Пвлов_PROCHNOST_2_FULL+PROTECTION
.pdf
P
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+ δ X ( r ) , |
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−1 |
∂ |
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Y |
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= Y |
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F * |
(Yk |
,X |
( r ) ) |
F * |
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( r ) |
δX ( r ) , |
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∂X ( r ) |
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∂Y |
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∂ |
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det |
F* (Y,k |
Xk(r) ) |
≠ 0. |
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∂Y |
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.
.
* "
(2.2.6) ( .2.2.3),
1 . 2.2.4.
( 2.2.3
( 2.2.4
2 ! 1 ,
--95 , .
% 3- ". !
2, . 2.2.5,
" ! ! "
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3 , " ",
! " 4,
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! 3./-3.
(.2.2.5
. ( "
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# . 2.2.6 :
“ ” 4 5
6=0,25 – , ,
! !. (
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#, " , !
. !
, ( ).
!
− [3-5]. 0 !
, -'
D.
( 2.2.6
% ϕ ( P ) .2.2.6 "" ". (
F(X,P) = 0
" . #
, 7.7. 7 ,
.
' ". 0
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(2.2.8 ) |
F ( ϕ , ϕ , P) = 0, |
ϕ – ,
– , :
F(ϕ, ) = 0 . |
(2.2.9) |
8 (2.2.9) ϕ " "" ",
"
. $ ,
dϕ
dP = ϕ 'p.
! (2.2.9) :
∂F + ∂F ϕ ′p = 0, ∂P ∂ϕ
∂F −1
ϕ ′p = − ∂ϕ
",
∂F |
. |
(2.2.10) |
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∂P |
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∂F = 0 |
∂F |
≠ 0 " ". % |
∂ϕ |
∂P |
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, " ,
ϕ " . .
, , ", ( |
. 2.2.6) − |
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" ∂F =0− !) " :
∂P
. "
, .
,
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∂F |
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∂F |
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δϕ + |
δ ϕ = 0. |
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∂ϕ |
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∂ϕ |
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eiΩ t |
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δ ϕ =δ ϕ |
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2 |
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∂F |
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∂F |
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− Ω |
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δ ϕ = 0. |
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δ ϕ + |
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∂ϕ |
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8 " Ω, −
. Ω 2
" . - ( )
, ,
∂F = 0 .
∂ϕ
*
, ,
,
" .
% ϕ ( P ) σ ( P ) .2.2.6
. ' ,
, " [5].
§3.
− “ ”
. 2.2.6.
ϕ ( p)
[4].
! " -
( ). #
$ .
% Υ ( ), ϕ (p) ( . 2.3.1) #&
. % , 0-0
α0 α.
! , ,
' . ( Υ( ) # , ϕ( ) -
. ) α0 α , Υ ϕ 1
' , , #
2
Pa. * , , '
& , , '. !
, 2, P1. , P1 < P ,
- , 2-3, ,
' P1. $ 1-1
2-2. ( ).
) P1 > P , ,
3 ( 3-3), , #
4, '. " ,
& ' P2. ) P2 < P ,
, ' P2 (# #
). ) P2 > P , ,
' 1, ' 2, .
% , #
# - # .
# ,
# , # . + # # , #
# , , ,
. $# #, '
, # #
. # # #
, , -.+ #
.
.# , . .
. . , , '#
#,
, #. "
.
*. 2.3.1
(2.2.6)
( ) .
# tx0 ty0 , tx ,ty m0 ,m, |
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, , . . |
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t0 = ta + tm |
, |
t |
x |
= ta + tm |
, |
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x |
x0 |
x0 |
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x x |
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t0 |
= ta |
+ tm |
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, |
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t |
y |
= ta + tm |
, |
(2.3.1) |
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y |
y0 |
y0 |
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y |
y |
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m0 = ma + mm |
, |
m = ma + mm . |
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0 |
0 |
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! #
# x0 , y0 /0 , x, y (2.2.2),
. 0 [16], ,