Astronomical Applications Department, U.S. Naval Observatory Precession Maple Page 1
Rigid Body Dynamics of a
Spinning Truncated Cone
Immersed in a Pressure Field
Marc A. Murison
Astronomical Applications Department
U.S. Naval Observatory
Washington, DC
murison@riemann.usno.navy.mil
http://aa.usno.navy.mil/murison/
17 March, 1998
Euler Equations of Motion for a Rigid Body
restart;
alias
=
I
I
=
( )
t
=
( )
t
=
( )
t
=
x
( )
x
t
=
y
( )
y
t
=
z
( )
z
t
=
( )
t
=
( )
t
,
,
,
,
,
,
,
,
,
(
=
( )
t )
In the frame of reference attached to the rotating body (the body frame), the equations of motion
are
EulerEqs
mat
+
-
I
x
t
x
(
)
-
I
z
I
y
y
z
K
x
+
-
I
y
t
y
(
)
-
I
x
I
z
x
z
K
y
,
,
:=
+
-
I
z
t
z
(
)
-
I
y
I
x
x
y
K
z
:=
EulerEqs
+
-
I
x
t
x
(
)
-
I
z
I
y
y
z
K
x
+
-
I
y
t
y
(
)
-
I
x
I
z
x
z
K
y
+
-
I
z
t
z
(
)
-
I
y
I
x
x
y
K
z
(
)
latex
,
EulerEqs "d:/dynamics/precession/EulerEqs.tex"
where
,
,
I
x
I
y
I
z
are the principal moments of inertia of the body,
,
,
x
y
z
are the angular
velocities of the body about the principal axes, and
,
,
K
x
K
y
K
z
are the components of the torque
acting on the body.
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