H2 H 42 lt 5 W2

Denoting the roots of this fourth-order equatior by s,, sf, s2, and sj, the time constants and frequencies are t,= - 1/Re(i,)«6.1 days t2 = — 1 /Re(i2)s»5.1 hours

The fact that these time constants are much greater than the orbit period (100 minutes) justifies the orbit averages of Eq. (18-77). The characteristic frequencies, /, and f2, are related to the gravity-gradient restoring torque and nutation, respectively. The very long time constants associated with the decay of transient pitch and roll oscillations required the development of a procedure which minimized the pitch and roll errors after attitude acquisition (see Section 19.5).

HCMM. The HCMM control system, as outlined in Table 18-2, provides pitch control by torquing the pitch wheel based on horizon scanner pitch angle data. The pitch wheel torque command, shown schematically in Fig. 18-15, is computed from the pitch angle and rate as

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