Dynamical Consequences of Special Relativity Einsteins Mass and Energy

7 DYNAMICAL CONSEQUENCES OF SPECIAL RELATIVITY EINSTEIN S MASS AND ENERGY 

There is commonly accepted that the dynamic properties of a system may be elegantly determined as based on the associated Lagrangian (Z) at its turn, the Lagrangian of a system determines the so-called action of the system defined by the integral 

For the relativistic systems, even in the absence of applied forces, the time evolution is intrinsically accounted by the inner universe line linking the temporal transformation respecting the proper time (with the considered innertially system) 

The minus sign is added for illustrating the loss of action in the environment by time passing, yet, even without having the minus sign explicitly here it will be reached in the final expression of the a constant to be 

Under the absence of the external forces (equivalently with free motion anyway) the above Lagrangian has to recover in the non-relativistic limit v c the classical Lagrangian limit (the kinetic energy in fact) of the free particle 

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