As an aside. SR eliminates infinite velocity singularities in classical mechanics, but there are other non-regular solutions in Classical Mechanics which are finite velocity. To eliminate those you would have to enforce C^2 on all constraint surfaces (and hope that covers all possible singularities). In many ways these surface is C^1 but not C^2 problems are easier to understand than space invaders because you don't have any messy infinities to deal with. So go read Norton's paper.