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