I am studying the Apollo Guidance, specifically the derivation of guidance equation. While laying the baseline, a Target-referenced time (T) is chosen as time variable for guidance calculation of the trajectory evolving backward in time from landing target. T remains negative at all points before landing. In general sense, I understand back propagation however w.r.t. Guidance I dont understand this:
It is convenient to think of the reference trajectory as evolving backwards in time from the target point, with the time variable T reaching zero at the target point and negative prior to that point. Thus target-referenced time (T) is to be distinguished from clock-time (t). Because guidance gains would become unbounded, the target point is never reached. Instead, a guided phase is terminated at a negative time T and the succeeding phase is started. Both the terminus and the target point lie on the reference trajectory, but the target point lies beyond the portion that is actually flown.
Klumpp, A. R., “Apollo Lunar Descent Guidance,” Automatica, Vol. 10, No. 2, 1974, pp. 133–146.
What is meant by and how would guidance gains become unbounded?
What is meant in the last sentence specifically in " ... target point lies beyond the portion that is actually flown"?
