1.
2.
3. .
1.
.. .. , .
, , , , , . .
, .
, , . , , .. , .
:
1) , .
, .
2) , , .
3) , , ( , ),
4) ,
5)
6) , .. ,
7) .
, w .
. 1. :
- ; -
.. ,
y = F(x), (1)
w a, ..
x = sin y, (2)
y = wt,
|
|
y1 = 1 sin(y + y1), (3)
1 ,
y1 - ;
.
. 2.
, .
(1) F(x) (2)
y1 = b1F siny + a1F cosy, (4)
b1F, a1F - , ( ), :
x(t)= siny, → ;
(p = d/dt):
px = ωcosy, →
..
q q¢
q = b1F/, q¢ = a1F/. .
, (5)
(1) (5) .
, (5), . , q q¢ w . , , .
q(, ω) q′(, ω) w ,
q() q′() ,
q′() = 0.
- .
- - |
:
:
. (6)
:
j, -
(7)
|
|
A(w, ) = mod W(jw, ) =
y(w, a) = arg W(jw, A) = arctg[q¢(, w)/q(, w)].
(3) (2) , ..
1 = ´A(w, ); y1 = y(w, ).
2.
g=0, = =
:
.
ω, , ω .
:
│W(,jω)│*│W(jω)│= 1;
arg [W(,jω)W(jω)] = -(2k+1) π, k =0,1,2,.
:
(, ω) * (ω) =1;
φ(,ω) + φ(ω) = -(2k+1) π, k =0,1,2,.
3.
.
.
(. 1),
:
.
:
(8)
. , , . , - , . : = 0 sin w0t, .. (8) 0 w0.
, .
(8).
, 0 w0 li = jw0 li+1 = -jw0.
.
.
3.1
p jw
(9)
:
, .
(10)
. , .
(11)
, , .
0 w0 (10) , , .
|
|
(11) , , k . (11) k , .. :
(12)
a0 = f(k), w0 = f(k) k, .
3.2 . ( , )
, [-1, j0]. , ..
W(jw, a) = -1. (13)
,
W(jw, a) = W(jw)´W(jw, a). (14)
(13)
W(jw) = - . (15)
(15) W(jw) , (. 3).
. W(jw), .
, .
. 3.
:
w0 a 0 , - , a 0+D a , , a 0-D a.
. 3 , , a 3 < a 0 < a 4 .
3.3
(13)
mod W(jw)W(jw, ) = 1;
arg W(jw)W(jw, ) = - (2k+1)p, k=0, 1, 2,...
L(w) + L(w, ) = 0; (16)
y(w) + y(w, ) = - (2k+1)p, k=0, 1, 2,... (17)
(16) (17) 0 w0 (8) L(w), y(w) L(w, ), y(w, ).
w0 0 , (8) .
, w = w0 = 0 + D a = 0 - D a, D a > 0 - . 0 + D a 0 - D a .
|
|
q¢() , , y(), .
(18)
, :
L(w) = - L(a); (19)
y(w) = - (2k+1)p, k=0, 1, 2,... (20)
(20) w = w0 , (19) - = 0.
. (. 4).
(18), .. [15]:
w = w0 a = a 0 , D a > 0 ( ) ( ) y(w) -p , L(w)³-L(w0, a 0+D a), , L(w)³-L(w0, a 0-D a).
. 4 . w01, w02 w03, y(w) -1800. a 01, a 02 a 03 (19) -L(w01, a), -L(w02, a) -L(w03, a).
. 2.12.
, . 4, . w = w01 a = a 01 , 1, L(w)³-L(w01, a 01+D a), y(w) -1800, 2, L(w)³-L(w01, a 01-D a), y(w) -1800. w = w02 a = a 02 , , L(w)³-L(w02, a 02+D a), y(w) -1800. w = w03 a = a 03 , , L(w)³-L(w03, a 03+D a), y(w) -1800, , L(w)³-L(w03, a 03-D a), y(w) -1800.
w03 a 03, - w01 a 01.