Consequences of the Law of Motion

The weak equivalence principle expresses an older version of the universal fall of bodies as a result of gravity. The advection equation of classical mechanics of a scalar quantity is based on the material derivative derived from the concept of a continuous medium where all quantities are located at the same point. The decomposed two-term, divergence-free, curl-free form of the equation of motion suggests a local form on a segment equivalent to Bernoulli's theorem for a perfect fluid. The conservations of the total energy associated with the acceleration and those of the compressive and rotational energies intrinsic to law of discrete mechanics directly follow there from. The law of discrete motion is free of any constitutive law directly integrated therein; only the longitudinal and transverse velocities appear. An essential aspect differentiates Noether's theory of invariances from discrete mechanics.