Page 18 - 6742

Vector’s indexes show direction of these vectors. For
example, the vector l is directed from the point O till point A.
OA
Incline of these vectors is determined by the angles .
і
Let’s project the system of vector equations on coordinate
axles. We obtained system of the trigonometric equations
l OA cos   l AB cos   c  l O 1B cos  ,
1
3
2
l OA sin   l AB sin   b  l O 1B sin  ,
1
2
3
l O 1C cos 3  l CD cos 4  b  0, (1.3)
l O1 C sin 3  l CD sin 4  y .
D
Rewrite the vector equations (1.1) and (1.2)
l OA e OA  l AB e AB  e c c  e а a  l O1 B e O1 B , (1.4)
l O1 C e O1 C  l CD e CD  e b b  y D e , (1.5)
D
where e – is unit vectors for vectors l (their projections in flat
i
i
coordinate system equal zero, z 0).
The equations (1.4) and (1.5) will take next view if unit
vectors will be written in form of one-dimensional array
cos i 


e i  sin i 
 
 0 
cos  1   cos  2    1    0  cos  3  






l OA  sin  1   l AB  sin  2   c  0   а  1   l O 1B  sin  3  , (1.6)
         
 0   0   0   0   0 
cos 3  cos 4     1  0 3  





l O 1C  sin 3   l CD  sin 4   b  0   y D  1 . (1.7)

       
 0   0   0   0 
System of the equations (1.3), (1.6) and (1.5) has unknown
parameters  ,  ,  і у .
D
4
3
2
System of the equations (1.3) is differentiated by time
17