Energy Conservation as the Basis of Relativistic Mechanics

The relativistic theory of collisions of macroscopic particles is developed from the two axioms of energy conservation and relativity, by use of standard relativistic kinematics (without, of course, assuming the mathematical expression for relativistic energy). We derive, in turn, the equivalence of rest-mass and rest-energy, the usual mathematical expression for the total energy in terms of the rest-energy, the conservation of 3-momentum, and the equivalence of total energy with inertial mass. We incidentally find all possible conservation laws of quantities described by the product of a scalar with a function of the speed.