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.

.1.

X0,Y0,Z0 - .

X1,Y1,Z1 -

.

X2,Y2,Z2 - .

Qij - j- i-

.

wij - j- i- .

wij' - j- i- .

Ji - i-

.

Jij - .

Mij -

j- i- .

a - Y1.

a' -

Y1.

a'' - Y1.

b - Z2.

b' - . Z2.

b'' - Z2.

i- :

dQxi/dt - Qyi×wzi + Qzi×wyi = Mxi

dQyi/dt - Qzi×wxi + Qxi×wzi = Myi

dQyi/dt - Qzi×wxi + Qxi×wzi = Myi

:

) :

dQy1/dt - Qz1×wx1 + Qx1×wz1 = My1

) :

dQx2/dt - Qy2×wz2 + Qz2×wy2 = Mx2

dQy2/dt - Qz2×wx2 + Qx2×wz2 = My2 (1)

dQz2/dt - Qx2×wy2 + Qy2×wx2 = Mz2

X1, Y1, Z1 :

Qx1 = Jx1×wx1 - Jxy1×wy1 - Jxz1×wz1

Qy1 = Jy1×wy1 - Jyx1×wx1 - Jyz1×wz1 (2)

Qz1 = Jz1×wz1 - Jzx1×wx1 - Jzy1×wy1

X2, Y2, Z2 :

Qx2 = Jx2×wx2 - Jxy2×wy2 - Jxz2×wz2

Qy2 = Jy2×wy2 - Jyx2×wx2 - Jyz2×wz2 (3)

Qz2 = Jz2×wz2 - Jzx2×wx2 - Jzy2×wy2

-, - .1, :

) :

wx1 = wx0×cos(a) - wz0×sin(a)

wy1 = wy0 + a' (4*)

wz1 = wx0×sin(a) + wz0×cos(a)

wx1' = wx0'×cos(a) - wz0'×sin(a)

wy1' = wy0' + a'' (4*')

wz1' = wx0'×sin(a) + wz0'×cos(a)

) :

wx2 = wx1×cos(b) + wy1×sin(b)

wy2 = wy1×cos(b) - wx1×sin(b) (5*)

wz2 = wz1 + b'

wx2' = wx1'×cos(b) + wy1'×sin(b)

wy2' = wy1'×cos(b) - wx1'×sin(b) (5*')

wz2' = wz1' + b''

2- (5*) , :

wy1=wx1×tg(b)+wy2/cos(b)

2- (5*') , :

wy1'=wx1'×tg(b)+wy2'/cos(b)

, , wy2, wz2, wy2', wz2' , .. , :

wx1 = wx0×cos(a) - wz0×sin(a)

wy1 = wx1×tg(b)+wy2/cos(b) (4)

wz1 = wx0×sin(a) + wz0×cos(a)

wx1' = wx0'×cos(a) - wz0'×sin(a)

wy1' = wx1'×tg(b)+wy2'/cos(b) (4')

wz1' = wx0'×sin(a) + wz0'×cos(a)

wx2 = wx1×cos(b) + wy1×sin(b) (5)

wx2' = wx1'×cos(b) + wy1'×sin(b) (5')

(2), (3) (1), :

Jy1×wy1' + (Jx1-Jz1)×wx1×wz1 + Jzx1×wx12 - Jxz1×wz12 +

+ Jzy1×wx1×wy1 - Jxy1×wy1×wz1 - Jyx1×wx1' - Jyz1×wz1' = My1 (6.1)

Jx2×wx2' + (Jz2-Jy2)×wy2×wz2 - 2×Jzy×wy22 + Jyz2×wz22 +

+ Jyx2×wx2×wz2 - Jzx2×wx2×wy2 - Jxz2×wz2' - Jxy2×wy2' = Mx2 (6.2)

Jy2×wy2' + (Jx2-Jz2)×wx2×wz2 + Jzx2×wx22 - Jxz2×wz22 +

+ Jzy2×wx2×wy2 - Jxy2×wy2×wz2 - Jyx2×wx2' - Jyz2×wz2' = My2 (6.3)

Jz2×wz2' + (Jy2-Jx2)×wx2×wy2 + Jxy2×wy22 - Jyx2×wx22 +

+ Jxz2×wy2×wz2 - Jyz2×wx2×wz2 - Jzx2×wx2' - Jzy2×wy2' = Mz2 (6.4)

(6.2), (6.3), (6.4) , (6.1) Y1. (6.1), (6.2), (6.3) A, B C, , :

My1 = A + B × sin(b) + C × cos(b) (7)

(7) A, B C y1.

