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MAE146: Astronautics – Homework
Assigned: Wednesday, January 6
th
,
2010
Due date: Friday , January 8
th
,
2010,
(at the beginning of the lecture)
Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forget
to write your name on your copy to receive credit.
Problem 1 (10pts): Elementary rotations
Given a reference frame
R
= (0
,
ˆ
e
1
,
ˆ
e
2
,
ˆ
e
3
), the elementary rotations are de±ned as the rotations transforming the
basis ( ˆ
e
1
,
ˆ
e
2
,
ˆ
e
3
) into a basis (
ˆ
f
1
,
ˆ
f
2
,
ˆ
f
3
) with one of the basis vector ±xed (that is
ˆ
f
i
= ˆ
e
i
for some index
i
). The other
basis vectors are rotated by a ±xed angle,
θ
, with positive angle being understood as counterclockwise rotations
when looking down the ±xed vector.
For example, the rotation leaving the 3
rd
axis ±xed is de±ned by the relations:
ˆ
f
1
=
cos(
θ
)
.
ˆ
e
1
+ sin(
θ
)
.
ˆ
e
2
(1)
ˆ
f
2
=

sin(
θ
)
.
ˆ
e
1
+ cos(
θ
)
.
ˆ
e
2
(2)
ˆ
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This note was uploaded on 03/13/2010 for the course MAE 19100 taught by Professor Villac during the Winter '10 term at UC Irvine.
 Winter '10
 Villac

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