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Af = acceleration command at rendezvous RTR = distance from receiver to tanker s = distance from receiver to target Vc = closing velocity Vf = final velocity constraint VR = receiver velocity, airspeed VRg = receiver velocity, groundspeed VT = tanker velocity, airspeed VTg = tanker velocity, groundspeed xR = receiver east position xRZ = rendezvous east position xT = tanker east position yR = receiver north position yRZ = rendezvous north position yT = tanker north position yRFE = distance from receiver to tanker in downtrack direction f = final line-of-sight constraint f = final heading constraint R = receiver heading RZ = desired heading at rendezvous T = tanker heading _ = derivative with respect to time
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Austin Smith (2008) studied this question.
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