inertia matrix for the entire spacecraft, when expressed in the spacecraft reference system, is therefore

This is the same quantity that was expressed earlier by (6.3), except now more detailed as needed for practical calculations. The computation required for finding the eigenvalues and eigenvectors of the spacecraft proceeds as in (6.8) and (6.7).

As a simple example we may consider a prismatic body of constant density. This is often a useful approximation for electronic boxes on spacecraft (Fig. 6.3b). In this example it is convenient to define the reference axes of the part to coincide with its principal axes. If the length, width, and height are b\, b2, and b3, the corresponding moments of inertia are easily found to be

" (mb/12) (bf + bj + b\ - bf) if i = j 0 if//;

where mb is the mass of the box. Hence from (6.13)

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