ij
1xa
aqxq
Ij
adxd
E
o
T
I
ɚ
I
q
I
ɛ
Ij
ɫxa
U
d
E
o
T
I
ɚ
Ɋɢɫȼɟɤɬɨɪɧɵɟɞɢɚɝɪɚɦɦɵɫɢɧɯɪɨɧɧɵɯɞɜɢɝɚɬɟɥɟɣ
ɹɜɧɨɩɨɥɸɫɧɨɝɨɚɧɟɹɜɧɨɩɨɥɸɫɧɨɝɨɩɪɢ
r1 = 0ɛ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢɫɢɧɯɪɨɧɧɵɯɝɟɧɟɪɚɬɨɪɨɜ
ɢɫɩɵɬɚɧɢɹɯ ɫɢɧɯɪɨɧɧɵɯ ɝɟɧɟɪɚɬɨɪɨɜ ɫɧɢɦɚɸɬ ɫɥɟɞɭɸɳɢɟ
ɉɪɢ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ±ɡɚɜɢɫɢɦɨɫɬɶU0 = E0 = f(iɜ)
ɩɪɢ
n1 = constɢIa = 0 ɪɢɫ
L
8
ɜ
5&
5
5/
5/
5
5&
Lɜ
Ɋɢɫɏɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɯɨɥɨɫɬɨɝɨɯɨɞɚ
Ɋɢɫȼɧɟɲɧɢɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
,D
ɊɢɫɊɟɝɭɥɢɪɨɜɨɱɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
,D
ɜɧɟɲɧɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ±ɡɚɜɢɫɢɦɨɫɬɢU = f(Ia)ɩɪɢn1 = constiɜ
= const, cos
M
= constɪɢɫ
ɪɟɝɭɥɢɪɨɜɨɱɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ±ɡɚɜɢɫɢɦɨɫɬɢiɜ = f(Ia)ɩɪɢ
n1 = constU = const, cosM = const ɪɢɫ
ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹɦɨɳɧɨɫɬɶ
Ɋ
ɢɜɪɚɳɚɸɳɢɣɦɨɦɟɧɬɫɢɧɯɪɨɧɧɵɯɞɜɢɝɚɬɟɥɟɣ
ȿɫɥɢɩɪɟɧɟɛɪɟɱɶɚɤɬɢɜɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɫɬɚɬɨɪɚ ɷɥɟɤɬɪɨɦɚɝ
ɧɢɬɧɭɸɦɨɳɧɨɫɬɶɩɟɪɟɞɚɜɚɟɦɭɸɫɨɫɬɚɬɨɪɚɧɚɪɨɬɨɪɩɨɫɪɟɞɫɬɜɨɦɦɚɝ
ɧɢɬɧɨɝɨɩɨɥɹɦɨɠɧɨɪɚɫɫɱɢɬɚɬɶɩɨɫɥɟɞɭɸɳɟɣɮɨɪɦɭɥɟ
2
mUE
Psin sin2P
ɷɦ ɨɫɧ ɞɨɩ
ɝɞɟ
xd = xad + x1, xq = xaq + x
0
x2xx
TT
dqd
ɦɚɲɢɧɵɫɨɨɬɜɟɬɫɬɜɟɧɧɨɩɨɩɪɨɞɨɥɶɧɨɣɢɩɨɩɟɪɟɱɧɨɣɨɫɹɦ
Ɋɚɡɞɟɥɢɜ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɭɸ ɦɨɳɧɨɫɬɶ ɧɚ ɫɢɧɯɪɨɧɧɭɸ ɭɝɥɨɜɭɸ
ɱɚɫɬɨɬ
ɜɪɚɳɟɧɢɹ
ɭ
P mUE
ɷɦ 0
Ɇ sin sin 2 ɆɆ.
ZZ Z
Z
ɩɨɥɭɱɢɦɜɪɚɳɚɸɳɢɣɦɨɦɟɧɬ
1
TT
11d 1qd
x2xx
ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɦɨɳɧɨɫɬɶ ɢɜɪɚɳɚɸɳɢɣ ɦɨɦɟɧɬ ɢɦɟɸɬ ɞɜɟ ɫɨ
ɫɬɚɜɥɹɸɳɢɟ ɨɫɧɨɜɧɭɸ ɨɛɭɫɥɨɜɥɟɧɧɭɸ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɦɚɝɧɢɬɧɵɯ ɩɨ
ɥɟɣ ɫɬɚɬɨɪɚ ɢ ɪɨɬɨɪɚ ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɨɛɭɫɥɨɜɥɟɧɧɭɸ ɢɫɤɪɢɜɥɟɧɢɟɦ
ɩɨɥɹ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɜɫɥɟɞɫɬɜɢɟ ɪɚɡɧɨɣ ɦɚɝɧɢɬɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɨ ɩɪɨ
ɞɨɥɶɧɨɣɢɩɨɩɟɪɟɱɧɨɣɨɫɹɦɁɚɜɢɫɢɦɨɫɬɶɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣɦɨɳɧɨɫɬɢɢɥɢ
ɦɨɦɟɧɬɚɨɬɭɝɥɚ
