, , , . , , .
1(t) - h(t) (.1.2)
. . , .
- d(t) - k(t) (.1.3)
- d(t) , (S=1). - . .
- (.1.4)
Xm jx, , Ym jy.
Ym jy y(t) w x(t). : (-) (-):
: - () , ;
: - .
W(p) (. 1.3).
1. .
2. .
3. . ?
4. , , .
1.2. ,
, . , , .
, , h(p) 1(p)=1/p,
,
(1.9)
(1.10)
, p, . :
|
|
(1.11)
, p - h(p), k(p) .., t - h(t), k(t) ..
, .
, , () .
I. .
.
1.
p
:
, :
(1.12)
2.
h(p) , 1.1:
(1.13)
p (1.13) , :
p, :
, , :
h (p) :
.1.1 , :
(1.14)
:
(1.15)
3.
.
h (t) , 1:
(1.16)
h (t) h=3, (1.16) .
.
, h (t) 5%- , . (1.16) , , 1. t1, 1- ,
2- :
t t1, t2, . t . , .
Δt , . : 5-10 , " " .
(1.17) t1 h (t), 1- , Δt1 0,32...0,64 . , t2, Δt2=0,04...0,08 . t 0 0,4 Δt1=0,08 , 3,2 - Δt2=0,4 .
|
|
k (t) (1.15) t, h (t).
1.2.
1.2
t | 0 | 0,08 | 0,16 | 0,24 | 0,32 | 0,4 | 0,8 | 1,2 | 1,6 | 2 | 2,4 | 2,8 | 3,2 | |
h (t) | 0 | 3 | ||||||||||||
k (t) | 1 | 0 |
h (t) k (t) (.1.5).
II.
, , .
, .
, , h (p) :
, , ,
, , :
:
.1.1 :
(1.17)
:
(1.18)
:
h (t)(1.17) :
(1.19)
sin:
(1.20)
0,242 0,97 cosg sing, , .. 1: 0,2422+0,972=1. sinw t cosw t ( w=2) (3.28) , .
C (1.20) h (t) :
,
( g ).
:
(1.21)
sin 1, , , :
(1.22)
. h (t), .. k (t):
k (t) =0, 1,875e-0,5tsin2t+e-0,5tcos2t=0, tg2t=-1/1,875=-0,533,
te=(arctg(-0,533)+pn)/2=-0,245+pn/2 (), n=1,2,3...
te: te1=1,325 c, te2=2,9 c; te3=4,465 c, te4=6,03 c ..
:
t=6,1 D t=1; t = 0..7.
(.1.3) t h (t) k (t) (.1.6).
1.3
t | 0 | 1,325 | 2 | 2,9 | 3,7 | 4,465 | 5 | 6,03 | 7 | ∞ |
h (t) | 0 | 1 | ||||||||
k (t) | 1 | 0 |
1. h (t) k (t),
2. h (t).
3. t h (t) ?
4. t h (t) ?
5. h (t)?
1.3.
: W (p) , W (jw) (), p jw.
|
|
.
:
(1.22)
: :
A (w) - ();
j (w) - ().
:
W(jw) =P (w) +jQ (w) (1.23)
: - () - ().
(.1.7).
A, j, P Q ( w ):
(1.24)
.
(1.25)
(1.25) .
(1.25) , :
- : (1.26)
- : (1.27)
, - :
(1.28)
, A (w), j (w), P (w) Q (w) . , , :
- w ( w 0 ¥)?;
- Dw ?
, () w Dw. , , .
:
1. , , , w 0 ¥.
, . :
P (w) =0 Þ -w4+2w2+9=0 Þ w=2,04, .. w5=2,04, .1.7;
Q (w) =0 Þ w(0,5w2+1,5) =0 Þ w=0, .. () w1=0.
P (w) Q (w) w=¥.
2. j (¥), ,
j (¥) =-90o (n-m), (1.29)
n m - p, , .
(.1.7).
3. , 5- (.1.4).
1.4
w | w1=0 | w2 | w3 | w4=2,04 | w5 | w6 | w7 | w=¥ |
P (w) | 0 | 0 | ||||||
Q (w) | 0 | 0 | ||||||
A (w) | 0 | |||||||
j (w) | 0 | -90o | -180o |
- w. (1.26)...(1.28).
w2 w3 , 4- . , , 4- , .. j 30 ( 30, , , 30 10). , 0 2,04 ( !) j. 30 10, ( - ) w2. 60 10, w3. w. w5...w7 3- .
|
|
. P (w) Q (w) W (jw)(.1.7), A (w) j (w) (.1.8).
(4.7) j , . - ARCTG (*), - -90 +90. , arctg, Q P . P>0, 1- 4- , P<0, 2- 3- . =0 90:
sign (Q)- Q.
.
1. "" "" ? ?
2. (ω) φ (ω)?
3. ?
4. φ (ω) ?
1.4. -
-
- (). ( ) , . () , .
, (1.30)
, , :
- , , ω , L (ω) ;
- .
W (p)
(1.31)
,
(1.31)
(1.32)
(1.32)
(1.33)
, (1.31) - :
1) (1.34)
(1.35)
. (1.34) 3 . , (.1.9).
2) (1.36)
(1.37)