Space Propulsion - IAP/TU Wien

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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
Space Propulsion forced limit cycle A forced limit cycle occurs when thrusters are fired in the direction of the external torque; that is, when the condition Θ L > n 2 L 2 16I v I 2 min T x is not met propellant consumed in a forced limit cycle is m p = IvR LΘ I 2 R [Hz] = 1/t cy = limit-cycle rate tm of the system t L sp m [s] = mission duration R can only be calculated numerically from a higher order equation containing the parameters I min , P W , T x , I v , L, Θ L .
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Space Propulsion - IAP/TU Wien

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