y1=Jxz1{wx12-wz12}+

+Jxz2cos(b)wx22-Jyz2sin(b)wy22+

+{Jyz2sin(b)-Jxz2cos(b)}wz22+

+{Jyz2cos(b)-Jxz2sin(b)}wx2wy2+

+{Jxy2sin(b)+(Jx2-Jz2)cos(b)}wx2wz2+

+{(Jz2-Jy2)sin(b)-Jxy2cos(b)}wz2wy2+ (8)

+{Jx2sin(b)-Jxy2cos(b)}wx2' +

+{Jy2cos(b)-Jxy2sin(b)}wy2'-

-{Jxz2sin(b)+Jyz2cos(b)}wz2'+

+Jyz1wx1wy1-

-Jxy1wz1wy1+

+(Jx1-Jz1)wx1wz1 -

-Jxy1wx1'-

-Jyz1wz1'+

+Jy1wy1'

y1, Mz2 (4), (4'), (5), (5') , y1, Mz2:

MZ2={cos(2b)-2}cos(a)2tg(b)2Jxy2(wx02+wz02)+

+{2tg(b)2sin(b)2-2cos(b)2+4}sin(a)cos(a)Jxy2wx0wz0+

+{(Jy2-Jx2)/cos(b)-2Jxy2sin(b)(1+tg(b)2)}cos(a)wx0wy2+

+Jyz2wz0wz2(sin(a)-cos(a))/cos(b)-

-Jxz2wx0'cos(a)/cos(b)+

+{2Jxy2(sin(b)tg(b)2+sin(b))sin(a)+(Jx2-Jy2)sin(a)/cos(b)}wy2wz0+

+Jxz2wz0'sin(a)/cos(b)+

+{Jxz2-Jyz2}wy2wz2tg(b)+

+{(Jy2-Jx2)tg(b)+Jxy2(1-tg(b)2)}wy22-

-{Jxz2tg(b)+Jyz2}wy2'+

+Jz2wz2'

(9)

My1={[Jxz2(tg(b)4+2/cos(b)2-1)cos(b)3+Jyz1tg(b)+Jxz1]cos(a)2+

+[[(Jx1-Jz1)-Jxy1tg(b)]cos(a)-Jxz1sin(a)]sin(a)}wx02+

+{[[Jxy1tg(b)+(Jz1-Jx1)]sin(a)-Jxz1cos(a)]cos(a)+

+[Jxz2cos(b)3[2/cos(b)2+tg(b)4-1]+Jyz1tg(b)+Jxz1]sin(a)2}wz02+

+{(Jx1-Jz1)cos(2a)+[1-tg(b)4-2/cos(b)2]Jxz2cos(b)3sin(2a)-

-[Jyz1tg(b)+2Jxz1]2sin(a)cos(a)-

-Jxy1tg(b)cos(2a)}wx0wz0+

+{[Jxy2sin(b)cos(b)(tg(b)2+1)+(Jx2-Jz2)]cos(a)}wx0wz2+

+{[Jxz2sin(b)cos(b)+Jxz2sin(b)3/cos(b)+Jyz2]cos(a)+

+[Jyz1cos(a)-Jxy1sin(a)]/cos(b)}wx0wy2-

-{[Jxz2sin(b)cos(b)(1+tg(b)2)+Jyz2]sin(a)+

+[Jyz1sin(a)+Jxy1cos(a)]/cos(b)}wz0wy2+

+{-[tg(b)2+1]sin(b)cos(b)Jxy2+(Jz2-Jx2)]sin(a)}wz0wz2+

+{[Jx2sin(b)cos(b)(1+tg(b)2)+Jy1tg(b)-(Jxy1+

+Jxy2)]cos(a)-Jyz1sin(a)}wx0'+

+{[-Jx2sin(b)cos(b)(1+tg(b)2)+(Jxy1+Jxy2)-

-Jy1tg(b)]sin(a)-Jyz1cos(a)}wz0'+

+{Jyz2sin(b)-Jxz2cos(b)]wz22-

-{Jxz2sin(b)+Jyz2cos(b)}wz2'+

+{(Jx2-Jy2)sin(b)+Jxy2cos(b)(tg(b)2-1)}wz2wy2+

+{Jx2sin(b)2/cos(b)-2Jxy2sin(b)+Jy2cos(b)+Jy1/cos(b)}wy2'

.

(9) , 2.

.2.

