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. . ...

-- [ 4 ] --

, 0 = -^ - m ( i ) A c o s ( o V + )- ( 4.4.2 ) , m ( t ) R ( ) = [ m (t)m (t t ) dt = l im - Zt 1 ) A c o s [ 0 (t + - 5- c o s 0.

\ A c o s ( (/ + ] d t = lim ) + r- Z 1 _j!

(4.4.3 ) , . , .

( 4.4. 1 ) R y = - J - c o s 0 + R x ( ). ( 4.4.4 ) , R x ( ) R y (x) .

4.4. , 2, , , , , l im R x ( ) = 0.

-* , y(t) , . . , R x ( x ) , R y {x) . , m (t). .

, ( ) X ( t ). X { t ), , t , .

X ( t ) , .

, m ( t ) ( 4.4.2 ). m ( t ) (0 = Z A n c o s ( nt + ). ( 4.4. 5 ) ( o 0) ( ) .

R m {%) R m = \ m(t) m {t + ) dt = H m -5=r T-oa _T - i l J OO oo K A k 5 cos (t + p] dt.

= J i r n -g f- X S + Ի) c o s t) + T-*oo - xi = 0 ( 4.4.6 ) 4 . k n= k -^- c o s c d t Rm = Y - ? r cos ( 4.4.7 ) j ~ , , . , , .

, , .

. 0 \ 2...

, 2 ( 4.4.7 ) , ( 4.4.5 ).

/? ( ) ( 4,4.7 ), ( ^2 \ cosco t. ( 4.4.8 ).. fl ( 4.4. 8 ) .

, . , , .

, . y(t) ( L, L ] , , , . , . 5 / 6 y(t). , , 4. .4 , .

. ( /) = *, ( /) + ,(/) ;

' if) = 2 (t) + m 2 ( /), ( 4.4.9 ) m i{ t ) m 2 (t) ;

jci (t) 2 ( t ) .

R y, v 20 0 = Rm\m-z 0 0 + R x 2m ( ).

i /?*,*2.() + ( ) + ( 4.4.1 0 ) , , . .

RxiKi ( ) = Rxi m2 ( ) = Rxitrii ( ) == 0, RyiyA^) = Rmxrnir). ( 4.4.1 1 ) , .

, ( 0 = c o s ((/ + ;

2 (t) 2 c o s { a Q + t 2) ( 4.4.1 2 ) Rm,m2( ) = \ A i COS (a0t + lim ,) 3 X - _J (t 2] d t = -j A i A 2 c o s [0 + X COS + ) + (2 1)], ( 4.4.1 3 ) . . , .

R m i m2 0 0 = R m im, ( ) = - J A i A 2 c o s [0 ( 2 ^ ]. ( 4.4. 1 4 ) . , 4 . .

, . . . .

( 4.4.2 ), 1 2 \ c o s R () d x 5 ( ) == \ c o s X Q 0).

X c o s 0 d x = ( ( 4.4.1 5 ) , - , . . 0. , {t).

( 4.4. 5 ) - ) 5 ( )= = ( 4.4.1 6 ) (1= . . , .

;

, , [ 0, ]. ( 4.4. 2 ) % % 1 S () = \ R () cos d x = \ cos co0r X X COS = 4 ~ s in -(a - - m) (a i co0 + -Sin e + (o0 4. 4. 1 7 )J ( 4 L = . S(co0 ^ 4 i ( ^ + - - | g ^ - ).

) (4.4.18) 4. .4 , , , , , w , , .

. ( 4.4.1 ), S y (co) = 5xN + 5 m (0 ). ( 4.4.1 9 ) S *(ft ) S m (co) .

, , m (t ), , S * (c o ) . , .,;

, . . , .

, , , , .

.

( , 0,0 5 ), , y ( t ) , . - , , , , .

4. , .

. . , X i ( t ) X 2 (t) R XtX ) R XlXl ( ) = # ( ) ( 4.4. 1 3 ) ( 4. 4. 1 4 ). ( ) :

Q (w ) . ( 3.3. 5 ) ( 3.3. 6 ) 2- S '* ( ~ )1 co s d x = ]. ( 4. 4. 2 0 ) ) 3 s in d x = Q ( ) = ~ ]. ( 4. 4. 2 1 ) , = = t g (1 ). ( 4.4.2 2 ) ( 4.4.2 3 ) , xz(t) , :

.

x(t), , ( 4.4. 2 3 ) qn 2, (t ). x 2 (t) x(t). x(t) , , .

x (t) , x (t ) , ( 4.4.2 3 ).

