I've been working on this for a while with little success. I'm trying to model a continuous burn orbit maneuver for say 5 minutes. I've tried to split the burn into multiple sub-burns that are calculated instantaneously, but this doesn't seem to work.
My end game here is to model 2 continuous burns both around apogee (so first burn, orbit around to apogee again, second burn). The error I'm currently getting is that if I compare the results for a single burn of length N to the results of two burns of length N/2, I use more propellant to get to my target perigee altitude. I've found references to Gauss planetary equations, and even a book they are in:
Battin RH (1999) Introduction to the Mathematics and Methods of Astrodynamics AIAA Education Series. American Institute of Aeronautics and Astronautics, Reston, Virginia
Apparently page 489 has the sorts of equations I'm looking for. But I can't get access to this book. Any online source of this book, or the appropriate method/equations would be a perfect answer!