Einstein's Special Relativity (ESR) in its original formulation, is limited to inertial motions only, while an insight into real-world shows that the motions are non-inertial. It is hard to accept that the launching of a rocket implies a succession of inertial motions. Similarly, during the re-entry of a satellite in the Earth's atmosphere, its continously decaying angular momentum and the violations of the Lorentz - Poincare symmetries, are then evident. Form the viewpoint of kinematics, defined as the science of pure motion, apart from causes, the motion may be either inertial of non-inertial. Since a motion cannot be, at the same time, either a uniform translation or a non-uniform motion, then they form a pair of complementary kinematic concepts, mutually exclusive. If the gravitational effects are neglected, ESR assumes uniform translations, while under similar circumstances (regarding the neglecting of the space curvature) to the best our our knowledge, nothing is known in the literature to take into consideration non-inertial motions. As a consequence, we shall denote by Special Relativity that branch of physics where by neglecting the gravitational effects, the motion may be either inertial or non-inertial, called in this paper permissible motions. As a consequence, the following chart of complementarities:
