Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 11
-
-
(
)
sin
K
z
- +
1
(
)
+
( )
cos
K
y
K
x
( )
sin
(
)
cos
I
xy
+
(
)
latex
,
% "d:/dynamics/precession/FirstOrderODEsK.tex"
Force-Free Motion of a Symmetric Top
:=
FFSymTop
(
)
subs
,
,
,
=
K
x
0
=
K
y
0
=
K
z
0 SymTop
FFSymTop
2
t
2
( )
cos
2
t
2
( )
sin
(
)
sin
+
:=
+
(
)
- +
1
t
(
)
cos
(
)
+
1
t
t
( )
sin
+
-
(
)
-
1
t
t
t
2
(
)
cos
(
)
sin
( )
cos
+
2
t
2
( )
sin
-
,
2
t
2
( )
cos
(
)
sin
+
(
)
- +
1
t
t
t
2
(
)
cos
(
)
sin
( )
sin
+
+
+
(
)
- +
1
t
(
)
cos
(
)
+
1
t
t
( )
cos
+
,
-
+
2
t
2
(
)
cos
t
(
)
sin
t
2
t
2
We notice that the third equation,
FFSymTop
3
-
+
2
t
2
(
)
cos
t
(
)
sin
t
2
t
2
can be written as
=
FFSymTop
3
'
'
t
+
t
(
)
cos
t
=
-
+
2
t
2
(
)
cos
t
(
)
sin
t
2
t
2
t
+
t
(
)
cos
t
-
(
)
rhs %
(
)
lhs %
0
Page 11
