Engineering Transactions, 69, 4, pp. 457–488, 2021

The Origins of Newton’s Mechanics. Mass, Force, and Gravity

Jan Rychlewski
Institute of Fundamental Technological Research, Polish Academy of Sciences

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.

In Translator opinion, the work contains a very original and elucidating approach towards classical dynamics and due to that deserves worldwide dissemination and knowledge. Nowadays, this can only be achieved, to the extent that the study deserves, by its publication in English language.

 Editorial note: The present document is an English translation of Appendix C of Jan Rychlewski’s book titled Dimensions and Similarity (original Polish title Wymiary i podobienstwo), Wydawnictwo Naukowe PWN, Warszawa, 1991, pp. 185–208, ISBN 83-01-10557-7.

Editorial note: Abstract by Andrzej Ziółkowski.

Keywords: axiomatic model of dynamics; operational definition of inertial mass; operational definition of force; axiomatic model of universal gravity; Newton’s dynamics; concept of attractor; concept of material particle; equivalence of inertial mass and gravitatio
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C.1. Newton I., Mathematical Principles of Natural Philosophy [in Latin: Philosophiae naturalis principia mathematica], London, 1687.

C.2. Euler L., Mechanical or Emotional Science Analytically Exposed [in Latin: Mechanica sive motus scientia analytice exposita], Vol. 1, Petropoli, 1736 (Opera omnia, ser. II, t. 1, 1912).

C.3. Mach E., About the definition of mass, [in:] Carl's Repertorium der Experimentalphysik, [in German: Über die Definition der Masse, [in:] Carl's Repertorium der Experimentalphysik], 4: 355–358, 1868 (The history and the root of the principle of the preservation of labor [in German: Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit], Prague, 1872).

C.4. Hertz H., Die Principien der Mechanik in neuem Zusammenhange dargestellt, Gesammelte Werke, Bd. 3, Leipzig, 1894–1895; also: The Principles of Mechanics, Presented in a New Form, Dover Publ., New York 1956.

C.5. Poincaré H., Hertz's ideas on mechanics, General Review of Pure and Applied Sciences [in French: Les idées de Hertz sur la Mécanique, Revue Générale des Sciences Pures et Appliquées], 18: 734–743, 1897.

C.6. Jammer M., Concepts of Mass in Classical and Modern Physics, Harvard University Press, Cambridge, Mass., 1961.

C.7. Juriew B.N., Experience of a New Formulation of the Basic Laws of Newtonian Mechanics [in Russian: Опыт новой формулировки основных законов механики Ньютона], Izd. AN SSSR, Moskwa 1952.

C.8. Hermes H., An Axiomatization of General Mechanics, Research on Logic and the Foundation of the Exact Sciences, Vol. 3 [in German: Eine Axiomatisierung der allgemeinen Mechanik, Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, Heft 3], Leipzig 1938.

C.9. Simon H.A, The axioms of Newtonian mechanics, The Philosophical Magazine, Ser. 7, 38: 888–905, 1947.

C.10. McKinsey R., Sugar A.C., Suppes P., Axiomatic foundations of classical particle mechanics, Journal of Rational Mechanics and Analysis, 2: 253–273,1953.

C.11. Bung M., Mach’s critique of Newtonian mechanics, American Journal of Physics, 34(7): 585–596, 1966.

C.12. Charlamow P.M., Foundations of Newtonian mechanics [in Russian: Основания механики Ньютона], Inst. Problem Mech., preprint 250, Moskwa, 1985.

C.13. Żurawlew W.F., Foundations of Mechanics. Methodological aspects [in Russian: Основания механики. Методические аспекты], Inst. Problem Mech., Preprint, 251, Moskwa 1985.

C.14. Worowicz I.I., Some questions of teaching the basics of classical mechanics in a university course [in Russian: Некоторые вопросы преподавания основ классической механики в университетском курсе], Inst. Problem Mech., preprint 252, Moskwa 1985.

C.15. Iszlinskij A.Ju., Two essays on mechanics [in Russian: Два очерка по механике], Inst. Problem Mech., preprint 287, Moskwa 1987.

C.16. – Orientation, gyroscopes and inertial navigation [in Russian: Ориентация, гироскопы и инерциальная навигация], Nauka, Moskwa 1976.

C.17. Wizgin W.P., Mach's role in the genesis of general relativity [in Russian: Рольдией Маха в генезисе общей теории относительности], Einsztiejnowskij Sbornik, 1986–1990, Nauka, pp. 49–96, 1990.

C.18. Arnold W.I., Mathematical methods of classical mechanics [in Polish: Metody matematyczne mechaniki klasycznej], PWN, Warszawa 1981.

C.19. Noll W., Space-time structures in classical mechanics, [in:] Delaware Seminar in the Foundation, of Physics, Vol. 1, pp. 28–34, Springer, Berlin, 1967

C.20. Kirsanow W.S., Michajlow G.K., On the 300th Anniversary of Newton's “Mathematical Origins of Natural Philosophy” [in Russian: В трехсотлетие «Математических истоков натурфилософии» Ньютона], Uspekhi Mekhaniki, 11(3): 127–175.

DOI: 10.24423/EngTrans.1415.20211210