@yizhang: Good point. Your are quite correct (though @LJDevlin did some interesting work a while back (which we hope to publish soon) that showed that RK45 was surprisingly competitive with respect to the much more complicated numerical integrator schemes often advocated in the context of astrodynamics, eg Gauss-Jackson, which admittedly isn’t symplectic either). It’s a bit of an aside, but we do plan to extend the work @gcook is currently doing to be relevant to low-altitude contexts where considering drag might be important. More specifically, our hope is to use Stan to schedule the Liverpool telescope to generate observations of MEV-2 (in October 2020) during its GTO phase. The Stan file posted here is a simplified version that @gcook has produced to replicate an issue that we encountered in the “real” (3d) geometry of interest.