Question 10.15: The uniform, monolithic 10,000 kg slab, having the dimension...
The uniform, monolithic 10,000 kg slab, having the dimensions shown in Figure 10.31, is in a circular LEO. Determine the orientation of the satellite in its orbit for gravity gradient stabilization, and compute the periods of the pitch and yaw/roll oscillations in terms of the orbital period T.
According to Figure 9.9c, the principal moments of inertia around the xyz axes through the center of mass are
A=\frac{10,000}{12}\left(1^{2}+9^{2}\right)=68,333 kg \cdot m ^{2}
B=\frac{10,000}{12}\left(3^{2}+9^{2}\right)=75,000 kg \cdot m ^{2}
C=\frac{10,000}{12}\left(3^{2}+1^{2}\right)=8333.3 kg \cdot m ^{2}
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