R.G. Melton
AERSP 309
HW #11
Fall 2005
(Due Monday Dec. 5 at beginning of class)
1.
(20 points)
Consider a rigid body with principal moments of inertia
I
1
=
I
2
= 5000 kg
⋅
m
2
and
I
3
= 9000 kg
⋅
m
2
.
It is rotating in a torquefree environment, with initial conditions
ω
1,0
= 0.2 rad/s,
2,0
= 0.35 rad/s, and
3,0
= 2.7 rad/s.
a.
(10 pts) Find the complete solutions for
1
(
t
),
2
(
t
), and
3
(
t
).
b.
(5 pts) Calculate the angle between
3
ˆ
and
b
K
c.
(5 pts) Show that
3
ˆ
and
,
,
b
H
K
K
all lie in the same plane at any time.
Remember
that 3 vectors are coplanar if any one of them is perpendicular to a vector created
by the cross product of the other two original vectors.
2.
(20 points)
A satellite that is spinning about its
3
ˆ
b
axis is initially oriented with
3
3
ˆ
to
parallel
ˆ
n
b
in the Newtonian frame as shown in the figure.
Mission requirements
call for reorienting the s/c by 30 deg. about the
2
ˆ
n
axis.
This is to be accomplished by
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 MELTON
 Angular Momentum, Moment Of Inertia, Rigid Body, Rotation, S/C

Click to edit the document details