The Origins of Newton’s Mechanics. Mass, Force, and Gravity - Jan RYCHLEWSKI (Engineering Transactions, 2021)
In this work, the axiomatic model of dynamics is developed corresponding to the classical model of Newton’s dynamics. The key elements of the model are the ability to distinguish isolated systems, and their subsequent division into a selected body (material particle) and its surroundings (attractor). The material particle (usually assumed to be small relative to surroundings), and the attractor are the axiomatic model’s primary concepts. The only fundamental state parameter of the model is acceleration (kinematic quantity), which is accepted as the starting point of dynamics. The concepts of mass (dynamic characteristic of the material particle) and force (dynamic characteristic of the surroundings impact on the material particle) are derivative quantities in the model. Two types of (acceleration) measurement procedures deliver precise operational definitions of inertial mass and force. Thus, difficulties with the ideas of mass and force present in original formulation of Newton’s laws of dynamics are removed. The present model shows that for formulation and interpretations of the laws of dynamics, the general ideas about the particle and the environment affecting its motion, and the concept of acceleration, are sufficient. Neither masses nor forces are necessary to formulate the essence of dynamics. However, the elegance and power of the concepts of force and mass prompt for their introduction in any isolated system with a separated body as very convenient and useful quantities. Following the developed methodology, an axiomatic model of Newton’s universal gravitation is formulated, and it is shown that neither inertial mass nor force is actually needed for that purpose. Moreover, in the closed world of gravity, the force concept cannot be introduced as a dynamic feature of an attractor only – it must be a feature characterizing a pair of the specific particle and attractor. Reconciliation of the axiomatic model of universal gravity with the axiomatic model of dynamics leads to the equivalence of gravitational mass and inertial mass concepts.