On the Principle of Conservation of Energy in the Relativistic Theory of Gravitation

The principle of conservation of energy has played a very important part in classical dynamics. But, as in almost a majority of cases where the motion of a system of particles or even of rigid bodies is studied, classical dynamics is generally replaced by relativity mechanics, it will be of some interest to examine this principle in the light of classical theory. Consider, for instance, the usual geodesic equations.