:

Jx1 = -------//------ Jx2= 2000 2 = 0.2 2

Jy1 = 1500 2 = 0.15 2 Jy2= 9500 2 = 0.95 2

Jz1 = -------//------ Jz2 = 10000 2 = 1 2

Jxy1 = Jyx1 = 0 Jxy2 = Jyx2 = 0.0085 2

Jxz1 = Jzx1 = 0 Jxz2 = Jzx2 = 0.023 2

Jzy1 = Jyz1 =1500 2 = 0.15 2 Jzy2 = Jyz2 = 0.04 2

.

wx0 = 1 /񠠠 wy2 = 2 /

wy0 = 1 /񠠠 wz2 = 2 /

wz0 = 1 /񠠠 wy2' = 3 /2 (10)

wx0'= 0,2 /2 wz2' = 3 /2

wy0'= 0,2 /2

wz0'= 0,2 /2

:

a = 2 . 120 . (10)

b = 1 . 60 .

MOMIN 1.

-:

1) ;

2) ;

3) ;

1) ,

.. :

wx0 = wy0 = wz0 = wx0' = wy0' = wz0' = 0 (11)

a ¹ 0; b ¹ 0; wy2¹ 0; wz2 ¹ 0; wy2' ¹ 0; wz2' ¹ 0

(11) (9), :

MZ2=+{Jxz2-Jyz2}wy2wz2tg(b)+

+{(Jy2-Jx2)tg(b)+Jxy2(1-tg(b)2)}wy22-

-{Jxz2tg(b)+Jyz2}wy2'+

+Jz2wz2'

MY1=+{Jyz2sin(b)-Jxz2cos(b)}wz22-

-{Jxz2sin(b)+Jyz2cos(b)}wz2'+

+{(Jx2-Jy2)sin(b)+Jxy2cos(b)(tg(b)2-1)}wz2wy2+

+{Jx2sin(b)2/cos(b)-

-2Jxy2sin(b)+Jy2cos(b)+Jy1/cos(b)}wy2'

, (10), :

) Y1: y1 = + = 5.68 + 0.14 = 5.82 ×.

a = 0.067 .

b = 1 .

wy2 = -2.0 /.

wy2' = 3.0 /2.

wz2 = 2 /.

wz2' = -3.0 /2.

- y1 , ;

- y1 , ;

:

= × 100% = 2.38 %

+

) Z2: z2 = + = 7.67 + 0.33 = 8.0 ×.

a = 0.067 .

b = 1 .

wy2 = 2.0 /.

wy2' = -3.0 /2.

wz2 = -2 /.

wz2' = 3.0 /2.

:

= × 100% = 4.2 %

+

2) ,

.. :

wy2= wy2'= wz2 = wz2' = 0; a ¹ 0; b ¹ 0; (12)

wx0 ¹ 0; wy0 ¹ 0; wz0 ¹ 0; wx0' ¹ 0; wy0' ¹ 0; wz0' ¹ 0

(12) (9) :

MZ2={cos(2b)-2}cos(a)2tg(b)2Jxy2(wx02+wz02)+

+{2tg(b)2sin(b)2-2cos(b)2+4}sin(a)cos(a)Jxy2wx0wz0+

-Jxz2wx0'cos(a)/cos(b)+

+Jxz2wz0'sin(a)/cos(b)+

MY1={[Jxz2(tg(b)4+2/cos(b)2-1)cos(b)3+Jyz1tg(b)+

+Jxz1]cos(a)2+

+[[(Jx1-Jz1)-Jxy1tg(b)]cos(a)-Jxz1sin(a)]sin(a)}wx02+

+{[[Jxy1tg(b)+(Jz1-Jx1)]sin(a)-Jxz1cos(a)]cos(a)+

+[Jxz2cos(b)3[2/cos(b)2+tg(b)4-1]+Jyz1tg(b)+

+Jxz1]sin(a)2}wz02+

+{(Jx1-Jz1)cos(2a)+[1-tg(b)4-2/cos(b)2]Jxz2cos(b)3

sin(2a)-[Jyz1tg(b)+2Jxz1]2sin(a)cos(a)-

-Jxy1tg(b)cos(2a)}wx0wz0+

+{[Jx2sin(b)cos(b)(1+tg(b)2)+Jy1tg(b)-(Jxy1+Jxy2)]cos(a)-

-Jyz1sin(a)}wx0'+

+{[-Jx2sin(b)cos(b)(1+tg(b)2)+(Jxy1+Jxy2)-Jy1tg(b)]sin(a)-

-Jyz1cos(a)}wz0'+

:

) Y1:

y1 = + = 0.154 + 0.551= 0.705 ×.

蠠 a = - 0.82 .

b = 1 .

wx0 = wz0 = 1 /.

wx0' = wz0' = 0.2 /2.

wy0 = 0.167 /c.

wy0' = 0.167 /2.

:

= × 100 % = 78.14 %

+

) Z2:

z2 = + = 0 + 0.07= 0.07 ×.

