A Novel General Theoretical Derivation of Newton-Experimental-Formula for Collision of Particles

Abstract

An experimental formula, sometimes named as Newton-collision-formula, (v1-v2) = - e.(u1-u2) relating relative-velocities before & after impact of two bodies under linear-collision, is commonly used successfully for study of collision-dynamics. Although it seems possible as shown in text-books [1,2] to derive this relation, assuming (defining) e as ratio of impulses during restitution & deformation; but as yet, neither a good theoretical-basis nor a general-derivation of this formula based on obvious choice of energy-consideration, has been reported. In this brief-paper a relativistic-theoretical-basis is adopted and a general formula-derivation is given. It is shown, interestingly, that proof of the Newton-collision-formula is hidden in Einstein-special-relativity.