Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 36
(
)
G
, , ,
,
,
a b h A
C
A
T
P
=
(
)
-
a
b (
)
-
+ +
A
C
1
2 A
C
( )
cos
2
(
)
+
( )
sin
h
( )
cos
a (
)
+
a
b
( )
sin
-
-
1
3
( )
cos
(
)
-
a
b A
C
( )
sin
( )
cos
(
)
-
a
b
( )
sin
(
)
+
+
a
2
a b
b
2
a
2
h (
)
- +
1
A
T
+
+
(
)
latex
,
FirstOrderODEs "d:/dynamics/precession/FirstOrderODEs.tex" ;
(
)
latex
,
(
)
mat gsubs
"d:/dynamics/precession/gsubs.tex"
Fast Spin Approximation
The equations of motion are
eqs :=
(
)
subs
,
,
(
)
op
(
)
select
,
,
has gsubs
=
(
)
G
, , ,
,
,
a b h A
C
A
T
G [
]
(
)
seq
,
FirstOrderODEs
,
k 1
=
k
..
4
6
(
)
mat %
(
)
sin
t
(
)
-
(
)
-
1
(
)
cos
(
)
+
1
=
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
G (
)
+
X
( )
cos
Y
( )
sin
I
xy
+
t
+
(
)
- +
1
2
(
)
cos
(
)
sin
(
+
=
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
G
(
)
-
-
+
(
)
sin
Z
(
)
cos
Y
( )
cos
( )
sin
(
)
cos
X
I
xy
)
(
)
sin
t
(
)
+
(
)
+
(
)
cos
2
1
(
)
- +
1
(
)
cos
=
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
G (
)
+
X
( )
cos
Y
( )
sin
(
)
cos
I
xy
-
For purposes of substitution, which we'll use in a moment, divide by
(
)
sin
where
appropriate.
select
,
,
has eqs
t
Page 36