, 4.4. 2 (to) + () Q ( 4.4.2 4 ) S x, () S X2 ( ) x (t) x 2(i) ( 4.4. 1 2 ) = F (0) = V s i n 2 ( ) + c o s ( ) = 1 ( 4.4.2 5 ) , ( ) 1 x(t) x 2 (t) ( 4.4.2 3 ). , . . . , .

5.1. ( ) . : ;

;

, . .

X ( t ) , [, 6 ], m x ( t ) = 0 R x { i u h ), t U ^ [ a, b ] \ { * (0 } . X ( t ) ( 5.1. 1 ) .

( 5.1. 2 ) X { t ) X n {t). ;

( 5.1.3 ) .

8 ( 5.1.4 ) , , {& ( } . , 5.1. { * (0 } , . , cpi ( t ), (0. ! (0 . ^ 1, 2{t),..., qn(t) ) . X (t) (t) kS 1 ^ ( ~ .

, , , .

X(t) tu fa, tm ;

{ * ( 0 } , t\, fa, X(t) - X(Xi,X2,..., X m ), ^ (ty), 2= (t2), X m= X(tm).

* (0 - (? * ) * (/) ti, . .

2= *(^)- ' = ( ).

a(oi, ..., ) b (bi, b2,..., ܄) 2, , ( = aibi = ) * (5.1.5) i= l , (5.1.6) / ? = 1 5. . . .

{ } * 1 k = l, , S,w - b k^L., X { } ~ (5.1.8) Aw = A k Ak = Z x $. ( 5.1.9 ) ( 5.1.8 ), , X { Z A kq$, i l, .

2,..., ( 5.1.1 0 ) X ( 5.1. 8 ) ( - ( i\ -" { I' ~ v w + ?, ˑ I f = \ x tx $ t f + iE l^ ?-2S I Z = k = i=1/= *l ti n m \ I, A kA t Z + Z ( 5.1. 1 1 ) J 1=1 i= I ( 5.1.1 1 ), ( 5.1. 7 ) X 2 2 / ;

5 -1 = 1 1=1 1= 1 &=1 &= 1 1= 1 / = S , 5.1.13) j= l = 1 1 / = R n X i = X ( t i ) X f = X ( t j ), . . -/ X.

5. .2 { *}, 2 , , , ( 5.1. 1 3 ) .

X, ( 5.1. 8 ) {*} .

, m ( 5.1. 1 4 ) , , {pfe}, bk .

5.2. (5.2.1 ) , ( 5. 2. 1 ) ' ( , ), , HR,-/II , 6, %k, \\Rij\\, %k |U?;

/I! ( 5. 2. 1 ), , .

, , .

= * , , K k Xi, I, m 10 - . 5. ...

( 5.2. 2 ) ? , ( 5.2. 3 ) cpf :

( 5.2.4 ) (5.2.5 ) ( 5.2. 5 ) ( 5.2.4 ), . ( 5.2.6 ) [ - \) ? | = Xk Xt 0, ^* = 0, . . 6 * ( \ = \U / { ' )1 )[ = /= ( 5.2.7 ) -1 - % , * (Pi. * ) , ( 5.2. 7 ) , .

, , .

1 , 2, ^ % ^ 3 ^ 2... ... .

.

. p(pi, ,..., ) E^/'pi'p- (5.2.9) = 1 /= 147 5.2. , Xi .

1, Xi.

, 1, 2, "-1 |/[, (5.2.9) |? /| , , = .

" . , ..., 1 2, | I, | I = ^5 + 22 +... + Cm.

(5.2.10;

(5.2.10) (5.2.9), mm mm mm *//= / 1 1= % =1 EWPi4' = i = l /= 1 m mm - A= I 4 l 1Ri,vhb i = /= f5.2.m .