蠠 a = - 0.785 .

b = 1 .

wx0 = wz0 = 1 /.

wx0' = wz0' = 0.2 /2.

wy0 = 0.167 /.

wy0' = 0.167 /c2

:

= × 100 % = 100 %

+

3) .

(9).

MZ2={cos(2b)-2}cos(a)2tg(b)2Jxy2(wx02+wz02)+

+{2tg(b)2sin(b)2-2cos(b)2+4}sin(a)cos(a)Jxy2wx0wz0+

+{(Jy2-Jx2)/cos(b)-2Jxy2sin(b)(1+tg(b)2)}cos(a)wx0wy2+

+Jyz2wz0wz2(sin(a)-cos(a))/cos(b)-

-Jxz2wx0'cos(a)/cos(b)+

+{2Jxy2(sin(b)tg(b)2+sin(b))sin(a)+(Jx2-

-Jy2)sin(a)/cos(b)}wy2wz0+

+Jxz2wz0'sin(a)/cos(b)+

+{Jxz2-Jyz2}wy2wz2tg(b)+

+{(Jy2-Jx2)tg(b)+Jxy2(1-tg(b)2)}wy22-

-{Jxz2tg(b)+Jyz2}wy2'+

+Jz2wz2'

MY1={[Jxz2(tg(b)4+2/cos(b)2-1)cos(b)3+Jyz1tg(b)+

+Jxz1]cos(a)2+

+[[(Jx1-Jz1)-Jxy1tg(b)]cos(a)-Jxz1sin(a)]sin(a)}wx02+

+{[[Jxy1tg(b)+(Jz1-Jx1)]sin(a)-Jxz1cos(a)]cos(a)+

+[Jxz2cos(b)3[2/cos(b)2+tg(b)4-1]+

+Jyz1tg(b)+Jxz1]sin(a)2}wz02+

+{(Jx1-Jz1)cos(2a)+[1-tg(b)4-2/cos(b)2]Jxz2cos(b)3

sin(2a)-[Jyz1tg(b)+2Jxz1]2sin(a)cos(a)-

-Jxy1tg(b)cos(2a)}wx0wz0+

+{[Jxy2sin(b)cos(b)(tg(b)2+1)+(Jx2-Jz2)]cos(a)}wx0wz2+

+{[Jxz2sin(b)cos(b)+Jxz2sin(b)3/cos(b)+Jyz2]cos(a)+

+[Jyz1cos(a)-Jxy1sin(a)]/cos(b)}wx0wy2-

-{[Jxz2sin(b)cos(b)(1+tg(b)2)+Jyz2]sin(a)+

+[Jyz1sin(a)+Jxy1cos(a)]/cos(b)}wz0wy2+

+{-[tg(b)2+1]sin(b)cos(b)Jxy2+(Jz2-Jx2)]sin(a)}wz0wz2+

+{[Jx2sin(b)cos(b)(1+tg(b)2)+Jy1tg(b)-(Jxy1+Jxy2)]

cos(a)-Jyz1sin(a)}wx0'+

+{[-Jx2sin(b)cos(b)(1+tg(b)2)+(Jxy1+Jxy2)-Jy1tg(b)]

sin(a)-Jyz1cos(a)}wz0'+

+{Jyz2sin(b)-Jxz2cos(b)}wz22-

-{Jxz2sin(b)+Jyz2cos(b)}wz2'+

+{(Jx2-Jy2)sin(b)+Jxy2cos(b)(tg(b)2-1)}wz2wy2+

+{Jx2sin(b)2/cos(b)-2Jxy2sin(b)+Jy2cos(b)+

+Jy1/cos(b)}wy2'

.

) Y1:

y1 = + = 8.1 + 1.65 = 9.75 ×

蠠 a = 0.776 .

b = 1.0 .

wy2 = -2 /.

wy2' = 3 /2.

wz2 = 2 /.

wz2' = -3 /2.

wx0 = wz0 = 1 /c.

wx0' = 0.2 /c2.

wz0' = - 0.2 /c2.

wy0 = 0.167 /c.

wy0' = 0.167 /c2.

:

= × 100 % = 16.9 %

y1+

) Z2:

z2 = + = 11.6 + 0.361 = 11.96 ×

蠠 a = -0.785 .

b = 1.0 .

wy2 = 2 /.

wy2' = -3 /2.

wz2 = -2 /.

wz2' = 3 /2.

wx0 = wz0 = 1 /c.

wx0' = wz0' = - 0.2 /c2.

wy0 = 0.167 /c.

wy0' = 0.167 /c2.

:

= × 100 % = 3.02 %

y1 +

. . . -2. - : Ô 򠠠

 

 

 

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