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Astronomical Applications Department, U.S. Naval Observatory - Precession Maple (Page 9)

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




+
(
)
- +
1




t
(
)
cos
(
)
+
1




t




t
( )
cos
K
y
I
xy
+
-
,
-
+
+


2
t
2
(
)
cos




t
(
)
sin




t


2
t
2
K
z
I
xy
(
)
- +
1

(
)
latex
,
SymTop
1
"d:/dynamics/precession/SymTop1.tex" ;
(
)
latex
,
SymTop
2
"d:/dynamics/precession/SymTop2.tex" ;
(
)
latex
,
SymTop
3
"d:/dynamics/precession/SymTop3.tex"
Conversion to a System of First-Order ODEs
We may write the equations of motion as a system of first-order differential equations.
:=
subslist




,
,
=
t
=
t
=
t
(
)
subs
,
subslist SymTop




solve
,
{
}
(
)
op %
{
}
,
,
t
t
t
(
)
collect
,
,
% [
]
,
,
,
I
xy
(
)
sin
factor
=
t
+




+
(
)
- +
1
2
(
)
cos
(
)
sin
-
+
K
y
( )
sin
( )
cos
K
x
I
xy
,

=
t
+
(
)
-
(
)
-
1
(
)
cos
(
)
+
1
(
)
sin
+
( )
cos
K
y
K
x
( )
sin
(
)
sin
I
xy
t
=
,


-
+
(
)
sin
+
(
)
- +
1
(
)
cos
(
)
+
1
(
)
sin
-
-
K
z
- +
1
(
)
+
( )
cos
K
y
K
x
( )
sin
(
)
cos
(
)
sin
I
xy
+

:=
foo
%




select
,
,
has foo
t
(
)
collect
,
,
(
)
op %
(
)
sin
[
]
,
,
I
xy
factor
:=
foo
union
(
)
minus
foo
%%
{
}
%
Page 9

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