(5.1.5) , m m m m ^/ /=/=1 4 [ 2= | * f = i / m m = v!*iE 4 =*, (5.2.12) - i fe=i (5.2.9) , = 1, Cj.-l, c2=... = = c m = 0.

..., 1, 2, "-1, (5.2.10) ci = ... = cn-i = 0 (5.2.12) mm m E*i/4W/- v i v= -2 5 - i = 1 /= (5.2.13) = . { 4 X (5.1.8) ' I Ri, I, I I | 4 = E * - =E v 2 5- -1) .

, , .

* 5. ...

{} * ( 5.1.8 ) . , R iM = \ 0 k I. ( 5. 2. 1 5 ) = Z * Z X = il /=1 1= %k , . , , m \, 2,. ., . , , . ipfe ( ^, q,..., ^ ), . . xi, i 1,2,..., = (5.2.1 6 ) ( - |2 \ / .

* || /;

||. ||/?/|| Ak.

, \, ( ). -, . A k, A i, 2, , . . . , 149 5.2. , \, 2,, , , , X k.

**?} A lU i-t ]2 = 11=1, ( 5.2.1 ( 5.2. 1 4 ) LR - Z K ( 5.2.1 9 ) u h ------- ( 5.2.2 0 ) k~\ Zh dn = ~ ~ ( 5 - 2.2 1 ) k=i .

, .

. ( 5.2.1 ), , ( ) ! + Ri2p2 + + ^ = 1 21 + (R 22 /? 1 + - + -^2 ~ Rmffll + Rm2^2 + (Rmm + 0 (5.2.2 2 ) 150 5. . . .

( 5.2. 2 2 ) , , , , . . R u R l2 R im.

22 .

R R.2 1 R zm = 0. ( 5.2.2 3 ) ^ Rm Rm l Rm tn . ( 5.2.2 3 ), Plx m~ l - 21~2 -... - _ - = _ 0. ( 5.2. 2 4 ) , ||# /|| - ( 5.2. 2 4 ) , , , ,..., , . 1 (tp j,.],..., ^), ( 5. 1. 8 ), ( 5.2. 2 2 ) = 1 . 2, 3,..., ( 5.2. 2 2 ) = , ,...

..., ( 5.2. 2 4 ) ||/? (/|| i, . pi .

, . , . - . , , . .

, . . 151 5.2. , . , . , , . , , .

, , . , . .

, , .

, . . . (1 0 0 0, 8 5 0, 7 0 0, 5 0 0, 2 0 0 200 ) : 10 , 2 3 1 1 9 6 9 ;

1 0 , 1 5 2 4 1 9 5 9 .;

11 , 1 6 1 9 5 9 .;

1 0 , 2 0 2 9 1 9 5 9 . , . , .

' . 990 , . 152 5: . . .

. , , ||/? /||, . , ||/?,-|| .

, , 5. 1 2 % dn % dn % h h dn! 1 80, 559,8 195,2 66,2 184,7 73,5 625,2 80, 2 94, 93,4 59,4 86,3 40,8 89,7 115,5 95, 3 92, 22,5 97,6 14,2 21, 18,5 95,3 97, 4 10,6 99,2 96,3 5,5 97,5 10,7 99, 1.

1, 5 3,6 4, 99,7 8,7 99,3 99,2 99, 5, 6 100 100 2, 2,1 1,9 2, .

. , .

. , , .

. 5.1 d n ( .

( 5.2.2 1 ) ), ( 5.1. 8 ) 1, 2, 3,..., 6, . . , , . . ( 5.1.8 ).

, 90 % , . . .

6.1. .

, , .

, .

[, , t, x ( t ) X ( t ), . t -f- ) t + , 0.

.

, , , . . , x (t) x(t-\-T).

L, X(t + T)r=L[X(t)]. ( 6.1.1 ) X ( t - \ - T ) , (6.1.1 ).

L, , , .

[ 2] = M { [ X { t + T )-L [ X ( ]2}. ( 6.1.2 ) L, ( 6.1. 2 ) , , ( 6.1.1 ) . 6. , L , X ( t ) . , . . . . . , . . .

, , (t) .


