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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 11)

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

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