167
1
S,68
-Sy68
0
-Sz98
1
0
Sy68
-S,6e
1
0
(5.40)
Dividing the small rotation angles, 68, about S into three
components 68&, 68y and 6,z about the axes of the global
system OXYZ, the rotation matrix can be expressed as
Rot(8ex, X) Rot(68y, Y)
1 0 0 0 1
0 1 -68x 0 0
0 66x 1 0 -68y
0 0 0 1 0
Rot(S68, Z)
0 69y 0 1
1 0 0 69,
0 1 0 0
0 0 1 0
0
0
0
1
(5.41)
e8y
-68x
1
0
where 688, 58y and 69z are all small angles. We therefore
simplify by neglecting the second and third order terms.
Comparing Eqs. (5.40) and (5.41), we obtain
(5.42)
8ey = SyX8
569 = S 58