6.2. ( ) , , X ( t ), . . x ( t ) t\, t2, tn(tl t2... tn) , , , X ( t ), .

x ( t n -\-T ), x ( t k) x(tn + T ) = t a kx ( t k), ( 6.2.1 ) k=i a k .

1, %..., , 2 ( a lt 2,..., ) = [ [ X (tn + )~ a kX (tk) J j ( 6.2.2 ) \, 2,..., , .

, .

, \, 2,..., ( ,,..., ) ? 155 6.2. ( ) ( 6.2. 2 ) j [ 2 ( 2,..., ) = (tn + ) - a kX ( * * ) ] * } = [ X 2 (tn + a kM [ X (tn + ) (/* )] + = )] - k~ a ka sM [ X (tk) X {ti)} = R x (0 ) - 2 a kR x (tn - t k + T) + + fe=i ;

= i fe=i + a ka,-Rx (tk - tj). ( 6.2.4 ) fe=i / = i ak ( 6.2.4 ) , Rx {{ tk + T) Z a-jRx (tk tj) = 0, 6=1,2, a. (6.2.5) ;

'=i ( 6.2. 5 ) 2 ( 2, , ). , \, 2,..., , ( 6. 2. 5 ), ( 6.2. 2 ) .

, ( 6.2. 5 ) \, az,...,. ( 6. 2. 1 ). R x ( t k tj) / , , , , .

2 ( \, 2,..., ) ctz, ., ( 6. 2. 5 ) * :

a ka j R x ( h t j ) = a kR x { t n tk + T). ( 6.2.6 ) k &= 1 / = I ( 6.2.4 ), 2 ( 2,..., ) = R x ( 0 ) a kR x (tn tk - f T). ( 6.2.7 ) ft=i ( 6.2.6 ), 2 ( 2,..., ) = R x (0 ) a ka sR x (tk - ts). ( 6.2.8 ) j=l 6. R x (%) , ( 6.2. 8 ) , , X ( t ). , ( ) , ( ). , , x ( t n -j-T) tn , . , , t = tn + t\, tz, tn, . . R x {tn tk + T ) = 0 k = 1, 2,..., , ( 6.2.5 ) a fR x (tk tf) = 0, k = 1, 2,..., . ( 6.2. 9 ) /= i , ( 6.2. 5 ) , , ( 6.2. 9 ) \ = 2 =... = = 0, ( 6.2.1 ) x ( t n ) = 0, . . , . 2 ( 2,..., a ) =.R x ( 0 ) .

, , t, /( ). t .

, U ( ) N i ( p i ), N 2 ( p 2), Nn{pn) JV0 ( p t ), .

, ( 6.2.1 ), f / ( p o ) = z W ( p fe).

fe~l a k P f t l) 2 CLjRu{\9k P /l) = - ( 6.2.1 0 ) /= 157 6.3. , 2, R u (l) /, I = |* / |, . . Nk(p_k) iV/(p/).

. .

, ( 6.2. 1 ) , . . , , , , flfe.

, , .


6.3. , , x ( t ) X ( t ) ( , 0, t R x { ).

, - x { t ) , .

x ( i -\- ) x ( t ) ( 5.1. 9 ) (6.3.1) x{t + T)= ^ g (t %)().

158 6. x(t) ( , t ), ( 6.3. 1 ) t x(t-\-T)= ^ g (t ) : ( ) d r, ( 6.3.2 ) , t g ( t ) .

( 6.3.2 ), g ( x ) x ( t x)dx, g(t) 0 t :(^ + 7 ) = ^ 0. ( 6.3.3 ) g (t), "I2 X(t + T )-\ g(r)X(t-x)dx I I ( 6.3.4 ) .

. ( 6.3.4 ).

o2= M [ X 2 (t + T)] 2 J g ( x ) M [ X { t + T)X(t-x)]dx + 5 d x ! jj g ( 2) [ X (t { ) X ( t 2)\ d x 2 = + 0.................................

= R X (0) 2 ^ g ( ) ( + x)dx + g ( x 2) R x ( x 2 x l) d x l d x 2^ jj 0 ( 6.3.5 ) , g ( t ), 2 .

g ( t ) 2 , , ( 6.3. 5 ) g ( t ) gi(t) = g(t) + aa(t), (6.3.6 ) ;

a ( t ) , 2 .

