Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 15
d
h
a
b
z
y
x
f
S
Figure 2
r
Transformation matrix from conical to Cartesian coordinates:
( )
sin
( )
cos

( )
sin
( )
cos
( )
cos
( )
sin
( )
sin
( )
cos
( )
cos
( )
sin

( )
cos
0
( )
sin
For later convenience, make this and its inverse into functions.
:=
M
%
:=
ConToCart
(
)
,
a b
(
)
evalm
(
)
subs
,
,
=
a
=
b
(
)
eval M
:=
CartToCon
(
)
,
a b
(
)
map
,
simplify
(
)
inverse
(
)
ConToCart
,
a b
(
)
latex
,
(
)
ConToCart
,
"d:/dynamics/precession/ConicalToCartesian.tex"
(
)
latex
,
(
)
CartToCon
,
"d:/dynamics/precession/CartesianToConical.tex"
Hence,
=
(
)
mat
,
,
xhat yhat zhat
(
)
ConToCart
,
&*
(
)
mat
,
,
rhohat etahat alphahat
Page 15