Few words about external ballistic on sample of one long range flight of 9M38M1, to present how difficult attempts to reproduce these flights can be. While flights of pure ballistic rockets are quite simple and easily can be programmed, these guided are completely other story.
9M38M1 fly in trajectories which are for every single impact point (точка встречи) different of course and defined by method of guidance. I will skip guidance because it’s not my field at all and get directly to pure kinematic.
One long range flight will be flight to 30km horizontal distance and 10km altitude. Polynomial functions give that trajectory of rocket to hit that point is best to be in form similar to this one

This is leading and starting point and rocket somehow must be forced to “lie down” on it.

It will be forced by kinematic overload which is predefined to each launching case and that is the most difficult part for us amateurs trying to draw some trajectories. Kinematic overload push rocket to predefined trajectory, to this overload always reserve overload (запас перегрузки) must be added and both make total overload as shown above.
This is of course very much simplified overload distribution and with lot of assumptions. In any case rocket has several arming intervals, one is always signal from linear acceleration but for this I think second is of more importance. Pressure drop, спад давления в ракетном двигателе. After boost stage finish then rocket can start chasing predefined trajectory and I take it to be 5,5 seconds after start. If I remember correctly, pressure drop signal suppose to be not more than 5,5 seconds after launch.
Before it starts, rocket is most likely “locked” to just keep some line, and I took it as kinematic overload of 1G just to try place rocket on some nearly linear trajectory.
After several attempts to find what overload and distribution should be to match predefined optimal trajectory, more than several actually
and here it is with belonging velocity-time distribution


This was just single one launch, of course this overload is different for some other impact point scenario and that’s exactly what makes this work horrible. This is how it looks in real cases on one other rocket but principle (difficulties) are same
