Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 28
K
x
K
y
K
z
0
2
P
( )
cos
(
)
-
a
b
=
+
+
-
( )
sin
B
2
( )
cos
C
1
( )
sin
B
1
Q
2
( )
sin
B
1
A
C
( )
cos
-
+
-
+
( )
cos
B
2
( )
sin
C
1
( )
cos
B
1
Q
2
( )
cos
B
1
A
C
( )
cos
(
)
-
+
( )
cos
B
2
( )
sin
B
1
Q
d
Finally, substitute for
cos
and the pressure components and perform the integration.
(
)
subs
,
,
Psubs
=
( )
cos
cos_chi %
(
)
map
,
,
int
(
)
map
,
,
collect
(
)
evalm
(
)
op
,
[
]
,
2 1
%
[
]
,
,
( )
sin
( )
cos
P
:=
foo
%
k
3
;
:=
foo
,
k 1
-
(
)
subs
,
=
2
foo
,
k 1
(
)
subs
,
=
0 foo
,
k 1
:=
foo
,
k 1
(
)
factor foo
,
k 1
for
to
do
od
(
)
factormat
,
,
foo collect [
]
,
,
X
Y
Z
=
(
)
mat
,
,
K
x
K
y
K
z
%
:=
torque_xyz_cone
%
K
x
K
y
K
z
P
(
)
-
a
b
=
(
)
-
+
+
+
+
( )
cos
2
B
2
( )
sin
2
B
2
4
( )
sin
B
1
A
C
( )
cos
C
1
( )
sin
2
( )
sin
B
1
Q
( )
cos
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
(
)
+
( )
cos
(
)
cos
( )
sin
( )
sin
( )
cos
X
[
(
)
-
+
( )
cos
(
)
cos
( )
cos
( )
sin
( )
sin
Y
Z
( )
cos
(
)
sin
+
-
]
(
)
-
( )
cos
( )
cos
( )
sin
(
)
cos
( )
sin
X
(
)
+
( )
cos
( )
sin
( )
sin
(
)
cos
( )
cos
Y
+
[
( )
sin
(
)
sin
Z
+
]
[ ]
0
(
)
latex
,
torque_xyz_cone "d:/dynamics/precession/ConeTorqueBody.tex"
We can simplify
C
1
and
C
2
somewhat:
Page 28
