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The notion of inertial reference frame is abandoned and I replaced it by alocal reference frame on which the fundamental law of mechanics is expressed.The distant interactions of cause and effect are modeled by the propagation ofwaves from one local reference frame to another. The derivation of the equationof motion on a straight segment serves to express the proper acceleration asthe sum of the accelerations imposed on it, in the form of an orthogonal localHelmholtz-Hodge decomposition, in one divergence-free and another curl-freecontribution. I wrote the inertia term in the form of a gradient of a scalarpotential and a dual curl of a vector potential. The adopted formalism opensthe way to a reformulation of the material derivative in terms of potentialsand allows me to remove the fictitious forces from continuum mechanics. Thediscrete equation of motion, invariant by rotation at constant angularvelocity, is used to conserve the angular momentum per unit of mass, inaddition to the conservation of energy per unit of mass and acceleration. Allthe variables in this equation are expressed only with two fundamental units,those of length and time.

On Helmholtz-Hodge decomposition of inertia on a discrete local frame of reference