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icj MANEUVER CHARACTERISTICS

Fig. 19-15. Computer Simulation Results for Momentum Transfer Maneuver (from Barba and Aubran, [1975D

offset, which is typically 5 to 10 deg. Figure 19-15c illustrates the characteristics of the maneuver.

If the transverse wheel moment, of inertia, AT„ is assumed to be small compared with the body moment of inertia about the z axis, lt, the initial state is

and the desired final state, in an inertial frame, is

where is the angular momentum of the body, L^ is the angular momentum of the wheel, A is a unit vector in the direction of the orbit normal, Iy is the moment of inertia of the spacecraft about the y axis, and h is the magnitude of the wheel momentum. Conservation of the total angular momentum, Lr, during wheel accleration ensures that, in an inertia! frame.

Lr = Ls(0) + MO) = ¡¿In = Lfl( 7") + L„( 7") (19-86)

Control over wheel speed during acceleration permits the relation Lw,(7)= - Ay to be obtained in body coordinales, but the identity

L*-h2 = constant = ¿J ( 7")+ 2Lfl( 7> 7") (19-87)

does not guarantee that Lg{T) is near the orbit normal although that desired configuration is consistent with the conservation of energy and momentum and is nearly obtained. The offset angle, 8, is approximately [Gebman and Mingori, 1975]

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