Ɇ
T
ɧɚɡɵɜɚɸɬɭɝɥɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɪɢɫ
Ɇ
ɨɫɧ
Ɇ
ɞɨɩ
§·
mU 1 1
¨¸
¨¸
©¹
±ɫɢɧɯɪɨɧɧɵɟɢɧɞɭɤɬɢɜɧɵɟɫɨɩɪɨɬɢɜɥɟɧɢɹ
1
2
§·
mU 1 1
¨¸
¨¸
©¹
Q
Q FRQVW
ɨɫɧ ɞɨɩ
,
Ɋɢɫɍɝɥɨɜɚɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɫɢɧɯɪɨɧɧɨɝɨɹɜɧɨɩɨɥɸɫɧɨɝɨ
ɞɜɢɝɚɬɟɥɹ
T
Ɇ
ɧɨɦ
ɊɢɫɆɟɯɚɧɢɱɟɫɤɚɹ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɫɢɧɯɪɨɧɧɨɝɨ
ɞɜɢɝɚɬɟɥɹ
Ɇ
PD[
Ɇ
ȼ ɹɜɧɨɩɨɥɸɫɧɵɯɞɜɢɝɚɬɟɥɹɯ ɚɦɩɥɢɬɭɞɚɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɫɨɫɬɚɜ
ɥɹɸɳɟɣɨɛɵɱɧɨɧɟɩɪɟɜɵɲɚɟɬ·ɨɫɧɨɜɧɨɣ
ȼ ɧɟɹɜɧɨɩɨɥɸɫɧɵɯ ɞɜɢɝɚɬɟɥɹɯ ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ
D
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣɦɨɳɧɨɫɬɢɢɦɨɦɟɧɬɚɨɬɫɭɬɫɬɜɭɟɬɬɤɜɧɢɯ
Ɋɚɛɨɱɢɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢɫɢɧɯɪɨɧɧɵɯɞɜɢɝɚɬɟɥɟɣ
Ɋɚɛɨɱɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɚɜɢɫɢɦɨɫɬɢ M2,
I
, cos
MK
a
, = f(P2) ɩɪɢ U = const, f = const, iɜ = const ɪɢɫ
FRVM
FRVM
K
,
Ɇ
xd § x
q
ɊɢɫɊɚɛɨɱɢɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɫɢɧɯɪɨɧɧɨɝɨ
Ƚɪɚɮɢɤ
Ɋ
ɧɨɦ
ɞɜɢɝɚɬɟɥɹ
cosM = f(Ɋ2) ɡɚɜɢɫɢɬ ɨɬ ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɬɨɤɚ
Ɋ
Ɋɢɫȼɚɪɢɚɧɬɵ
ɡɚɜɢɫɢɦɨɫɬɢFRV
ɨɬɩɨɥɟɡɧɨɣɦɨɳɧɨɫɬɢ
Ɋ
M
ɜɨɡɛɭɠɞɟɧɢɹɢɦɨɠɟɬɩɪɢɧɢɦɚɬɶɜɢɞɩɨɤɚɡɚɧɧɵɣɧɚɪɢɫ
8ɨɛɪɚɡɧɵɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢɫɢɧɯɪɨɧɧɵɯɞɜɢɝɚɬɟɥɟɣ
U-ɨɛɪɚɡɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ±
ɡɚɜɢɫɢɦɨɫɬɢ
Iɚ = f(iɜ)ɩɪɢɆ
= const
ɩ.ɞ
U = constɢf = const ɪɢɫɊɚɡ
ɥɢɱɚɸɬ ɪɟɠɢɦɵ
ɧɨɪɦɚɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ, ɧɟɞɨɜɨɡɛɭɠɞɟɧɢɹ ɢ ɩɟɪɟɜɨɡɛɭɠɞɟɧɢɹ.
Ʉɚɤ ɢ ɩɨɥɨɠɟɧɨ ɞɜɢɝɚɬɟɥɶ
ɜɫɟɝɞɚ ɩɨɬɪɟɛɥɹɟɬ ɢɡ ɫɟɬɢ ɚɤɬɢɜɧɭɸ
ɦɨɳɧɨɫɬɶ Ⱥ ɜɨɬ ɫ ɪɟɚɤɬɢɜɧɨɣ ɦɨɳ
ɧɨɫɬɶɸ ɜɨɡɦɨɠɧɵ ɜɚɪɢɚɧɬɵ ɩɪɢ
ɧɨɪɦɚɥɶɧɨɦ ɜɨɡɛɭɠɞɟɧɢɢ ɪɟɠɢɦ
cosM=1ɞɜɢɝɚɬɟɥɶɧɟɩɨɬɪɟɛɥɹɟɬɢɧɟ
ɨɬɞɚɟɬ ɪɟɚɤɬɢɜɧɭɸ ɦɨɳɧɨɫɬɶ ɉɪɢ
ɧɟɞɨɜɨɡɛɭɠɞɟɧɢɢɫɥɟɜɚɨɧɩɨɬɪɟɛ
ɝɪɚɧɢɰɚɫɬɚɬɢ
ɱɟɫɤɨɣɭɫɬɨɣ
I
a
ɱɢɜɨɫɬɢ
ɡɨɧɚɧɟɞɨ
ɜɨɡɛɭɠɞɟɧɢɹ
Ɋɢɫ8ɨɛɪɚɡɧɵɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɫɢɧɯɪɨɧɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɜɨɡɛɭɠɞɟɧɢɟ
Ɋ
Ɋ
Ɋ
ɡɨɧɚɩɟɪɟ
ɜɨɡɛɭɠɞɟɧɢɹ
Ɋ
ɧɨɪɦɚɥɶɧɨɟ
M
FRV
!3
!