, 2, , = 0, . . = 0 .

159 6.3. ( 6.3.6 ) ( 6.3.5 ), 2 () =-- R x ( 0 ) 2 ^ [ g (t) + act (/)] R x ( T + x)dx + oo oo + \ dxx [g (tO + at(tj)] [g(2) + a (t2)] Rx c a t,) dx2= (t n o oo \g R x (0 ) - (x) R x ( T + T) d x + = oo oo + 5 $ g ( Ti ) ( T2 ) ^ * ( T2 TI) d T 1 rfT2 + oo oo " 2a \ - R x (T + x ) + \ g ( x ) R x (t - x) d x \ d t + + a ( 0 0 J oo oo (6.3.7) a 2 ij jj a ( t, ) a ( t 2) R x ( t 2 Tj) d x x d x 2.

+ ( 6.3. 7 ) a , ^ L = - 2 \ ()R x ( T + x)dx + g ( $ ( 2) d x 2 ^ R x ( 2 ,) d x t + + g ( 2) R x ( ^ ({) d x { ^ tj) dx2 = + 0. ( 6.3.8 ) t i %, 2 , ( 6.3. 8 ) 2 jj () R x ( + ) d x + 2 jj ( 2) d x 2 ^ g ( ^ R x ( 2 Tj) d x y = , 0 ( 6.3.9 ) .

$ (/) + ( ) * ( * - ) * | = 0. ( 6.3.1 0 ) L J 160 6. ( 6.3.1 0 ) a (t), g ( r )-Rx(?~ r ) d r = 0 t^O.

+ J ( 6.3.1 1 ) , ( 6.3. 1 1 ) 2 .

, .

, , 2, g (t ), ( 6.3.1 1 ). ' , , .

g ( t ), , ( 6.3. 3 ) g (t) .

2 . ( 6.3. 5 ) , ( 6.3.1 1 ), , 02= R X (0 ) J \ g { x x) g { x 2) R x {x2 x l ) d x l d x 2. ( 6.3.1 3 ) ( 6.3.1 3 ), 5 () X ( t ), R x ( 2 t i ) Rx(x2 ~ Ti) = ^ {^ ~ X,)S X () da. (6.3.14) 161 6.3. .

0 5 \ (T i) ( 2) R x ( ^ i) d x v d x 2 = = \ \ g ( T i ) g ( t 2) J e ia ix^ x'}S x () da d x y d x 2 = 00 ' oo p oo I r o "I e ia^ g ( x 2) d x 2 |s *. ( a O A o.

= $ J e -,e T,g ( f 1) d T I ( 6.3.1 5 ) -oo *-0 J L0 J ( 4.1.1 0 ), g ( T) e~ iaxd x = L(&) , g ( t ), . " , ^ g { ) d x ~ L * {) ( 6.3.1 6 ) , .

( 6.3.1 5 ) 5 S ( x i ) g ( x 2) R x ( \ X i)d x xdx2 = jj | L () |2 S x () dto. ( 6.3.1 7 ) ( 6.3.1 7 ) ( 6.3.1 3 ), a 2 = i?x ( 0 ) - 5 | L () |2 S x () d a = J [1 - | L(co) \2] S X ()cfco. ( 6. 3. 1 8 ) , ( 6.3.1 1 ) g ( t ) ( 6.3.3 ).

.ft* ( ) S*(co), g ( t ) 11 . . 162 6. L (to ).

R x (* ) = $ e iwxS x () d a ;

( 6.3.1 9 ) 2 5 ^L(a)da ^ )= = ( 6.3. 2 0 ) ( 6.3. 1 1 ) 1 Γ " ( ) da ^ e iaV - x)S x () d a oo O O 0 J oo J e im + T) S x ( a ) d a 0, ( 6.3.2 1 ) O O , ( 6.3.2 1 ) f * 5 j ~5 S ^ * - (Sh) d x ?! ' () ^ ( i) ' 0 ^ t^O.

(+)5 :( ) | = 0 ( 6.3. 2 2 ) - ei (ra-ffl.) a 5 ( f _L _ ^ (Oj). ( 6.3.2 3 ) ( 6.3. 2 2 ) ^ e iaiiL () S * ()]) ( ax) d a { () S x () ( 6.3.2 4 ) - .

