Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 40
subs
,
,
=
t
=
t
%
(
)
convert
,
(
)
expansion
,
,
% [
]
,
,
G
1
diff
(
)
Collect
,
,
% [
]
G
factor
:=
eqs2
(
)
invsubs
,
[
]
,
(
)
op gsubs
=
(
)
lhs
(
)
op
(
)
select
,
,
has gsubs G
G
%
(
)
mat %
(
)
sin
2
t
2
=
-
-
(
)
- +
1
(
)
g
0
,
(
)
g
2
,
(
)
G
, , ,
,
,
a b h A
C
A
T
I
xy
(
)
- +
1
2
2
(
)
sin
=
2
t
2
-
(
)
- +
1
(
)
g
0
,
(
)
G
, , ,
,
,
a b h A
C
A
T
(
)
g
1
,
I
xy
(
)
- +
1
2
2
(
)
sin
2
t
2
(
)
- +
1
2
(
)
cos
2
(
)
sin
=
(
)
- +
1
(
)
cos
(
)
g
0
,
(
)
G
, , ,
,
,
a b h A
C
A
T
(
)
g
2
,
I
xy
+
Since
is large, we may also assume its rate of change is small, hence
=
2
t
2
0
. The first
consequence of this is that the angular velocity of the inclination,
, exhibits simple
harmonic motion: the solution of
=
+
+
2
t
2
(
)
-
1
2
2
(
)
-
1
(
)
g
0
,
(
)
G
, , ,
,
,
a b h A
C
A
T
(
)
g
1
,
I
xy
0
is just
collect subs
=
=
g
0
(
)
g
0
,
=
g
1
(
)
g
1
,
,
,
,
(
(
(
)
dsolve
,
(
)
subs
,
,
,
=
=
(
)
g
1
,
g
1
=
(
)
g
0
,
g
0
%
) [
]
,
_C1 _C2
factor
,
,
)
=
+
+
(
)
g
0
,
(
)
G
, , ,
,
,
a b h A
C
A
T
(
)
g
1
,
(
)
- +
1
I
xy
_C1
(
)
cos (
)
- +
1
t
_C2
(
)
sin (
)
- +
1
t
Page 40
