Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 32
,
=
B
1
-
1
2
(
)
+
a
b
( )
cos
U
( )
sin
2
1
3
+
+
a
2
a b
b
2
( )
sin
2
=
B
2
1
2
(
)
+
a
b U Q
( )
sin
subslist
[
]
,
,
=
Q
-
1
A
C
=
U
+
( )
sin
h
( )
cos
a
=
V
(
)
-
1
A
C
(
)
+
( )
sin
h
( )
cos
a
Simplification of the Torque Combinations
Let's check the commonality between the two torque combinations.
(
)
mat
,
+
K
x
( )
sin
K
y
( )
cos
-
K
x
( )
cos
K
y
( )
sin
=
(
)
factormat
,
,
,
(
)
subs
,
subslist
1
(
)
mat
,
torque
torque
collect [
]
,
,
B
1
B
2
C
1
factor
+
( )
cos
K
y
K
x
( )
sin
-
+
K
y
( )
sin
( )
cos
K
x
P
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
(
=
2
( )
sin
( )
cos
(
)
-
a
b (
)
+
1
A
C
B
1
(
)
-
( )
sin
( )
cos
(
)
+
( )
sin
( )
cos
(
)
-
a
b B
2
+
( )
sin
(
)
-
a
b C
1
a
2
h (
)
- +
1
A
T
+
+
)
+
X
( )
cos
Y
( )
sin
-
-
+
(
)
sin
Z
(
)
cos
Y
( )
cos
( )
sin
(
)
cos
X
:=
torque_terms
%
(
)
select
,
,
has
(
)
rhs %
a
2
( )
sin
( )
cos
(
)
-
a
b (
)
+
1
A
C
B
1
(
)
-
( )
sin
( )
cos
(
)
+
( )
sin
( )
cos
(
)
-
a
b B
2
+
( )
sin
(
)
-
a
b C
1
a
2
h (
)
- +
1
A
T
+
+
:=
L
(
)
location
,
%% %
:=
L
[
]
,
2 4
(
)
subs
,
,
,
Csubs Bsubs subslist
1
%%
2
( )
sin
( )
cos
(
)
-
a
b (
)
+
1
A
C
-
1
2
(
)
+
a
b
( )
cos
U
( )
sin
2
1
3
+
+
a
2
a b
b
2
( )
sin
2
1
2
(
)
-
( )
sin
( )
cos
(
)
+
( )
sin
( )
cos
(
)
-
a
b (
)
+
a
b U (
)
-
1
A
C
( )
sin
+
(
)
-
a
b
-
1
2
(
)
+
a
b U
1
3
( )
cos
(
)
+
+
a
2
a b
b
2
(
)
-
1
A
C
( )
sin
a
2
h (
)
- +
1
A
T
+
+
Page 32
