Principle of Least Action, 3.3

Instead, the energy is universally defined in such a way that it is conserved as a result of the time-translational symmetry; and the action is defined in such a way that the condition δS=0 (stationarity of the action) is equivalent to the equations of motion. These are the general conditions that define the concepts in general and that make them important; particular formulae for the energy or action are just particular applications of the general rules.

— Lubos Motl

2011.06.06 Monday ACHK