A satellite controls its rotational velocity by extending an arm much like a balle- rina in a spin or a figure skater. Changing the length, L, of the arm changes the inertia of the satellite. The transfer function between the rotational velocity, w(s), and the incremental change in L, called AL(s) is given as w(s) AL(s) 2(s+4) (s +5) (s + 1)² The change in length is given as 1 AL(s) == S (4) (5) Determine the response to the change in length of the satellite's angular veloc- ity, w(t), in the time domain using partial fractions.

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A satellite controls its rotational velocity by extending an arm much like a balle-
rina in a spin or a figure skater. Changing the length, L, of the arm changes the
inertia of the satellite. The transfer function between the rotational velocity,
w(s), and the incremental change in L, called AL(s) is given as
w(s)
AL(s)
2(s+4)
(s +5) (s + 1)²
The change in length is given as
1
AL(s) ==
S
(4)
(5)
Determine the response to the change in length of the satellite's angular veloc-
ity, w(t), in the time domain using partial fractions.
Transcribed Image Text:A satellite controls its rotational velocity by extending an arm much like a balle- rina in a spin or a figure skater. Changing the length, L, of the arm changes the inertia of the satellite. The transfer function between the rotational velocity, w(s), and the incremental change in L, called AL(s) is given as w(s) AL(s) 2(s+4) (s +5) (s + 1)² The change in length is given as 1 AL(s) == S (4) (5) Determine the response to the change in length of the satellite's angular veloc- ity, w(t), in the time domain using partial fractions.
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