Currently, I am developing a trajectory optimization tool for launch vehicle from lift-off to orbit using python for my project. Since I'm new to optimization problem, I am finding it hard to understand the different maneuvers in each phase of flights and how to program those maneuvers in different frames.

Can someone please give a clear idea about defining Equation of motions for different phases of flight with maneuvers and reference python code deals with similar problem.

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    $\begingroup$ You may have an easier time finding reference code in MATLAB $\endgroup$ – CourageousPotato Aug 20 '19 at 7:04
  • $\begingroup$ Can you please specify some sources for them $\endgroup$ – Astrolien Aug 22 '19 at 17:35
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    $\begingroup$ I do it in GMAT (but I program liftoff and ascent phase myself (in the language very similar to MATLAB)). GMAT does all optimization work. It looks like You can find and see GMAT source codes (in C/C++). I'm not sure about Python. $\endgroup$ – Peter Nazarenko Aug 30 at 19:25
  • $\begingroup$ @PeterNazarenko How did you program maneuvers during the ascending phase in your code? GMAT source code has ascenting phase of launch vehicle? $\endgroup$ – Astrolien Sep 4 at 16:53
  • $\begingroup$ @Astrolien No, GMAT doesn't calculate ascend phase itself. I do it manually in script by means of "while" or "for" statements. Something like this while ship.Earth.Altitude <= alt1 some stuff EndWhile; $\endgroup$ – Peter Nazarenko Sep 4 at 18:16

The problem with such tools is that they may be considered a national security risk as the principles are similar to those of missiles.

However, there are excellent Master theses and PhD dissertations on the topic of optimal control for landing rockets, such as this MSc thesis and this SpaceX paper. These will explain the equations of motion and part of the derivation and problem solving methods. You will mostly likely have to write your own code.

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