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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 18)

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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple
for
in
do
od
p
(
)
select
,
,
has
(
)
indets %
signum
(
)
subs
,
=
p
1 %
(
)
subs
,
=
P
P %
:=
mag_dF
(
)
rhs %
=
dF
P dS
( )
cos
+
4
( )
cos
2
A
C
(
)
-
A
C
1
2
Now,
=
cos
P
P
. Hence,
=
cos
-
P
P
or
=
cos
(
)
subs
,
,
,
=
P
X
X
=
P
Y
Y
=
P
Z
Z
-
Pbody
3
:=
cos_chi
(
)
rhs %
(
)
latex
,
% "d:/dynamics/precession/cos_chi.tex"
cos
( )
cos
( )
cos
(
)
-
( )
cos
( )
cos
( )
sin
(
)
cos
( )
sin
(
-
=
( )
cos
( )
sin
(
)
-
-
( )
sin
( )
cos
( )
cos
(
)
cos
( )
sin
( )
sin
(
)
sin
( )
sin
+
+
)
X
(
-
( )
cos
( )
cos
(
)
+
( )
cos
( )
sin
( )
sin
(
)
cos
( )
cos
( )
cos
( )
sin
(
)
-
+
( )
sin
( )
sin
( )
cos
(
)
cos
( )
cos
( )
sin
(
)
sin
( )
cos
+
-
)
Y
(
)
+
+
( )
cos
( )
cos
( )
sin
(
)
sin
( )
cos
( )
sin
( )
cos
(
)
sin
( )
sin
(
)
cos
Z
-
where
,
,
=
X
P
X
P
=
Y
P
Y
P
=
Z
P
Z
P
.
dF
parallel
can be written
=
dF
parallel
dF
parallel
(
)
-
P
(
)
dot
,
P N N
-
P
(
)
dot
,
P N N
. But
=
-
P
(
)
dot
,
P N N
(
)
cross
,
P N
or
=
-
P
(
)
dot
,
P N N
P
( )
sin
, and
=
(
)
dot
,
P N
P
-
( )
cos
, so we can write
=
dF
parallel
dF
parallel
+
P
P
( )
cos
N
P
( )
sin
=
dF
parallel
dF
parallel
+
P
P
( )
cos
N
P
( )
sin
In component form,
(
)
subs
,
,
,
,
=
P
Q
=
P
(
)
mat
,
,
P
P
P
=
Q
P
=
N
(
)
mat
, ,
0 0 1
%
Page 18

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