Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 4
:=
( )
cos
-
( )
sin
0
t
Finally, the component along the Z'' axis is simply
:=
(
)
mat
, ,
0 0 1
t
:=
0
0
1
t
Hence, we have the angular velocity vector in the body frame,
=
mat
seq
,
+
+
(
)
evalm
,
i 1
(
)
evalm
,
i 1
(
)
evalm
,
i 1
=
i
..
1
3
=
+
t
( )
sin
(
)
sin
t
( )
cos
-
t
( )
cos
(
)
sin
t
( )
sin
+
t
(
)
cos
t
(
)
latex
,
% "d:/dynamics/precession/OmegaBodyFrame.tex"
:=
Obody
(
)
convert
,
(
)
rhs %
vector
Rigid Body Equations -- General Case
Equations of Motion
Substituting back into the Euler equations, we find
:=
xyz
[
]
, ,
x y z
:=
MI
[
]
,
,
I
x
I
y
I
z
subs
,
seq
,
=
( )
xyz
k
t
Obody
k
=
k
..
1
3
(
)
evalm EulerEqs
I
x
t
+
t
( )
sin
(
)
sin
t
( )
cos
(
)
-
I
z
I
y
-
t
( )
cos
(
)
sin
t
( )
sin
+
t
(
)
cos
t
K
x
+
-
I
y
t
-
t
( )
cos
(
)
sin
t
( )
sin
Page 4
