Пвлов_PROCHNOST_2_FULL+PROTECTION
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§ 2.2
§2.1
, ( ) ( )
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,
( ).
! , "
, "
. #
! Ry, "
, , − !
Rx. $ !, Ry ,
" . % !,
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. & ,
" " − "
(") [3].
"
( ) .
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! , |
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, !. ' z |
z0 |
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y |
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, x x0 ,
( . 2.2.1, ). ' , . .
, H i , Ri
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(. 2.2.1
# " ! " i- H i ,
, Si
( ) − , Ri −
H i Si , H i Ri Si .
) , ,
, . * ! H i , Ri Si ,
, " (
). γ 0 = γ = 0 , Si = 0,
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* : |
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R0 |
- " ! i- , x |
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xi |
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R0 |
- " ! i- , y |
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yi |
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R0 |
- " ! i- , z |
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zi |
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' " ! , ! |
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(2.1.4), |
. . 0 , " α 0 , β 0 ϕ 0 , ! , " |
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α , β ϕ . |
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$ ! i- " i0 ,
i .
" ! "
( . 2.2.1).
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Rxi |
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i0 |
Ryi0 |
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Rzi |
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HiRiSi
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Rxi |
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Ryi = Ri |
(2.2.1) |
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Rzi |
Si |
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+ , , ,
! R0 R .
) ,
[16], ,
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t 0 = ρV∞2 ( b 0 + b)[S1 ( α 0 + ϕ 0 ) + S2 ( α 0 + α + ϕ ) ]; t = ρV∞2 ( b 0 + b)[− S3 ( α 0 + ϕ 0 ) + S4 ( α 0 + α + ϕ ) ];
m 0 = − ρV∞2 ( b 0 + b) 2 [Ω 1 ( α 0 + ϕ 0 ) + Ω 2 ( α 0 + α + ϕ ) ];(2.2.2) m = − ρV∞2 ( b 0 + b) 2 [Ω 3 ( α 0 + ϕ 0 ) + Ω 4 ( α 0 + α + ϕ ) ].
)
S |
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= θ + sinθ − |
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S |
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+ sinθ − θ; S |
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Ω= 1 ( θ − sinθ ) 2 ;
1 4 π
Ω2 = 41π [π ( θ − sinθ cosθ) − ( θ − sinθ ) 2 ];
Ω3 = 41π [( θ − sinθ ) 2 − π ( θ − 2sinθ + sinθ cosθ ) ];
Ω |
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( π − θ + sinθ ) 2 |
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π |
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θ –
b 0 + l k |
= b 0 + b(1− cosθ ), |
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b 0 b – ;
b 0 + l k– ;
V∞ – " ,
ρ –
M x, M y, M z, Qx
" i -
( . 2.2.2):
l0 n
1
M xi0 = − ty0 dz0 dz0 − δ k Ryk0 (Zk0 − Zi0 )
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M yi0 = − tx0 dz0 dz0 + 1 |
δ k Rxk0 (Zk0 − Zi0 ) |
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l 0 |
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M zi0 = |
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− Yzi0 |
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( X 0 |
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[(Y 0 |
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ϕ 0 ) − Y 0 ] |
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− 1δ |
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+ X |
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+ 1δ |
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Qxi0 = tx0dz0 + |
δ k Rxk0 |
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Mxi = − ty dz dz − δ k Ryk (Zk − Zi ); |
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M yi = tx dz dz + δ k Rxk (Zk − Zi ); |
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z i |
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Mzi = l [mz − tx (Y − Yzi ) + ty(X − Xzi )]dz − |
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− n |
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1 δ |
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xk |
[(Y |
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+ X |
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ϕ |
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) − Y )]+ |
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+ n |
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1 δ |
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[(X |
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Q xi = t x dz + δ k Rxk ; |
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- (2.2.3) .
)c : – ,
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Zky |
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δ k |
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Zky |
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(2.2.1) (2.2.3) .
# ! :
= 1,2,3, ..., n ;
! : i=1,2,3,..., n1;
(. 2.2.2
* ! "
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(
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) " |
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, ! |
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0 , |
" ξ η ζ , |
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. #, , "
! (2.1.3), (2.1.7).
. , !
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r = r + x |
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(2.2.4) |
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) x |
= {x |
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z |
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= {x ,0,0}. ( .2.2.2) |
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r 0 |
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r + x − x = r 0 + 0 x0 |
− x0 |
(2.2.5) |
!
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$ $-/, "
, - . '
F(x, p)= 0, |
(2.2.6) |
" " (2.1.3-2.1.11),
: , (2.2.1)-(2.2.4).
) x = (α ,β ,ϕ ,α 0 ,β 0 ,ϕ 0 ,C) |
(2.2.7) |
-" , ,
" " ,
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-
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"
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, ! ,
" (2.2.5).
# , ,
" ,
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, " ",
. $ ! ,
" : = Pk X = Xk,
= Pk + δ X = X k + δX.
(2.2.6) " " ,
∂ |
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∂ |
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)δ P = 0, |
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F |
(Xk, Pk |
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F |
(Xk, Pk |
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∂ X |
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∂P |
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∂ |
δÕ = − |
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∂ X |
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∂ |
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F ( X k, Pk ) |
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F ( X k, Pk )δ P. |
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∂P |
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*, (2.2.6) =Pk ,
" : 1)
Pk+1= Pk + δ P ;
2) δ X ,
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Xk+1 = X k + δX .
-! X = X ( P ) ,
" X δ P ,
. ! "
. ) X
.
0 ! # " − %,
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!:
q+1 |
q |
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∂ |
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−1 q |
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X k |
= X k |
− |
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F (X k0, Pk ) |
F (X k |
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∂ X |
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X |
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) " X 0 |
− , |
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k |
k |
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!
=0, X . *,
δP= P , " "
X(P) |
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$ |
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∂ |
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, ! |
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F ( |
X ,P) , . . |
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∂ X |
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det |
∂ |
F(X,P) ≠ 0; |
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∂ X |
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= [X k( 1 ) , |
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X k( 2 ), |
..., X k( i ), ..., X k( n ) |
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dX |
( r ) |
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dX ( i ) |
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dP |
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" , Y.
/ Y X, (P) P. .
(2.2.6)
F * (Y ,X ( r ) )= 0