iɜ
ɥɹɟɬɪɟɚɤɬɢɜɧɭɸɦɨɳɧɨɫɬɶɚɩɪɢɩɟɪɟɜɨɡɛɭɠɞɟɧɢɢɫɩɪɚɜɚ±ɨɬɞɚɟɬɟɟ
ɜɫɟɬɶɪɢɫ
ɊɚɊɪ
ɪ
ɋȾ
ɇɨɪɦɚɥɶɧɨɟɜɨɡɛɭɠɞɟɧɢɟ
Ɋɢɫɉɨɜɟɞɟɧɢɟɫɢɧɯɪɨɧɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɜɡɚɜɢɫɢɦɨɫɬɢɨɬɪɟɠɢɦɚɜɨɡɛɭɠɞɟɧɢɹ
ɣɫɬɜɨ ɫɢɧɯɪɨɧɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɛɵɬɶ ɩɨɬɪɟɛɢɬɟɥɟɦ ɢɥɢ ɢɫɬɨɱ
ɋɜɨ
ɇɟɞɨɜɨɡɛɭɠɞɟɧɢɟ
ɊɚɊ
ɋȾ
Ɋ
ɪ
ɉɟɪɟɜɨɡɛɭɠɞɟɧɢɟ
Ɋɚ
ɋȾ
ɧɢɤɨɦɪɟɚɤɬɢɜɧɨɣɦɨɳɧɨɫɬɢɹɜɥɹɟɬɫɹɜɚɠɧɵɦ ɟɝɨ ɞɨɫɬɨɢɧɫɬɜɨɦɢ ɲɢ
ɪɨɤɨɢɫɩɨɥɶɡɭɟɬɫɹɜɩɪɚɤɬɢɤɟɷɤɫɩɥɭɚɬɚɰɢɢɷɧɟɪɝɨɭɫɬɚɧɨɜɨɤ
ɉɭɫɤɫɢɧɯɪɨɧɧɨɝɨɞɜɢɝɚɬɟɥɹ
ȿɫɥɢɜɨɡɛɭɠɞɟɧɧɵɣ ɫɢɧɯɪɨɧɧɵɣɞɜɢɝɚɬɟɥɶɜɤɥɸɱɢɬɶ ɜɫɟɬɶɬɪɟɯ
ɮɚɡɧɨɝɨɬɨɤɚɪɨɬɨɪɧɟɫɞɜɢɧɟɬɫɹɫɦɟɫɬɚɩɨɫɤɨɥɶɤɭɢɡɡɚɛɨɥɶɲɨɣɢɧɟɪ
ɰɢɨɧɧɨɫɬɢ ɟɝɨ ɩɨɥɸɫɚ ɧɟ ɭɫɩɟɜɚɸɬ ɫɰɟɩɥɹɬɶɫɹ ɫ ɜɪɚɳɚɸɳɢɦɫɹ ɩɨɥɟɦ
ɫɬɚɬɨɪɚ ɉɨɷɬɨɦɭɬɨ ɢ ɬɪɟɛɭɟɬɫɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɣ ɪɚɡɝɨɧ ɪɨɬɨɪɚ ɞɨ ɱɚ
ɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɛɥɢɡɤɨɣ ɤ ɫɢɧɯɪɨɧɧɨɣ ɉɪɨɳɟ ɜɫɟɝɨ ɷɬɨ ɨɫɭɳɟɫɬɜɢɬɶ
ɩɭɬɟɦ
ɚɫɢɧɯɪɨɧɧɨɝɨ ɩɭɫɤɚ ɫɢɧɯɪɨɧɧɨɝɨ
ɊɢɫɊɚɡɦɟɳɟɧɢɟɩɭɫɤɨɜɨɣ
ɨɛɦɨɬɤɢɜɫɢɧɯɪɨɧɧɵɯ
ɞɜɢɝɚɬɟɥɹɯ±ɩɨɥɸɫɵɪɨɬɨɪɚ
±ɤɨɪɨɬɤɨɡɚɦɵɤɚɸɳɢɟɤɨɥɶɰɚ
±ɫɬɟɪɠɧɢɛɟɥɢɱɶɟɣɤɥɟɬɤɢ
±ɩɨɥɸɫɧɵɟɧɚɤɨɧɟɱɧɢɤɢ
ɞɜɢɝɚɬɟɥɹ.
ɧɚɤɨɧɟɱɧɢɤɚɯ ɭɤɥɚɞɵɜɚɸɬ ɩɭɫɤɨɜɭɸ
ɨɛɦɨɬɤɭ ɫɨɫɬɨɹɳɭɸ ɢɡ ɦɟɞɧɵɯ ɢɥɢ
ɥɚɬɭɧɧɵɯ ɫɬɟɪɠɧɟɣ ɡɚɦɤɧɭɬɵɯ ɩɨ
ɬɨɪɰɚɦ ɤɨɪɨɬɤɨɡɚɦɵɤɚɸɳɢɦɢ ɤɨɥɶɰɚ
ɦɢɩɨɥɭɱɚɟɬɫɹɨɛɦɨɬɤɚɬɢɩɚ©ɛɟɥɢ
ɱɶɟɣɤɥɟɬɤɢªɪɢɫ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ Ɉɛɦɨɬɤɭ ɜɨɡ
ɛɭɠɞɟɧɢɹ ɡɚɦɵɤɚɸɬ ɧɚ ɚɤɬɢɜɧɨɟ ɫɨ
ɩɪɨɬɢɜɥɟɧɢɟ ɜ · ɪɚɡ ɛɨɥɶɲɟɟ ɱɟɦ
ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɚɦɨɣ ɨɛɦɨɬɤɢ ɟɫɥɢ
Ⱦɥɹɷɬɨɝɨɜɩɨɥɸɫɧɵɯ
ɉɭɫɤ ɞɜɢɝɚɬɟɥɹ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ
ɨɫɬɚɜɢɬɶɟɟɪɚɡɨɦɤɧɭɬɨɣɬɨ ɜ ɧɟɣɧɚɜɟɞɟɬɫɹɛɨɥɶɲɚɹ
ɢɡɨɥɹɰɢɢ ɉɨɫɥɟ ɱɟɝɨ ɨɛɦɨɬɤɭ ɫɬɚɬɨɪɚ ɜɤɥɸɱɚɸɬ ɜ ɫɟɬɶ ɢ ɞɜɢɝɚɬɟɥɶ
ɧɚɱɢɧɚɟɬ ɪɚɡɝɨɧɹɬɶɫɹ ɤɚɤ ɚɫɢɧɯɪɨɧɧɵɣ Ʉɨɝɞɚ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɞɨ
ɫɬɢɝɧɟɬ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɫɢɧɯɪɨɧɧɨɣ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ ɨɬ
ɤɥɸɱɚɸɬ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɢ ɩɨɞɤɥɸɱɚɸɬ ɤ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ
ɧɚɩɪɹɠɟɧɢɹ Ⱦɜɢɝɚɬɟɥɶ ɜɬɹɝɢɜɚɟɬɫɹ ɜ ɫɢɧɯɪɨɧɢɡɦ ɢ ɩɪɨɞɨɥɠɚɟɬ ɪɚɛɨ
