Implications of the disagreement between newtonian and relativistic low-speed trajectories

It was shown recently for a chaotic and a nonchaotic slow-moving dynamical system that the Newtonian and special relativistic trajectories eventually disagree completely. Here, it is argued that once the Newtonian trajectory is completely different from the relativistic trajectory, Newtonian mechanics can no longer be used to study the trajectory of the slow-moving system. Special relativistic mechanics must be used instead. For a nonchaotic system, Newtonian mechanics can still be used for a very long time. However, for a strongly chaotic system, Newtonian mechanics cannot be used essentially from the outset.