where A , Ay, and At are the Euler rotation matrices (see Section 12.1) and terms of order £ are omitted in Eq. (18-46) and throughout this section. Thus, BXJ= +L and 2*23= ~ The error quaternion is measured onboard the HEAO-1 spacecraft by continuously propagating a reference attitude (measured on the ground using star tracker data) with rate-integrating gyros (see Section 6.5.2). The gyros also measure the body rates, which may be compared with the desired rates of uxftn3r^0 and uzss0.18 deg/sec. The position and rate error for either the X or Y axis are combined as shown schematically in Fig. 18-11 to yield a desired thruster burn duration, tx=Kx(-B23+Txulx)

where Kx and Kr are the system gains, tx and ry are lead time constants, and tx and ty are the desired thruster burn durations. Errors about the X and Y body axes are corrected independently (the small gyroscopic coupling between the X and Y axes through the angular momentum about the Z body axis is ignored).



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