ɬɚɬɶɤɚɤɫɢɧɯɪɨɧɧɵɣ
Ɂɚɦɤɧɭɬɚɹɧɚɫɨɩɪɨɬɢɜɥɟɧɢɹɨɛɦɨɬɤɚɜɨɡɛɭɠɞɟɧɢɹɬɨɠɟɭɱɚɫɬɜɭ
ɟɬ ɜ ɩɭɫɤɟ ɞɜɢɝɚɬɟɥɹ ɫɨɡɞɚɜɚɹ ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɨɞɧɨɨɫɧɵɣ ɦɨɦɟɧɬ
ɭɯɭɞɲɚɸɳɢɣɩɭɫɤɨɜɵɟɫɜɨɣɫɬɜɫɢɧɯɪɨɧɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɋɢɧɯɪɨɧɧɵɣɬɚɯɨɝɟɧɟɪɚɬɨɪ
ɋɢɧɯɪɨɧɧɵɣ ɬɚɯɨɝɟɧɟɪɚɬɨɪ ɹɜɥɹɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɪɨɫɬɵɦ ɬɚ
ɯɨɝɟɧɟɪɚɬɨɪɨɦ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ Ʉɨɧɫɬɪɭɤɬɢɜɧɨ ɨɧɩɨɞɨɛɟɧ ɨɞɧɨɮɚɡ
ɧɨɦɭ ɫɢɧɯɪɨɧɧɨɦɭɝɟɧɟɪɚɬɨɪɭ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɫ ɪɨɬɨɪɨɦ ɜ ɜɢɞɟ
ɩɨɫɬɨɹɧɧɨɝɨɦɚɝɧɢɬɚɡɜɟɡɞɨɱɤɢ
ɉɪɢɜɪɚɳɟɧɢɢɪɨɬɨɪɚɜɨɛɦɨɬɤɟɫɬɚɬɨɪɚɢɧɞɭɰɢɪɭɟɬɫɹ
ɫɬɜɭɸɳɟɟɡɧɚɱɟɧɢɟɤɨɬɨɪɨɣɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɱɚɫɬɨɬɟɜɪɚɳɟɧɢɹ
E4,44fwkɎ 4,44( pn / 60 )wk Ɏ kn.
ȼɫɢɫɬɟɦɚɯɚɜɬɨɦɚɬɢɤɢɫɢɧɯɪɨɧɧɨɣɬɚɯɨɝɟɧɟɪɚɬɨɪɩɪɚɤɬɢɱɟɫɤɢɧɟ
ɩɪɢɦɟɧɹɟɬɫɹ ɩɨɫɤɨɥɶɤɭ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɢɡɦɟɧɟɧɢɟɦ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ
ɜɪɚɳɟɧɢɹ
ɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɤɨɬɨɪɭɸ ɨɧ ɪɚɛɨɬɚɟɬȼ ɪɟɡɭɥɶɬɚɬɟɩɨɹɜɥɹɸɬɫɹ ɡɧɚɱɢɬɟɥɶɧɵɟɚɦɩɥɢɬɭɞ
ɧɚɹ ɢ ɮɚɡɨɜɚɹ ɩɨɝɪɟɲɧɨɫɬɢ ɂɫɩɨɥɶɡɭɸɬ ɢɯ ɜ ɨɫɧɨɜɧɨɦ ɞɥɹ ɢɡɦɟɪɟɧɢɹ
ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɦɚɲɢɧ ɢ ɦɟɯɚɧɢɡɦɨɜ ɩɨɞɤɥɸɱɚɹ ɤ ɜɨɥɶɬ
ɦɟɬɪɭɫɨɲɤɚɥɨɣɨɬɝɪɚɞɭɢɪɨɜɚɧɧɨɣɜɨɛɨɪɨɬɚɯɜɦɢɧɭɬɭ
nɢɡɦɟɧɹɟɬɫɹɱɚɫɬɨɬɚɬɨɤɚɜɫɬɚɬɨɪɟfɢɡɦɟɧɹɟɬɫɹɢɧɞɭɤɬɢɜɧɨɟ
x = 2SfL ɤɚɤ ɫɚɦɨɝɨ ɬɚɯɨɝɟɧɟɪɚɬɨɪɚ ɬɚɤɢ ɧɚɝɪɭɡɤɢɧɚ
om om
ɗȾɋɨɩɚɫɧɚɹ ɞɥɹ
ɗȾɋɞɟɣ
n
ɋɩɟɰɢɚɥɶɧɵɟɫɢɧɯɪɨɧɧɵɟɞɜɢɝɚɬɟɥɢ
ɪɨɧɧɵɟ ɞɜɢɝɚɬɟɥɢɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɨɬ ɞɟɫɹɬɵɯ ɞɨɥɟɣ
ɋɢɧɯ
ɜɚɬɬɚɞɨ ɧɟɫɤɨɥɶɤɢɯɫɨɬɟɧɜɚɬɬɲɢɪɨɤɨɢɫɩɨɥɶɡɭɸɬɫɹɜɫɢɫɬɟɦɚɯɚɜɬɨ
ɦɚɬɢɤɢ ɬɟɥɟɦɟɯɚɧɢɤɢ ɫɱɟɬɧɨɪɟɲɚɸɳɟɣ ɬɟɯɧɢɤɟ ɜ ɦɟɞɢɰɢɧɟ ɛɵɬɭɢ
ɞɪɭɝɢɯ ɩɪɢɜɨɞɚɯ ɝɞɟ ɬɪɟɛɭɟɬɫɹ ɩɨɫɬɨɹɧɧɚɹ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ȼ ɡɚɜɢ
ɫɢɦɨɫɬɢɨɬɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣɫɢɫɬɟɦɵɞɜɢɝɚɬɟɥɢɩɨɞɪɚɡɞɟɥɹɸɬɧɚɫɥɟ
ɞ
ɞ
ɞɭɸɳɢɟɜɢɞɵ
ɋɢɧɯɪɨɧɧɵɟ ɞɜɢɝɚɬɟɥɢ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɦɚɝɧɢɬɚɦɢ ɧɚ ɪɨɬɨɪɟ
(ɋȾ ɫ ɉɆ).
