As rrf-rcf is, in general, not perpendicular to hr, there is some leftover RSO’s angular momentum that needs to be neutralized by the contributing chaser’s angular momentum at capture hc(tf). Additionally, the tumbling RSO center-of-mass is assumed to be initially at rest with respect to the inertial frame I. Thus, before the capture occurs, the RSO’s linear velocity and momentum are zero. Spinning only at a 1.44 deg/s, INTELSAT VI required multiple capture attempts before it was manually captured and detumbled by three space walking astronauts. The capture and detumble of INTELSAT VI by the STS-49 crew in 1992 (Bennett, 1993) exemplifies some of these challenges. Under these assumptions, the equation of motion in Equation (19) can be further simplified, yielding Equation (43). The position, velocity and acceleration of the unique shifting mass with respect to the body axes is denoted by x, y and the shifting mass velocity with respect to the body reference frame B0 by ẋ′, ẏ′.
Une grande liberté de mouvement
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Une grande flexibilité, permettant de s’adapter au pied
It is immediately clear from Equation (45) that to generate a control torque it is much more effective for the mass to move perpendicular to the relative flow (in this case y) than parallel to it (along x). The capture objective is casted as a terminal constraint on the chaser’s end-effector position and velocity, whereas the detumble objective is formulated from a momenta standpoint and casted as terminal constraint on the chaser’s momenta. Additionally, in order to avoid colliding with the target, a keep-out zone constraint is used. This underlying terminal constraint can be casted in terms of generalized velocities u and incorporated in an optimization-based guidance approach.
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• Reduced Model Controller Asm.5: Shifting mass velocities and accelerations have negligible effects on the dynamics. • Reduced Model Controller Asm.4: The relative position, velocity and acceleration of the shifting mass are known. It is clear that the mass of the shifting mass and the available shifting range are the two variables at the designer disposal to regulate the control authority of the system. This controller also carries the underlying assumption that the shifting mass can instantaneously move, without lag, from one position to another one.
However, in the context of VLEO, these strong secular torques may be a burden for other attitude control methods as well (e.g., rapidly saturating reaction wheels) and thus holding attitudes far from the aerodynamic equilibrium points is an intrinsic challenge for spacecraft operating in VLEO. These two sets of terminal constraints are then fused into a unified and coherent set. The complete maneuver is recovered as the combination of the two sub-maneuvers. Figure 7. Required 3σ shifting range (A) and 3σ attitude error (B) with respect to the shifting mass fraction for a 10 cm radius spherical spacecraft. Figure 8. Required 3σ shifting range (A) and 3σ attitude error (B) with respect to the CoP to CoM distance dCoM0 for a 10 cm radius spherical spacecraft. болка в крака подагра
. As expected the required mass fraction and required shifting range decrease as the CoP gets closer to the CoM. The aerodynamic disturbances have low frequencies (similar to the orbit frequency) and so it is expected that the motion of the shifting mass will be also slow (small velocities and accelerations), thus limiting the dynamic effects of the shifting mass.