, ( 6.3. 2 2 ) jj [ L () S x () e iaTS x ()] d a = t^Q.

0 ( 6.3.2 5 ) ( 6.3. 2 5 ) f (t) f ( t ) ^ \ e iit \L (a )S x ( a ) - e i x (a)}da.

*TS (6.3.26) 163 6.3. F(v)) = [ L ( ( S i ) - e l aT] S x (a). ( 6.3.2 7 ) , F(a) . t ^ 0 ( 6.3.2 5 ).

.

f ( t ) , (0, ) \ e ~ te* f { t y d t.

f(M ) = i F(id) F(t,) = + iX.

F(Q , F(i ( ) ) 0, , 0.

m = (0, ) , ( , 0), .

, ( 6.3.2 7 ) F(t,) .

, . . - (. - S i ( ( o ) 5 ( ( ), S i () , = - f iX, S a ( c o ) , .

, (f \ () ( ) Q (co ) (0.

.

S i () , , 5 ( ) 164 6. , , S (c o ) , ( ) Q (ff) , , - , S i ( ), . . . S x { a ) S i () 5 ;

(), ( 6.3.2 8 ) -Si () ;

S 2 ( ) . ( 6.3. 2 8 ) ( 6. 3. 2 7 ) F () = [ L ( ) \ S x () S 2 () ( 6.3.2 9 ) S i ( ), v/yw '!

^ - = [ L ( co) - ^ ]S 2 ( ). ( 6.3. 3 0 ) F () ^^ , F ( a ), a S i () .

, (0, ), . . ( 6.3.3 0 ), S ()d a jj [ L () ] S 2 () d a = t^ 0 0.

( 6.3.3 1 ) ^ L () S 2 () e iat d a = ^ S 2 (co) e iat+T) d a, t~^ 0, ( 6.3.3 2 ) oo L (c o ) , , , , .

, L ( gi) S 2 (o ) , , , - cp(t)= ^ L () S 2 () da = 0 t 0.

- (6.3.33) 165 6.3. , q(t), () S 2 () = J q (t) ~ d t =* L = ~ \ e ~ iai ^ S 2 { i ) eta,t d i d t. ( 6.3.3 4 ) oo oo ( 6.3. 3 2 ) t ^ 0 ( 6.3. 3 4 ) ( 6.3. 3 2 ) ~ ^ S 2 { {) e i ' + T'di1 dt.

L ( ) S 2 (cd) = -^ -J ( 6.3.3 5 ) 2 ^ 2 (0 3 ) \ ~ \ S 2 ((i)i)eia^ t + T ^d(i)idt.

Z,(tn) = ( 6.3.3 6 ) , g{t).

, L (c o ) :

1) S x ( );

2 ) S x ((o) , S i () , , 5 ( ) ;

3 ) ( 6.3.3 6 ).

( 6.3.3 6 ) J_ (J t a + W t * (6 3 3 * ^ W ^ [ ( + ib)]n \ / 0 _ 2 . . , L (c o ), ( 6.3.3 6 ), , ( 6.3.2 7 ).

, , 1) F ( ) ;

2 ) L ( c ) ;

6. 3) ( 6.3.1 8 ) 5 I L M P S, ()*. ( 6.3.3 8 ) , - .

1. , ( , t) X(t), R x () = - | S.,( ) , 3.2, 1 , . , . Da Sx (G) = t ( + i 2 2) (6.3.27) , F () = [L () - ] r-f = L ( ) ~* ..

(2 + 2) ( )( + ) 1 F(i ) . = , , = ia, .

, L ( - 1() = ), L ( )= ~.

1 2 L(a) , f(to) . , , , () 2 ,.. . , L( ) . 3 Z,( ) .

(6.3.38) L ( d ) L ( | ) S x ( ) d(n = \L ( |2 D.

) () |2 Sx jj | =| J , L () = ~ = const.

() ~ ~ 6 (t).

g ( 0 = --L - jj rfco = jj dco = 167 6.3. (6.3.3) x(t + T) = e ~ ^ (t ) 6 () dx = ~ (t) - .

, x(f+T) t.



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, .
, , , , 1-2 .