Kinematical review on the theory of special relativity

Abstract

The total mass of a system of non-interacting point particles is defined by linear sum of masses of the particles and the total momentum of it is defined by linear sum of momenta of them. Combining this linear sum rules of masses and momenta with the violation of the absolute invariant of motion of the inertial mass of a body, it is shown that the kinematics of the theory of special relativity can be reformulated, especially the relativistic generalization of the inertial mass can be obtained without any appeals to the thought-experiments of idealized particle-collisions.