Leonhard Euler and the historical episode of the formulation of the Fundamental Principle of Dynamics: F = MA
DOI:
https://doi.org/10.4025/rvc.v3i1.63965Keywords:
F=ma, Leonhard Euler, Second law of motion, History of Science, Isaac NewtonAbstract
This paper, part of a doctoral thesis, seeks to provide a detailed picture of Euler's contribution to the construction of the Fundamental Principle of Dynamics. Euler modified the content of the Fundamental Principle and formulated a new one, expanding the understanding of the law proposed by Newton (known as F=ma). The main factors that contributed to the production of this new principle, the main names involved, and the consolidation of the principle now called Newton's Second Law are discussed. Euler's insertion in the construction of 18th century mechanics is presented, his conceptual conceptions and achievements, as well as the elements used by him for the elaboration of the new principle, in addition to the specific approach to the construction of the fundamental law of motion, as we know it today. Finally, the complete picture of Euler's new principle, drawn from Newtonian mechanics, is presented, which serves as an example of how scientific work occurs.
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References
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EULER, L. Scientia navalis seu tractatus de construendis ac dirigendis navibus Pars prior complectens theoriam universam de situ ac motu corporum aquae innatantium, 1749a.
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MELI, D. B. The emergence of reference frames and the transformation of mechanics in the Enlightenment. Historical Studies in the Physical Sciences, v.23, p.201–335, 1993.
SITKO, C. M. Why Newton´s Second Law is not F=ma. Acta Scientiae. v. 21, n. 1, p. 83-94, 2019a.
SITKO, C. M. Os desenvolvimentos da Mecânica Analítica que culminaram na elaboração de F=ma. Caderno Brasileiro de Ensino de Física. v. 36, n. 1, 2019b.
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STAN, M. Euler, Newton, and Foundations for Mechanics. In Chris Smeenk & Eric Schliesser (eds.). The Oxford Handbook of Newton. (1-22). Oxford University Press, 2017.TRUESDELL, C. Rational Fluid Mechanics, 1687-1765. In: C. A. Truesdell (Ed.), Opera Omnia (Series II, Vol. 12). Lausanne: Orell Fí¼ssli, 1955.
TRUESDELL, C. The rational mechanics of flexible or elastic bodies, 1638-1788. Birkhí¤user Basel, 1960.
TRUESDELL, C. Essays in the History of Mechanics. New York: Springer-Verlag, 1968.
TRUESDELL, C. Ensayos de historia de la mecânica (J. C. N. Howard & E. T. Perez-Relaí±o Trad). Madrid: Tecnos, 1975.
WHITROW, G. The laws of motion. The British Journal for the History of Science. v.5, n.19, p.217–234, 1971.
CALINGER, R. Leonhard Euler: The First St. Petersburg Years (1727–1741). Historia Mathematica. v. 3, n. 15, p.121–166, 1996.
COELHO, R. L. On the deduction of Newton´s second law. Acta Mechanica. v. 229, n. 5, p. 2287–2290, 2018.
CUNHA, E. B. M. Uma nova visão da história da Mecânica. Revista Brasileira de Ensino de Física, v. 5, n.1.
DIAS, P. M. C. Leonhard Euler´s “principle of mechanics†(an essay on the foundations of the equations of motion). Revista Brasileira de Ensino de Física, v. 39, n.4, e4601, 2017.
EULER, L. Mechanica sive motus scientia analytice exposita. Opera Omnia, série II, VOL. 1 E 2, 1736.
EULER, L. Dissertation sur la meilleure construction du cabestan, Originalmente publicado em Piece qui a remporte le prix de l'academie royale des sciences 1741 (data de apresentação), p. 29-87, 1745.
EULER, L. Scientia navalis seu tractatus de construendis ac dirigendis navibus Pars prior complectens theoriam universam de situ ac motu corporum aquae innatantium, 1749a.
EULER, L. Recherches sur le mouvement des corps celestes em general, Mem. Acad. Roy. Sci. Berlin, 1747 (data de apresentação). v.3, p. 43-143, 1749b.
