Unified Law of Motion

The meaning of a unified law of motion is determined by the extent of potential applications. The goal is to extend the Galilean principle of relativity to the two uniform expansion and rotation motions and to no longer consider the latter to be an accelerated motion as in classical mechanics. The distinction between accelerated and non-accelerated motions seems trivial if the acceleration field is taken into consideration; for an unaccelerated motion, simply has to be equal to zero. The law of conservation of total energy is established in a local reference frame by abstracting motions of uniform expansion with velocity and uniform rotation. The profound meaning of inertia in mechanics still has no intrinsic definition; it is often defined with respect to mass. In classical or relativistic mechanics, the Galilean reference frame is related to motion at constant velocity; this is a very restrictive case that deserves an extension to other simple motion.