6.31 At the tips of the endcaps, this would correspond to a deflection of l.34xl04 meter (.134 millimeter) for the .75g example. VI.5.3: Uncontrolled Variations in the Hull Spin Axis: Were the hull a pure gyro, the analysis and equations in Section VI.5.2 would accurately predict its behavior. Then the spinning hull's axis of symmetry could be pointed at the Sun and the colony could thereafter be provided with a constant precessive torque. However, the hull was not a simple gyro, and its behavior was complicated by extra precession and nutation. If a mass of 5000 kg were accelerated at lm/sec 2 , parallel to the spin axis, in the agricultural area, then the reaction force required would apply a torque to the hull: (Torque applied) = (5000) (1) (100) = 5x10 5 kg-m 2 /sec 2 By the equations of Section VI.5.1, the hull would respond by precessing with angular velocity: l1 = 5xl0 5 hull 2.89xl011 l.73xl06 radian/sec If the torque were applied for 10 seconds (the mass would then travel on at constant velocity), the hull would precess through l.73xl05 radian, with an endcap-tip deflection of 2.59xl03 meter. The effect in this example is not very significant but such torqueproducing accelerations and torques on mountings of rotating machinery could add up to uncontrolled precession of the spin axis. Furthermore, if there were asymmetries in the mass distribution of the hull, then it would not spin around its nominal axis of symmetry. This is called nutation; physically, it would cause a wobbling motion in the hull's spin. Asymmetries were unavoidable since machines, goods, and people move around within the hull. For example, a gathering of 1000 people would be a mass concentration of 5xio 5 kg. The ES group did not have the time or skills to do detailed analyses of the effects of uncontrolled precession and nutation on the orientation and position of the spin axis. (Such calculations
RkJQdWJsaXNoZXIy MTU5NjU0Mg==