Graphics Reference
In-Depth Information
Y
34
Z
4
ψ
(4, 34)
FIGURE 2.7
Projection of desired orientation vector onto
y-z
plane.
5
p
and cos
c ¼
p
34
5
p
. The
x
-axis rota-
rotate the orientation vector down in
y
, we have sin
c ¼
4/
=
tion matrix looks like this:
2
4
3
5
2
4
3
5
10 0
10 0
p
34
p
17
2
2
p
2
4
3
5
¼
4
50
10 0
0
0
p
50
p
0
5
5
R
x
¼
cos
c
sin
c
¼
(2.16)
p
34
2
2
p
p
17
sin
c
cos
c
0
4
50
0
p
p
50
0
5
5
After the pitch rotation has been applied, a
y
-axis rotation is required to spin the aircraft around
(yaw) to its desired orientation. The sine and cosine of the
y
-axis rotation can be determined by looking
at the projection of the desired orientation vector in the
x-z
plane. This projection is (3, 0, 5). Thus, a
positive
y
-axis rotation with sin
j ¼
3
p
and cos
j ¼
3
=
5
=
rotation matrix looks like this:
2
3
5
34
3
34
p
p
0
2
3
4
5
cos
j
0
sin
j
4
5
¼
010
R
y
¼
0
1
0
(2.17)
3
34
5
34
sin
j
0
cos
j
p
0
p
The final transformation of a point
P
would be
P
0
¼ R
y
R
x
P
.
5
Z
φ
3
(3, 5)
X
FIGURE 2.8
Projection of desired orientation vector onto x-z plane.
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