An organization of classical particle mechanics

Certain techniques, concepts and methods used to model and analyze the motion of massive bodies under forces are not admissible under the Newtonian axioms. Among them are: forces acting on massles components rather than on particles, using the so-called free-body diagram technique, and the existence of infinite forces of bounded impulse. Moreover, modeling physical space by Euclidean 3-space introduces some basic difficulties which are usually silently ignored. We propose here an organization of classical particle mechanics which provides the additional axioms and defined terms needed to legitimize the mathematical models and methods presently used in the analysis of Newtonian systems.