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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 13)

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


collect
,
,


simplify
%
I
xy
[
]
,
,
,
I
xy
simplify
=
E
I
xy
+
+
+


-
+
1
2
1
2
(
)
cos
2
1
2
I
z
(
)
cos
2
I
xy
2
I
z
(
)
cos
I
xy
1
2
2
1
2
I
z
2
I
xy
(
)
collect
,
,
(
)
algsubs
,
=
I
z
I
xy
(
)
-
1
%
[
]
factor
=
E
I
xy
-
+
+
2




-
1
2
1
2
(
)
cos
2
(
)
- +
1
(
)
cos
1
2
2




-
1
2
1
2
2
:=
KE
%
Steady Precession Solution
Suppose we look for a solution such that
is constant. Then we have




eval




subs
,
=
t
0 FFSymTop
+


2
t
2
( )
sin
(
)
sin




-
(
)
-
1




t




t




t
2
(
)
cos
(
)
sin
( )
cos
,

+


2
t
2
( )
cos
(
)
sin




+
(
)
- +
1




t




t




t
2
(
)
cos
(
)
sin
( )
sin
,
+


2
t
2
(
)
cos


2
t
2

The first two equations can be combined to yield
=


collect
,
,
+
%
1
( )
sin
%
2
( )
cos
(
)
sin
[
]
diff
simplify
0
=
2
t
2
0
Hence, solutions with
=
const
force a constant precession,
=
t
const
. From the third
equation, we then see that
=
t
const
as well.


subs
,
=
2
t t
0 %%
1
Page 13

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