EULER, L. Découverte d´un nouveau principe de Mécanique. Mem. Acad. Roy. Sci. Berlin, 1750 (data de apresentação). v. 6, p. 185-217, 1752.
EULER, L. Theoria motus corporum solidorum seu rigidorum. Rostockii. et Gryphiswaldiae: A. E. Roser, 1765.
EULER, L. Formulas generales pro translatione quacunque corporum rigidorum, Novi Commentarii academiae scientiarum Petropolitanae, v. 20, p. 189-207, 1776a.
EULER, L. Nova methodus motum corporum rigidorum degerminandi. Novi Commentarii academiae scientiarum Petropolitanae. v.20, p. 208-238, 1776b.
EULER, L. Letters of Euler on different subjects in natural philosophy addressed to a german princess (D. Brewster Trad, 3ª ed.), Londres, 1823.
GAUKROGER, S. The Metaphysics of Impenetrability: Euler's Conception of Force. The British Journal for the History of Science. v.15, n.2, p.132-154, 1982.
GUICCIARDINI, N. Dot-Age: Newton´s mathematical legacy in the eighteenth century. Early Science and Medicine. Newtonianism: Mathematical and 'Experimental'. v. 9, n.3, p.218-256, 2004.
HEPBURN, B. S. Equilibirum and explanation in 18th century mechanics. (Tese de doutorado). 134f. Faculty of arts and sciences. University of Pittsburgh. Pittsburgh, 2007.
HERMANN, J. Phoronomia sive de viribus et motivus corporum solidorum et fluidorum libri duo. Amsterdam, 1716.
MALTESE, G. La storia di “F=ma†– La seconda legge del moto nel XVIII secolo. Firenze: Biblioteca di nuncius, 1992.
MALTESE, G. On the Relativity of Motion in Leonhard Euler´s Science. Arch. Hist. Exact Sci. v.54, p.319–348, 2000.
MARONNE, S. & PANZA, M. Euler, Reader of Newton: Mechanics and Algebraic Analysis. Advances in Historical Studies. v.3, n.1, p.12-21, 2014.
MAUGIN, G. A. Continuum Mechanics Through the Eighteenth and Nineteenth Centuries - Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914). Switzerland: Springer Internacional Publishing, 2014.
MELI, D. B. The emergence of reference frames and the transformation of mechanics in the Enlightenment. Historical Studies in the Physical Sciences, v.23, p.201–335, 1993.
SITKO, C. M. Why Newton´s Second Law is not F=ma. Acta Scientiae. v. 21, n. 1, p. 83-94, 2019a.
SITKO, C. M. Os desenvolvimentos da Mecânica Analítica que culminaram na elaboração de F=ma. Caderno Brasileiro de Ensino de Física. v. 36, n. 1, 2019b.
SITKO, C. M. For an undistorted view of Newton's Second Law. Revista Acta Scientiae, v. 22, p. 122-133, 2020.
STAN, M. Euler, Newton, and Foundations for Mechanics. In Chris Smeenk & Eric Schliesser (eds.). The Oxford Handbook of Newton. (1-22). Oxford University Press, 2017.TRUESDELL, C. Rational Fluid Mechanics, 1687-1765. In: C. A. Truesdell (Ed.), Opera Omnia (Series II, Vol. 12). Lausanne: Orell Fí¼ssli, 1955.
TRUESDELL, C. The rational mechanics of flexible or elastic bodies, 1638-1788. Birkhí¤user Basel, 1960.
TRUESDELL, C. Essays in the History of Mechanics. New York: Springer-Verlag, 1968.
TRUESDELL, C. Ensayos de historia de la mecânica (J. C. N. Howard & E. T. Perez-Relaí±o Trad). Madrid: Tecnos, 1975.
WHITROW, G. The laws of motion. The British Journal for the History of Science. v.5, n.19, p.217–234, 1971.
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Published
2022-06-14
How to Cite
Sitko, C. M. (2022). Leonhard Euler and the historical episode of the formulation of the Fundamental Principle of Dynamics: F = MA. Vitruvian Cogitationes, 3(1), 145–164. https://doi.org/10.4025/rvc.v3i1.63965
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