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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 23)

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


-
( )
sin
V
-
+
-
( )
sin
(
)
-
Q
2 A
C
( )
cos
(
)
+
( )
sin
( )
cos
V
2
( )
cos
U
( )
cos
A
C
-
Q
( )
sin
( )
cos
V
d
d
where
(
)
mat subslist


=
Q
-
1
A
C
=
U
+
( )
sin
h
( )
cos
a
=
V
(
)
-
1
A
C
(
)
+
( )
sin
h
( )
cos
a
and
=
( )
cos
cos_chi
( )
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
-
Partial Evaluation of the Torque Integral in the Conical Frame
torque_cone_integral


K
K
K
0
2
f
+
f
S
P
( )
cos
=


-
( )
sin
V
-
+
-
( )
sin
(
)
-
Q
2 A
C
( )
cos
(
)
+
( )
sin
( )
cos
V
2
( )
cos
U
( )
cos
A
C
-
Q
( )
sin
( )
cos
V
d
d
We can do the integral over
right away. We note that
=
f
a
( )
sin
and
=
S
-
b
a
( )
sin
. Hence,




subs
,
,
=
+
f
S
b
( )
sin
=
f
a
( )
sin
%
Page 23

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