ȿɫɥɢɩɪɢɧɹɬɶr
= 0ɬɨɜɪɚɳɚɸɳɢɣɦɨɦɟɧɬɦɨɠɧɨɧɚɣɬɢɩɨ
1
ɮɨɪɦɭɥɟ
2
mUE
0
Msin sin2
ZZ
1d 1 q d
TT
x2xx
§·
mU 1 1
¨¸
¨¸
©¹
ɆɆ.
ɨɫɧ ɞɨɩ
ɉɨɫɤɨɥɶɤɭ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɚ ɥɢɲɶ ɧɟɦɧɨɝɨ
ɛɨɥɶɲɟ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜɨɡɞɭɯɚ ɬɨ ɫ ɭɱɟɬɨɦ ɦɚɝɧɢɬɧɵɯ ɫɜɨɣɫɬɜ ɩɭɬɟɣ
ɩɨɤɨɬɨɪɵɦɡɚɦɵɤɚɸɬɫɹɩɨɬɨɤɢɩɪɨɞɨɥɶɧɨɣɢɩɨɩɟɪɟɱɧɨɣɪɟɚɤɰɢɢɹɤɨɪɹ
xd < xq. ɉɨɷɬɨɦɭ ɭɝɥɨɜɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɞɜɢɝɚɬɟɥɹɫ ɩɨɫɬɨɹɧɧɵɦɢ ɦɚɝ
ɧɢɬɚɦɢɪɢɫɚɫɭɳɟɫɬɜɟɧɧɨɨɬɥɢɱɚɟɬɫɹ ɨɬ ɭɝɥɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɞɜɢɝɚɬɟɥɹɫɨɛɦɨɬɤɨɣɜɨɡɛɭɠɞɟɧɢɹɭɤɨɬɨɪɨɝɨ
Ɇ
ɚ
Ɇ
ɨɫɧ
ɛ
Ɇ
ɨɫɧ
xd > x
ɪɢɫɛ
q
0
0
ɚ
0
ɪɟɡ
T
Ɇ
Ɇ
S
ɨɩ
ɊɢɫɁɚɜɢɫɢɦɨɫɬɢɦɨɦɟɧɬɨɜɨɬɭɝɥɚT
ɋȾɫɉɆɚɢɫɨɛɦɨɬɤɨɣɜɨɡɛɭɠɞɟɧɢɹɛ
S
ɨɩ
T
0
ɬɨɪ
ɊɢɫɁɚɜɢɫɢɦɨɫɬɢ
0 IVɞɥɹɞɜɢɝɚɬɟɥɹ
ɫɩɨɫɬɨɹɧɧɵɦɢɦɚɝɧɢɬɚɦɢ
V
ȿɫɬɶɨɬɥɢɱɢɹɢɜɩɭɫɤɨɜɨɣɯɚɪɚɤɬɟɪɢɫɬɢɤɟɜɤɨɬɨɪɨɣɩɨɹɜɥɹɟɬɫɹ
ɞɨɫɬɚɬɨɱɧɨɝɥɭɛɨɤɢɣ ɩɪɨɜɚɥ ɜɵɡɜɚɧɧɵɣɬɟɦ ɱɬɨ ɩɨɤɚ ɫɤɨɪɨɫɬɶ ɪɨɬɨɪɚ
ɧɟ ɞɨɫɬɢɝɥɚ ɫɢɧɯɪɨɧɧɨɣ ɩɨɫɬɨɹɧɧɵɟ ɦɚɝɧɢɬɵ ɢɧɞɭɰɢɪɭɸɬ ɜ ɨɛɦɨɬɤɟ
ɫɬɚɬɨɪɚ
ɗȾɋ ɢ ɬɨɤɢɱɚɫɬɨɬɨɣ ɨɬɥɢɱɧɨɣɨɬ ɱɚɫɬɨɬɵɫɟɬɢ ɗɬɢɬɨɤɢ ɡɚ
ɦɵɤɚɹɫɶɱɟɪɟɡ ɢɫɬɨɱɧɢɤ ɢɜɡɚɢɦɨɞɟɣɫɬɜɭɹɫ ɩɨɥɟɦɦɚɝɧɢɬɚ ɪɚɡɜɢɜɚɸɬ
ɬɨɪɦɨɡɧɨɣɦɨɦɟɧɬɪɢɫ
ɋɢɧɯɪɨɧɧɵɟ ɪɟɚɤɬɢɜɧɵɟ ɞɜɢɝɚɬɟɥɢ – ɞɜɢɝɚɬɟɥɢ ɜɪɚɳɚɸɳɢɣ
ɦɨɦɟɧɬɤɨɬɨɪɵɯ ɫɨɡɞɚɟɬɫɹ ɬɨɥɶɤɨ
ɆȾɋɫɬɚɬɨɪɚ ɡɚɫɱɟɬ ɪɚɡɧɨɣɦɚɝɧɢɬ
ɧɨɣɩɪɨɜɨɞɢɦɨɫɬɢɩɨɩɪɨɞɨɥɶɧɨɣɢɩɨɩɟɪɟɱɧɨɣɨɫɹɦɦɚɲɢɧɵɉɪɢɧɰɢɩ
ɞɟɣɫɬɜɢɹ ɬɚɤɢɯɞɜɢɝɚɬɟɥɟɣ ɨɫɧɨɜɚɧɧɚ ɭɩɪɭɝɢɯɫɜɨɣɫɬɜɚɯ ɫɢɥɨɜɵɯ ɥɢ
