Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 20
=
dF
dF
dF
P
( )
cos
dS
-
(
)
-
A
C
1
-
(
)
-
A
C
1
-
-
2 A
C
( )
cos
(
)
-
A
C
1
Thus, the force integrated over the cone surface is
=
(
)
mat
,
,
F
F
F
d
0
2
d
f
+
f
S
(
)
subs
,
=
dS
( )
sin
(
)
rhs %
=
F
F
F
d
0
2
d
f
+
f
S
P
( )
cos
( )
sin
-
(
)
-
A
C
1
-
(
)
-
A
C
1
-
-
2 A
C
( )
cos
(
)
-
A
C
1
:=
Fintegral
%
(
)
latex
,
% "d:/dynamics/precession/ConeForceIntegral.tex"
Torque Due to Radiation Pressure on the Cone Surface
Radius Vector to Cone Surface
To calculate the torque, we first need the radius vector to a point on the surface of the
cone. The transformation from conical to cartesian body coordinates is
,
,
=
x
( )
sin
( )
cos
=
y
( )
sin
( )
sin
=
z
-
+
h
( )
cos
a
( )
tan
.
:=
xyz
%
Hence, the radius vector from the center of mass to a point on the cone surface is, in the
conical frame,
(
)
subs
,
xyz
(
)
CartToCon
,
&*
(
)
mat , ,
x y z
(
)
map
,
,
,
collect
(
)
evalm %
[
]
,
h a
simplify
:=
r_cone
%
( )
sin
( )
cos
( )
sin
( )
sin
-
( )
cos
-
( )
sin
( )
cos
0
( )
cos
( )
cos
( )
cos
( )
sin
( )
sin
&*
( )
sin
( )
cos
( )
sin
( )
sin
-
+
h
( )
cos
a
( )
tan
-
-
+
( )
cos
h
( )
cos
2
a
( )
sin
0
+
( )
sin
h
( )
cos
a
Page 20
