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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 21)

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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple
(
)
latex
,
(
)
mat xyz
"d:/dynamics/precession/ConicalCoordinates.tex"
(
)
latex
,
r_cone "d:/dynamics/precession/r_cone.tex"
Statement of the Torque Integral in the Conical Frame
The torque integrated over the cone surface is therefore
(
)
subs
,
=
F
K
(
)
subsop
,
=
[
]
, ,
2 1 1
(
)
'
'
cross
,
(
)
eval r_cone
(
)
op
,
[
]
, ,
2 1 1
Fintegral
Fintegral
:=
torque_cone_integral
%


K
K
K
0
2
f
+
f
S
=


cross
,


-
-
+
( )
cos
h
( )
cos
2
a
( )
sin
0
+
( )
sin
h
( )
cos
a
P
( )
cos
( )
sin


-
(
)
-
A
C
1
-
(
)
-
A
C
1
-
-
2 A
C
( )
cos
(
)
-
A
C
1
d
d
which can be simplified as follows.
(
)
op
,
[
]
, ,
2 1 1
torque_cone_integral
(
)
+
( )
sin
h
( )
cos
a
P
( )
cos
( )
sin
(
)
-
A
C
1
,

(
)
+
( )
sin
h
( )
cos
a
P
( )
cos
( )
sin
(
)
-
A
C
1
-


-
-
+
( )
cos
h
( )
cos
2
a
( )
sin
P
( )
cos
( )
sin
(
)
-
-
2 A
C
( )
cos
(
)
-
A
C
1
-
,
-


-
-
+
( )
cos
h
( )
cos
2
a
( )
sin
P
( )
cos
( )
sin
(
)
-
A
C
1

(
)
factormat
,
,
,
(
)
mat
(
)
subs
,
=
-
A
C
1
-
Q
(
)
eval %
collect [
]
,
,
,
, ,
Q
A
C
factor
P
( )
cos
[
]
-
(
)
+
( )
sin
h
( )
cos
a
( )
sin
Q
(
)
+
(
)
-
+
( )
sin
( )
cos
(
)
+
( )
sin
h
( )
cos
a
(
)
+
( )
sin
h
( )
cos
a
( )
sin
Q
[
2
( )
sin
A
C
( )
cos
2
( )
cos
(
)
+
( )
sin
h
( )
cos
a
( )
cos
A
C
+
-
]
[
]
(
)
-
( )
sin
( )
cos
(
)
+
( )
sin
h
( )
cos
a
Q
(
)
subs
,
=
+
( )
sin
h
( )
cos
a
U %
Page 21

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