I was wondering if anyone may have useful links to the mathematics used by the F9R that allowed it to fly back to LZ-1 and land successfully. I'm hoping to find some papers that will give the broadest (i.e. easiest) mathematical approximation, where the F9R is treated as a point-mass (i.e. no need to model the rigid-body dynamics, cold-gas thrusters, grid-fin aerodynamics or nozzle thrust vectoring).

I'd like to be able to build a 3D Earth model and use some differential equations to model the F9R's motion, but would also like to be able to model a simplified version of its flyback and landing maneuver to be incorporated into the DEs.

Any help would be greatly appreciated, thanks!

EDIT: Having found a webpage listing Lars Blackmore's (SpaceX flyback engineer) publications (http://web.mit.edu/larsb/www/), it seems that he did a lot of work on powered descent guidance for Mars landings. I'm assuming this has been generalized for use in the Falcon 9 flyback maneuver. Unfortunately optimization isn't one of my fortes.

  • $\begingroup$ I wonder if they have any patents with a description of this in? $\endgroup$
    – pjc50
    Commented Jan 5, 2016 at 12:47
  • $\begingroup$ To simulate the flyback and landing, you have to simulate the optimal controller. So you have to implement Lars's convexification scheme for the optimizer, and you have to run it in parallel with the simulation, just as the real craft does :) $\endgroup$ Commented Jan 13, 2016 at 20:23
  • $\begingroup$ Numerical Analysis of Static and Dynamic Performances of Grid Fin Controlled Missiles Behind a pay wall unfortunately. $\endgroup$ Commented Aug 9, 2016 at 23:46