Find Docs

Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 2)

Wodocs >> Science : Astronomy >> Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 2
Astronomical Applications Department, U.S. Naval Observatory - Precession Maple
Eulerian Angle Transformation
Rotation Matrix
Construct a rotation matrix that transforms coordinates from the fixed frame (X,Y,Z) to the
body frame (x,y,z). First, rotate the coordinates ccw around the Z axis.
:=
r1


( )
cos
( )
sin
0
-
( )
sin
( )
cos
0
0
0
1
Next, rotate ccw around the X' axis.
:=
r2


1
0
0
0
(
)
cos
(
)
sin
0
-
(
)
sin
(
)
cos
Next, rotate ccw around the Z'' axis.
:=
r3


( )
cos
( )
sin
0
-
( )
sin
( )
cos
0
0
0
1
Now combine the rotations into a single rotation matrix.
R :=
(
)
, ,
p q r
(
)
evalm (
)
(
)
subs
,
=
r
(
)
eval r3
`&*`
(
)
subs
,
=
q
(
)
eval r2
`&*`
(
)
subs
,
=
p
(
)
eval r1
Hence, we have the coordinate transformation
=
(
)
mat , ,
x y z
(
)
R
,
,
&*
(
)
mat
, ,
X Y Z


x
y
z
=
[
,
,
]
-
( )
cos
( )
cos
( )
sin
(
)
cos
( )
sin
+
( )
cos
( )
sin
( )
sin
(
)
cos
( )
cos
( )
sin
(
)
sin
-
-
( )
sin
( )
cos
( )
cos
(
)
cos
( )
sin
-
+
( )
sin
( )
sin
( )
cos
(
)
cos
( )
cos
[
,
,
( )
cos
(
)
sin
]
[
,
,
]
(
)
sin
( )
sin
-
(
)
sin
( )
cos
(
)
cos
&*


X
Y
Z
(
)
latex
,
% "d:/dynamics/precession/FixedToBody.tex"
The diagram below illustrates the three rotations.
Page 2

<< Previous       1 2 3 4 5 6 7 8 9 10 11 12 13 14 15       Next >>



Other Documents:
Curves 3 D, NOVAS 2004 Overview, NOVAS 2006 Overview, thesis, Ranson,


WODocs | |
All rights reserved. wodocs.comę 2009
WODocs


New Docs

Documents Category:
Arts (Design, Movies, Music, Radio, Television)
Automotive (Cars, Marine, Motorcycle, ATV, Snowmobiles)
Business (Biotechnology and Pharmaceuticals, Chemicals, Construction and Maintenance, Materials, Real Estate, Services)
Electronics (Computers, Motion Control, Power Supply)
Games (Board, Family, Party, Card, Construction, RC Toys)
Health (Animalm, Beauty, Healthcare, Medicine, Pharmacy, Surgery, Weight Loss)
Home (Accessories, Cooking, Decor and Design, Electrical, Family, Pets)
News (Newspapers, Sports, Television)
Recreation (Collecting, Hiking, Scouting, Survival, Travel)
Reference (Education, Libraries and Archives, Museums)
Science (Agriculture, Astronomy, Biology, Chemistry)
Shopping (Antiques and Collectibles, Clothing, Flowers, Food, Home and Garden)
Sports (Bicycle, Snowboard, Skiing, Other)