Space Propulsion - IAP/TU Wien

One sided limit cycle, ct‘d
Space Propulsion
S/C rotation is accelerated by from zero speed at the extreme limit +Θ L (point 1) through an angular path
of < 2ΘL with an angular acceleration α x , generated by the external torque only. The opposite
limit angle will be reached after an angular interval 2Θ L and a “pass” time t p (approximately equal to
half the cycle time t cy ).
Θ
1
=
2
2
2
L
α
x p
t
t
cy
Θ
L
= ~ 2t
p
= 4 = 4
α
x
ΘLI
T
x
v
angular speed ω L , at the end of the cycle, at – Θ L (at point 2) is
ω
L
= α t / 2 = 2
x
cy
T
x
I
Θ
v
L
Now the thrusters are firing, producing a thrusting angular
acceleration α. They reduce this angular speed to 0
(at the turning point 3) after a burning time of P W /2
ω
L
= α. P / 2 =
W
nLFP
2I
v
W
From that follows the impulse per thruster, required to turn
around the angular speed of the S/C, so that it moves against
external torque up to an angle of not larger than Θ L
FP
W
≤ 4
nL
T
x
I
v
Θ
L
If minimum impulse bits I min are used, the rotation limit must be
wider than a minimum Θ L , in order to avoid thrusters being fired
in the direction of external torque. This would cause excessive
propellant consumption.
Θ
L
>
2 2 2
n L I
16I
T
v
min
x