I can't believe this is so far down. This is exactly why I don't need to pay attention to someone's weird magnet arrangement or marble track geometry to create

I can't believe this is so far down. This is exactly why I don't need to pay attention to someone's weird magnet arrangement or marble track geometry to create a proportioal motion machine, I know they're playing with conservative fields and it isn't going to work. However in this case, there is some significant acceleration which implies GR which is not in general conservative. I suspect it is though if you restrict yourself to the special case of accelerations with no significant gravity. In general, however, this is still the correct approach to thinking about such problems. If you can find a no-go theorem, then you needn't concern yourself with the complex details. That said, if you can find a weird place where it looks like momentum isn't being conserved, it probably is because you are inadvertently predicting an effect of the theory that will take care of that problem.