Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 30
(
)
+
( )
cos
(
)
cos
( )
sin
( )
sin
( )
cos
X
(
)
-
+
( )
cos
(
)
cos
( )
cos
( )
sin
( )
sin
Y
+
[
Z
( )
cos
(
)
sin
-
]
(
)
-
( )
cos
( )
cos
( )
sin
(
)
cos
( )
sin
X
(
)
+
( )
cos
( )
sin
( )
sin
(
)
cos
( )
cos
Y
+
[
( )
sin
(
)
sin
Z
+
]
[ ]
0
:=
torque_xyz_top
%
(
)
latex
,
torque_xyz_top "d:/dynamics/precession/FlatTopTorqueBody.tex"
The Equations of Motion
The equations of motion are
(
)
mat FirstOrderODEsK
=
t
=
t
=
t
=
(
)
sin
t
+
(
)
-
(
)
-
1
(
)
cos
(
)
+
1
+
( )
cos
K
y
K
x
( )
sin
I
xy
=
t
+
+
(
)
- +
1
2
(
)
cos
(
)
sin
-
+
K
y
( )
sin
( )
cos
K
x
I
xy
(
)
sin
t
(
)
+
(
)
+
(
)
cos
2
1
(
)
- +
1
(
)
cos
=
-
-
(
)
sin
K
z
- +
1
(
)
+
( )
cos
K
y
K
x
( )
sin
(
)
cos
I
xy
+
Torque Combinations
Assemble the torque combinations.
:=
Kcone
(
)
convert
,
(
)
evalm
(
)
rhs torque_xyz_cone
vector
:=
Ktop
(
)
convert
,
(
)
evalm
(
)
rhs torque_xyz_top
vector
+
(
)
+
Kcone
1
Ktop
1
( )
sin
(
)
+
Kcone
2
Ktop
2
( )
cos
Page 30
