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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 16)

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


xhat
yhat
zhat


( )
sin
( )
cos
-
( )
sin
( )
cos
( )
cos
( )
sin
( )
sin
( )
cos
( )
cos
( )
sin
-
( )
cos
0
( )
sin
&*


rhohat
etahat
alphahat
and
=
(
)
mat
,
,
rhohat etahat alphahat
(
)
CartToCon
,
&*
(
)
mat
,
,
xhat yhat zhat
=


rhohat
etahat
alphahat


( )
sin
( )
cos
( )
sin
( )
sin
-
( )
cos
-
( )
sin
( )
cos
0
( )
cos
( )
cos
( )
cos
( )
sin
( )
sin
&*


xhat
yhat
zhat
Radiation Pressure
Let
[
]
,
,
P
X
P
Y
P
Z
be the pressure vector in the fixed frame. Then the conical coordinates
representation of
P
is
=
(
)
mat
,
,
P
P
P
(
)
(
)
CartToCon
,
&* (
)
R
,
,
&*
(
)
mat
,
,
P
X
P
Y
P
Z


P
P
P


( )
sin
( )
cos
( )
sin
( )
sin
-
( )
cos
-
( )
sin
( )
cos
0
( )
cos
( )
cos
( )
cos
( )
sin
( )
sin
&*

=
[
,
,
]
-
( )
cos
( )
cos
( )
sin
(
)
cos
( )
sin
+
( )
cos
( )
sin
( )
sin
(
)
cos
( )
cos
( )
sin
(
)
sin
-
-
( )
sin
( )
cos
( )
cos
(
)
cos
( )
sin
-
+
( )
sin
( )
sin
( )
cos
(
)
cos
( )
cos
[
,
,
( )
cos
(
)
sin
]
[
,
,
]
(
)
sin
( )
sin
-
(
)
sin
( )
cos
(
)
cos

&*


P
X
P
Y
P
Z
(
)
latex
,
% "d:/dynamics/precession/PressureBodyFrame.tex"
:=
Pbody
(
)
convert
,
(
)
evalm
(
)
rhs %
vector
(
)
simplify
(
)
mag %
+
+
P
Y
2
P
X
2
P
Z
2
Page 16

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