The dynamics-first approach (which I’ll admit to being more sympathetic to myself) just takes as a definition that ‘inertial frames’ are frames in which force-free bodies move inertially. From that point of view, there isn’t really any further analysis of the frames to be given: the laws of physics just make the claim that there are some frames with respect to which force-free bodies move in straight lines at constant speed, and then defines those as the inertial frames.
dynamic first approach
