Математическое моделирование применительно к литейному производству. Черный А.А. - 27 стр.

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;
)xxx(
yxxx
b
N
u
u,ru,n
u,n
uu,r
N
u
u,nu,n
r,n,n
∑
∑
=
=
⋅⋅
⋅⋅⋅
=
1
2
13
2
1
1
32
132
;
)xx(
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b
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u
u,r
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1
2
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21
;
)xx(
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u
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1
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;
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;
)xxx(
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)xxx(
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b
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u
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u
u,ru,n
r,r,n
∑
∑
=
=
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⋅⋅⋅
=
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2
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3
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;
)xxx(
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b
N
u
u,ru,r
u,r
uu,r
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u
u,ru,r
r,r,r
∑
∑
=
=
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⋅⋅⋅
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где
x
1n,u
= x
n
1,u
+v
1
; x
1r,u
=x
r
1,u
+a
1
⋅x
n
1,u
+c
1
x
2n,u
= x
n
2,u
+v
2
; x
2r,u
=x
r
2,u
+a
2
⋅x
n
2,u
+c
2
x
3n,u
= x
n
3,u
+v
3
; x
3r,u
=x
r
3,u
+a
3
⋅x
n
3,u
+c
3
. 
                        N
                      ∑ x2n ,u ⋅ x3n ,u ⋅ x1r ,u ⋅ yu
                      u =1
 b2 n ,3n ,1r =        N
                                                            ;
                       ∑ ( x2n ,u ⋅ x3n ,u ⋅ x1r ,u )   2

                      u =1
                  N                                             N
                 ∑ x1r ,u ⋅ x2r ,u ⋅ yu                         ∑ x1r ,u ⋅ x3r ,u ⋅ yu
                 u =1                                           u =1
 b1r ,2 r =       N
                                             ; b1r ,3r =         N
                                                                                            ;
                 ∑ ( x1r ,u ⋅ x2r ,u )   2
                                                                ∑ ( x1r ,u ⋅ x3r ,u )   2

                 u =1                                           u =1
                 N                                                  N
              ∑ x2r ,u ⋅ x3r ,u ⋅ yu                                ∑ x1n ,u ⋅ x2r ,u ⋅ x3r ,u ⋅ yu
              u =1                                                  u =1
 b2 r ,3r =    N
                                             ; b1n ,2 r ,3r =        N
                                                                                                      ;
              ∑ ( x2r ,u ⋅ x3r ,u )2                                ∑ ( x1n ,u ⋅ x2r ,u ⋅ x3r ,u )2
              u =1                                                  u =1


                        N
                      ∑ x2n ,u ⋅ x1r ,u ⋅ x3r ,u ⋅ yu
                      u =1
 b2 n ,1r ,3r =        N
                                                            ;
                      ∑ ( x2n ,u ⋅ x1r ,u ⋅ x3r ,u )    2

                      u =1
                      N
                      ∑ x3n ,u ⋅ x1r ,u ⋅ x2r ,u ⋅ yu
                      u =1
 b3n ,1r ,2 r =        N
                                                            ;
                      ∑ ( x3n ,u ⋅ x1r ,u ⋅ x2r ,u )    2

                      u =1


                   N
                  ∑ x1r ,u ⋅ x2r ,u ⋅ x3r ,u ⋅ yu
                  u =1
b1r ,2 r ,3r =     N
                                                        ;
                  ∑ ( x1r ,u ⋅ x2r ,u ⋅ x3r ,u )    2

                  u =1


где
                             x1n,u = xn1,u+v1; x1r,u=xr1,u+a1⋅xn1,u+c1
                             x2n,u = xn2,u+v2; x2r,u=xr2,u+a2⋅xn2,u+c2
                             x3n,u = xn3,u+v3; x3r,u=xr3,u+a3⋅xn3,u+c3.

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