Compute the pitching motion of the spacecraft, Physics

A spacecraft design similar to GEOSAT proposes to use passive gravity-gradient stabilization for pitch attitude control (motion about the y-axis).  The satellite consists of a tip mass, separated from the main satellite body mass by a rigid boom with length 10 m.  The z-body axis is along the boom, and pitching motion is along the y-body axis (which is opposite the angular momentum vector of the orbit; the +y-axis is into the page).  The spacecraft is in circular LEO (altitude = 800 km).  The satellite is axis-symmetric, and the moments of inertia are Izz = 85 kg-m2, and  Ixx = Iyy =2530 kg-m2.

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Compute (by hand) the pitching motion of the spacecraft in LEO for an initial pitch angle of 5 deg.  Assume that the only torque acting on the satellite is the gravity-gradient torque and that the initial angular rates are zero and that no roll/yaw motion exists.  Sketch the pitching motion vs. time for one orbital revolution.

Posted Date: 2/19/2013 2:18:03 AM | Location : United States

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