ɧɢɣ ɩɨɥɹ ɩɨ ɝɢɩɨɬɟɡɟ Ɏɚɪɚɞɟɹ ɨɧɢ ɩɨɞɨɛɧɵ ɪɟɡɢɧɨɜɵɦ ɠɝɭɬɚɦ
ɉɪɢ
r1 = 0ɦɨɦɟɧɬ ɛɭɞɟɬ
2
M
mU 1 1
ɋɢɧɯɪɨɧɧɵɟ
ɪ
()sin2.
2xx
Z
1q d
ɝɢɫɬɟɪɟɡɢɫɧɵɟ ɞɜɢɝɚɬɟɥɢ.
T
Ɇɨɦɟɧɬ ɝɢɫɬɟɪɟɡɢɫɧɨɝɨ
ɞɜɢɝɚɬɟɥɹɨɛɭɫɥɨɜɥɢɜɚɟɬɫɹɹɜɥɟɧɢɟɦɝɢɫɬɟɪɟɡɢɫɚɢɞɟɣɫɬɜɢɟɦɜɢɯɪɟɜɵɯ
ɬɨɤɨɜɜɪɨɬɨɪɟ
ɝɞɟ
ɆɊ/ Ɋ / Ɋ s/ ɆɆ,
Ɋ
, Ɋ
ɝ.ɤ
±ɩɨɬɟɪɢɧɚɝɢɫɬɟɪɟɡɢɫɢɜɢɯɪɟɜɵɟɬɨɤɢɜɪɨɬɨɪɟɩɪɢɩɭɫɤɟ
ɜɬ.ɤ
ZZ Z
ɷɦ 1 ɝ.ɤ 1 ɜɬ.ɤ 1, ȽȼɌ
ɞɜɢɝɚɬɟɥɹ
Ƚɢɫɬɟɪɟɡɢɫɧɵɟ ɞɜɢɝɚɬɟɥɢ ɦɨɝɭɬ
ɪɚɛɨɬɚɬɶ ɤɚɤ ɫɢɧɯɪɨɧɧɵɟ ɢ ɤɚɤ ɚɫɢɧ
ɯɪɨɧɧɵɟ ɩɥɚɜɧɨ ɩɟɪɟɯɨɞɹ ɢɡ ɨɞɧɨɝɨ
ɪɟɠɢɦɚɜɞɪɭɝɨɣɉɨɤɚ ɦɨɦɟɧɬ ɧɚɝɪɭɡ
ɤɢ ɧɟ ɩɪɟɜɵɲɚɟɬ ɡɧɚɱɟɧɢɹ ɜ ɬ ©
ɫª
ɪɢɫ ɫɤɨɥɶɠɟɧɢɟɪɚɜɧɨ Ⱦɜɢɝɚ
ɬɟɥɶ ɪɚɛɨɬɚɟɬ ɤɚɤ ɫɢɧɯɪɨɧɧɵɣ ȿɫɥɢ
ɦɨɦɟɧɬ ɩɪɟɜɵɫɢɬ ɷɬɨɡɧɚɱɟɧɢɟ ɞɜɢɝɚ
ɬɟɥɶ ɩɟɪɟɣɞɟɬ ɜɚɫɢɧɯɪɨɧɧɵɣ ɪɟɠɢɦ ɢ
ɛɭɞɟɬɪɚɛɨɬɚɬɶɫɨɫɤɨɥɶɠɟɧɢɟɦ
s
a
ȼ ɨɬɥɢɱɢɟ ɨɬ ɞɪɭɝɢɯ ɫɢɧɯɪɨɧ
0
D
Ϭ ϭ
ɊɢɫɆɟɯɚɧɢɱɟɫɤɚɹ
ɝɢɫɬɟɪɟɡɢɫɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɢɟɟɫɨɫɬɚɜɥɹɸɳɢɟ
0
D
ʧ
D
ʦ˃
Ɛ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɫɢɧɯɪɨɧɧɨɝɨ
Ɛ
ɧɵɯ ɞɜɢɝɚɬɟɥɟɣ ɝɢɫɬɟɪɟɡɢɫɧɵɟɧɟ ɢɦɟ
ɸɬɩɭɫɤɨɜɨɣɨɛɦɨɬɤɢ
Ɋɚɫɫɦɨɬɪɟɧɧɵɟɫɢɧɯɪɨɧɧɵɟ ɞɜɢɝɚɬɟɥɢɜɵɩɨɥɧɹɸɬɫɹɛɟɡɨɛɦɨɬɤɢ
ɜɨɡɛɭɠɞɟɧɢɹ ɧɚɪɨɬɨɪɟ ɱɬɨ ɡɧɚɱɢɬɟɥɶɧɨɩɨɜɵɲɚɟɬ ɢɯ ɷɤɫɩɥɭɚɬɚɰɢɨɧ
ɧɭɸɧɚɞɟɠɧɨɫɬɶɢɭɩɪɨɳɚɟɬɤɨɧɫɬɪɭɤɰɢɸ
ɒɚɝɨɜɵɟɞɜɢɝɚɬɟɥɢ
ɒɚɝɨɜɵɟ ɞɜɢɝɚɬɟɥɢ (ɒȾɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣɫɢɧɯɪɨɧɧɵɟ ɦɢɤɪɨɞɜɢɝɚɬɟɥɢ, ɩɪɟɨɛɪɚɡɭɸɳɢɟ ɭɩɪɚɜɥɹɸɳɢɣ ɫɢɝɧɚɥ ɜ ɞɢɫɤɪɟɬɧɨɟ ɭɝɥɨɜɨɟ
ɩɟɪɟɦɟɳɟɧɢɟ ɪɨɬɨɪɚ.
