During axial thrusting of a spinning spacecraft, misalignments and center-of-mass offset result in velocity pointing errors. These pointing errors cause the spacecraft to deviate from its desired trajectory. Typically the axial thrust behaves like a step function, jumping from zero to its maximum value. Alternatively, by ramping-up the axial thrust from zero to its maximum value, the velocity pointing errors are significantly reduced compared to those arising from the step function. Cubic ramp-up profiles are analyzed to heuristically find a suboptimal solution to minimize the velocity pointing error. Some of these cubic profiles drive the velocity pointing error to nearly zero and hence qualify as optimal solutions (for all practical purposes).
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