I have been reading up on the mathematic of atmospheric entry. I have found different methods to theoretically calculate the corridor width but I don't understand how to define the overshoot and undershoot boundaries. I hope this question will be somewhat coherent, but I'm just very confused. I understand that the undershoot boundary means the spacecraft experiences too much deceleration and the overshoot boundary means it doesn't decelerate enough, but mathematically I don't know how to calculate this. It seems just a blind collection of data, but it just seems there should be a simpler approach. I have found two calculation methods. First a perigee parameter developed by Dean Chapman: Link to paper on corridor analysis
And then a planar equation developed from Loh's second order equation. Link to book (Chp.8)
Any help or pointers would be much appreciated.