ɸɳɢɯ ɫɬɚɪɬɫɬɨɩɧɨɟ ɞɜɢɠɟɧɢɟ ɥɟɧɬɨɩɪɨɬɹɠɧɵɟ ɭɫɬɪɨɣɫɬɜɚ ɞɥɹ ɜɜɨɞɚ
ɢ ɜɵɜɨɞɚ ɢɧɮɨɪɦɚɰɢɢ ɫɱɟɬɱɢɤɢ ɫɬɚɧɤɢ ɫ ɩɪɨɝɪɚɦɦɧɵɦ ɭɩɪɚɜɥɟɧɢɟɦ
ɢɬɞ
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɢɩɚ ɷɥɟɤɬɪɨɧɧɨɝɨ ɤɨɦɦɭɬɚɬɨɪɚ ɭɩɪɚɜɥɟɧɢɟ
ɒȾɦɨɠɟɬɛɵɬɶ
Ɉɧɢɩɪɢɦɟɧɹɸɬɫɹɞɥɹɩɪɢɜɨɞɚ ɦɟɯɚɧɢɡɦɨɜ ɢɦɟ
x ɨɞɧɨɩɨɥɹɪɧɵɦ ɢɥɢ ɪɚɡɧɨɩɨɥɹɪɧɵɦ;
x ɫɢɦɦɟɬɪɢɱɧɵɦ ɢɥɢ ɧɟɫɢɦɦɟɬɪɢɱɧɵɦ;
x ɩɨɬɟɧɰɢɚɥɶɧɵɦ ɢɥɢ ɢɦɩɭɥɶɫɧɵɦ.
ɉɪɢɨɞɧɨɩɨɥɹɪɧɨɦɭɩɪɚɜɥɟɧɢɢɧɚɩɪɹɠɟɧɢɟɤɚɠɞɨɣɮɚɡɵɢɡɦɟɧɹ
ɟɬɫɹɨɬ
ɤɨɦɦɭɬɚɰɢɢɡɚɞɟɣɫɬɜɭɟɬɫɹ ɨɞɢɧɚɤɨɜɨɟ ɱɢɫɥɨɨɛɦɨɬɨɤ ɢ
ɧɵɦ
ɧɹɟɬɫɹ ɬɨɥɶɤɨ ɜ ɦɨɦɟɧɬɵ ɩɨɫɬɭɩɥɟɧɢɹ ɭɩɪɚɜɥɹɸɳɢɯ ɢɦɩɭɥɶɫɨɜ ɉɪɢ
ɨɬɫɭɬɫɬɜɢɢ ɭɩɪɚɜɥɹɸɳɟɝɨ ɫɢɝɧɚɥɚ ɨɛɦɨɬɤɚ ɢɥɢ ɝɪɭɩɩɚ ɨɛɦɨɬɨɤ ɧɚɯɨ
ɞɢɬɫɹ ɩɨɞ ɧɚɩɪɹɠɟɧɢɟɦ ɪɨɬɨɪ ɮɢɤɫɢɪɭɟɬɫɹ ɩɨɥɟɦ ɨɛɦɨɬɨɤ ɉɪɢ
ɩɭɥɶɫɧɨɦ
ɨɬɪɚɛɨɬɤɢ ɲɚɝɚ ɩɨɫɥɟ ɱɟɝɨ ɨɧɨɫɧɢɦɚɟɬɫɹ ɢɪɨɬɨɪ ɭɞɟɪɠɢɜɚɟɬɫɹɜɡɚ
ɞɚɧɧɨɦ ɩɨɥɨɠɟɧɢɢ ɥɢɛɨɪɟɚɤɬɢɜɧɵɦ ɦɨɦɟɧɬɨɦ ɥɢɛɨɜɧɟɲɧɢɦ ɮɢɤɫɢ
ɪɭɸɳɢɦɭɫɬɪɨɣɫɬɜɨɦ
ɞɟɥɚɯɨɞɧɨɝɨɨɛɨɪɨɬɚɪɨɬɨɪɚ
ɩ
ɬɨɪɚ
ɢɦɩɭɥɶɫɨɜ ȼ ɡɚɜɢɫɢɦɨɫɬɢɨɬ ɷɬɨɝɨ ɪɚɡɥɢɱɚɸɬɫɥɟɞɭɸɳɢɟ ɪɟɠɢɦɵ ɪɚ
ɛɨɬɵ ɲɚɝɨɜɵɯ ɞɜɢɝɚɬɟɥɟɣ
ɜɢɜɲɢɣɫɹ; ɩɟɪɟɯɨɞɧɵɣ
0ɞɨ+Uɚɩɪɢɪɚɡɧɨɩɨɥɹɪɧɨɦ±ɨɬ–Uɞɨ+U
ɍɩɪɚɜɥɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ
ɫɢɦɦɟɬɪɢɱɧɵɦ ɟɫɥɢ ɜ ɤɚɠɞɨɦ ɬɚɤɬɟ
ɧɟɫɢɦɦɟɬɪɢɱ-
±ɟɫɥɢɪɚɡɧɨɟ
ɉɪɢ
ɩɨɬɟɧɰɢɚɥɶɧɨɦ ɭɩɪɚɜɥɟɧɢɢ ɧɚɩɪɹɠɟɧɢɟɧɚ ɨɛɦɨɬɤɚɯ ɢɡɦɟ
