First of all, I am not a physicist, so I cannot guarantee things I say will make sense. I will try my best, though.
In classical mechanics we have the notion of inertial frame of reference. If my understanding is correct, such frames are exactly those for which Newton's laws of motion have the usual form. I believe I have also heard, that they are the frames that are "moving at a constant speed" with respect to some distinguished point in space.
So we have to be careful whether our frame is accelerated or not. Which makes me wonder:
Does there exist a set of physical laws (of same descriptive power Newton's laws have, but perhaps expressing relations in some other set of physical quantities) such that the laws from this set look the same, no matter how the frame of reference moves?
Does such a set of physical laws exist if we restrict to polynomially moving frames of reference? (By this I mean that the motion of the frame is described by a polynomial in $t$, where $t$ is time.)
I imagine this could simplify some calculations.