and T is the wheel acceleration time (assuming a constant torque), /, > /2 > /3 are the ordered body moments of inertia, is the transverse wheel moment of inertia, and lw is the axial wheel inertia. Equations (19-88) and (19-89) assume that the /3 axis (the smallest moment-of-inertia axis) is parallel to the wheel axis (!y in the example). Thus, reduced offset angles are achieved, for a given configuration, by reducing the wheel acceleration torque, h/T.

As an example of the application of the momentum transfer maneuver, we consider a proposed acquisition sequence for CTS [Lerner, el al., 1976], The mission mode angular momentum was 20 N-m-s (3750 rpm) and 0.01 N-m-s (1 rpo) for the wheel and body, respectively, along the positive orbit normal. The angular momentum at the start of the acquisition was — 9726 N-m-s (60 rpm along the negative orbit normal). The proposed acquisition sequence was as follows:

1. Use gas jets to despin to - 1.25 rpm to obtain a total angular momentum of 20 N-m-s ii.

2. Accelerate the wheel until the body rate is ~ I rpo, at which time the wheel speed will be near 3750 rpm.

3. Damp the resultant nutation, using thrusters as described in Section 18.4 (typical half-cone angles are 8 to 10 deg).

4. Use thrusters to precess the attitude to orbit normal, as described in Section 19.3, to achieve the final attitude (typical attitude errors are 7 to 13 deg).

Table 19-2 summarizes the results of simulated momentum transfer sequences for CTS as a function of wheel acceleration time.

Deadbeat Boom Deployment. Deadbeat deployment consists of either extending booms or antennas so as to minimize attitude librations after deployment or using extendable appendages to remove existing libratiops. The former procedure was used on RAE-1 and -2 and the latter on GEOS-3. Such maneuvers are called

Table 19-2. Simulated Momentum Transfer Acquisition Maneuvers for CTS
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