Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 39
Y
(
)
cos
t
( )
cos
Y
(
)
sin
( )
sin
t
X
(
)
cos
t
( )
sin
-
+
+
X
(
)
sin
( )
cos
t
+
G (
)
+
X
( )
cos
Y
( )
sin
(
)
cos
I
xy
-
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
G
-
+
X
( )
sin
t
Y
( )
cos
t
(
)
cos
I
xy
+
(
)
-
+
(
)
cos
Z
Y
(
)
sin
( )
cos
X
(
)
sin
( )
sin
G (
)
+
X
( )
cos
Y
( )
sin
(
)
sin
t
I
xy
Substitute for
t
,
t
, and
t
using the original equations of motion. Then, assume
is large and the pressure terms (i.e.,
(
)
G
, , ,
,
,
a b h A
C
A
T
) are small. We find the resulting
second-order differential equations,
subsODEs
,
ode odesubs
proc(
)
:=
local
;
,
, ,
,
q Lq u Lu eqn
:=
eqn
(
)
copy ode ;
not (
)
and
(
)
isdiff eqn
<
1
(
)
difforder eqn
q
eqn
for
in
do
if
then
:=
Lq
(
)
location
,
eqn q ;
and
( )
isdiff q
=
( )
difforder q
1
:=
q
(
)
subs
,
odesubs q
if
then
and
<
1
( )
nops q
not
( )
isdiff u
:=
q
(
)
procname
,
q odesubs
elif
then
fi;
:=
eqn
(
)
subsop
,
=
Lq
q eqn
od
fi;
(
)
eval eqn
end
Check:
for
to
do
od
ii
3
(
)
factor
-
(
)
subs
,
odesubs
(
)
rhs eqs2
ii
(
)
subsODEs
,
(
)
rhs eqs2
ii
odesubs
0
0
0
(
)
subsODEs
,
eqs2 odesubs
Page 39