ɭɩɪɚɜɥɟɧɢɢɧɚɩɪɹɠɟɧɢɟɧɚɨɛɦɨɬɤɢɩɨɞɚɟɬɫɹɬɨɥɶɤɨɧɚɜɪɟɦɹ
ȼɞɜɭɯɩɨɥɸɫɧɨɣɦɚɲɢɧɟɱɢɫɥɨɭɫɬɨɣɱɢɜɵɯɩɨɥɨɠɟɧɢɣ
ɫɥɟɞɭɸɳɟɟm±ɱɢɫɥɨɮɚɡ
ɩɪɢɨɞɧɨɩɨɥɹɪɧɨɦɫɢɦɦɟɬɪɢɱɧɨɦɭɩɪɚɜɥɟɧɢɢ
ɩɪɢɪɚɡɧɨɩɨɥɹɪɧɨɦɫɢɦɦɟɬɪɢɱɧɨɦɭɩɪɚɜɥɟɧɢɟɦ
ɩɪɢɪɚɡɧɨɩɨɥɹɪɧɨɦɧɟɫɢɦɦɟɬɪɢɱɧɨɦɭɩɪɚɜɥɟɧɢɢ
ɇɟɫɢɦɦɟɬɪɢɱ
ȼɦɧɨɝɨɩɨɥɸɫɧɵɯ
ɪɨɩɨɪɰɢɨɧɚɥɶɧɨɱɢɫɥɭɩɚɪɩɨɥɸɫɨɜ
Ɋɟɠɢɦɵɪɚɛɨɬɵɲɚɝɨɜɵɯɞɜɢɝɚɬɟɥɟɣɏɚɪɚɤɬɟɪɞɜɢɠɟɧɢɹɪɨ
ɧɨɟɭɩɪɚɜɥɟɧɢɟɜɨɡɦɨɠɧɨɬɨɥɶɤɨɩɪɢP
ɒȾɱɢɫɥɨ ɭɫɬɨɣɱɢɜɵɯɩɨɥɨɠɟɧɢɣ ɜɨɡɪɚɫɬɚɟɬ
ɪ.
n = m
n = 2m
n = 4m
t
ɒȾɨɩɪɟɞɟɥɹɟɬɫɹɱɚɫɬɨɬɨɣ ɢɯɚɪɚɤɬɟɪɨɦɢɡɦɟɧɟɧɢɹɭɩɪɚɜɥɹɸɳɢɯ
ɫɬɚɬɢɱɟɫɤɢɣ; ɤɜɚɡɢɫɬɚɬɢɱɟɫɤɢɣ; ɭɫɬɚɧɨ-
ɢɦ-
nɜɩɪɟ
ɋɬɚɬɢɱɟɫɤɢɣ ɪɟɠɢɦ±ɷɬɨɪɟɠɢɦɩɪɢɤɨɬɨɪɨɦɩɨɨɛɦɨɬɤɚɦɫɬɚ
ɬɨɪɚ ɩɪɨɬɟɤɚɟɬ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ ɫɨɡɞɚɸɳɢɣ ɧɟɩɨɞɜɢɠɧɨɟ ɜ ɩɪɨɫɬɪɚɧ
ɫɬɜɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟɪɨɬɨɪ ɧɟ ɜɪɚɳɚɟɬɫɹɉɨɞ ɞɟɣɫɬɜɢɟɦ ɧɚɝɪɭɡɤɢɪɨ
ɬɨɪɥɢɲɶɨɬɤɥɨɧɹɟɬɫɹɨɬɩɨɥɨɠɟɧɢɹ
Ɇ = 0ɧɚɧɟɤɨɬɨɪɵɣɭɝɨɥ
Ʉɜɚɡɢɫɬɚɬɢɱɟɫɤɢɣ ɪɟɠɢɦ ± ɷɬɨ ɪɟɠɢɦ ɨɬɪɚɛɨɬɤɢ ɟɞɢɧɢɱɧɵɯ
ɲɚɝɨɜ ɩɪɢ ɤɨɬɨɪɨɦ ɩɟɪɟɯɨɞɧɵɟ ɩɪɨɰɟɫɫɵ ɨɬ ɩɪɟɞɵɞɭɳɟɝɨ ɬɚɤɬɚ ɤɨɦ
ɦɭɬɚɰɢɢ ɩɨɥɧɨɫɬɶɸ ɡɚɬɭɯɥɢ ɢ ɫɤɨɪɨɫɬɶ ɪɨɬɨɪɚ ɜ ɧɚɱɚɥɟ ɫɥɟɞɭɸɳɟɝɨ
ɲɚɝɚ ɪɚɜɧɚ ɧɭɥɸ Ɉɧ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɫɬɚɪɬɫɬɨɩɧɵɯ ɥɟɧɬɨɩɪɨɬɹɠɧɵɯ
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]