Question 10.5: A rigid spacecraft is modeled by the solid cylinder Bwhich h...

For the cylindrical shell A, we have
\begin{matrix} r_{B}=0.5  m & l_{B}=1.0  m & m_{B}=300   kg\end{matrix}

The principal moments of inertia about the center of mass are found in Figure 10.9(b),
I_{B_{x}} =\frac{1}{4}m_{B}r^{2}_{B}+\frac{1}{12}m_{B}l^{2}_{B}= 43.75   kg·m^{2}
I_{B_{y}} = I_{B_{xx}} = 43.75 kg·m^{2}
I_{B_{z}} =\frac{1}{2}m_{B}r^{2}_{B}=37.5  kg·m^{2}
The properties of the transverse rod are
\begin{matrix} l_{R}=1.0m&m_{R}=30 Kg\end{matrix}
Figure 10.9(a), with r = 0, yields the moments of inertia,
I_{R_{y}} = 0
I_{R_{z}} = I_{R_{x}} =\frac{1}{12}m_{A}r^{2}_{A} = 10.0  kg·m^{2}
The moments of inertia of the assembly is the sum of the moments of inertia of the cylinder and the rod,
I_{x} = I_{B_{x}} + I_{R_{x}} = 53.75  kg·m^{2}
I_{y} = I_{B_{y}} + I_{R_{y}} = 43.75  kg·m^{2}
I_{z} = I_{B_{z}} + I_{R_{z}} = 47.50  kg·m^{2}
Since I_{z} is the intermediate mass moment of inertia, rotation about the z axis is unstable. With energy dissipation, rotation is stable in the long term only about the major axis, which in this case is the x axis.