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Appendix I / Utilities / Axis Transforms
_ _
22.4.12 Skew x Transformation Matrix Product
SM_X_DC takes a [3,3] matrix [A], and a 3-vector (V), and returns their
[3x3] matrix product [B].
⎡ a
⎢
⎢
B : = ⎢ a
⎢
⎢
⎢
⎣ a
21
31
11
⋅ V
⋅ V
⋅ V
Z
X
Y
− a
− a
− a
31
11
21
SM_X_DC
⋅ V
⋅ V
⋅ V
Y
Z
X
22.4-8
( [ A ] , V , [ B ] )
[ V × ] A
B : = − ⋅
,
,
,
a
a
a
22
32
12
⋅ V
⋅ V
⋅ V
22.4.13 Transformation x Skew Matrix Product
Z
X
Y
− a
− a
− a
32
12
22
⋅ V
⋅ V
⋅ V
Y
Z
X
,
,
,
a
a
a
Equation 22.4-49
Equation 22.4-50
23
33
13
⋅ V
⋅ V
⋅ V
Z
X
Y
− a
− a
− a
33
13
23
⋅ V
⋅ V
⋅ V
Y
Z
X
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Equation 22.4-51
DC_X_SM takes a [3,3] matrix [A], and a 3-vector (V), and returns their
[3x3] matrix product [B].
⎡ a
⎢
⎢
B : = ⎢ a
⎢
⎢
⎢
⎣ a
13
23
33
⋅ V
⋅ V
⋅ V
Y
Y
− a
− a
− a
22
32
DC_X_SM
⋅ V
⋅ V
⋅ V
Z
Z
B
( [ A ] , V , [ B ] )
[ × ]
: = A ⋅ V
21
31
⋅ V
⋅ V
⋅ V
22.4.14 Vector Projection onto Reference Planes
Y
12
Z
,
,
,
a
a
a
11
Z
Z
Z
− a
− a
− a
13
23
33
⋅ V
⋅ V
⋅ V
X
X
X
,
,
,
a
a
a
Equation 22.4-52
Equation 22.4-53
12
22
32
⋅ V
⋅ V
⋅ V
X
X
X
− a
− a
− a
11
21
31
⋅ V
⋅ V
⋅ V
Y
Y
Y
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
Equation 22.4-54
XYZ_TO_RAD takes the Cartesian position of point (b) with respect to point
(a), expressed in frame (A), and returns the projection of the vector onto the
principal planes of frame (A) as determined by (k).