Maupertuis And The Principle Of Least Action In Mechanics: A Critical Analysis [maupertuis E O Princípio Mecânico De Ação Mínima: Uma Análise Crítica]

In a paper presented in 1746 Maupertuis communicated the principle of least action as a general and universal principle. He claimed that it could not only explain the laws of motion but also prove the existence of God. He applied the principle to the study of the collision between elastic and inelastic bodies and to the equilibrium of a lever, finding correct results. In this article we present a detailed analysis of Maupertuis' demonstrations and we show that they had serious problems. His mistakes were criticized by d'Alembert and d'Arcy shortly after the publication of his work. Copyright by the Sociedade Brasileira de Física.294625633Roberto de Andrade Martins e Ana Paula Bispo da Silva, Revista. Brasileira de Ensino de Fisica 29, 455 (2007)Pierre de Castro Moreau, Revista Brasileira de Ensino de Física 21, 172 (1999)Louis, P., Maupertuis, M., (1746) Histoire de l'Academie Royale des Sciences et Belles Lettres de Berlin 267Bentley Glas. in Dictionory of Scientific Biography. editado por C.C. Gilliespie (Charles Scribner's Sons, New York, 1970), v. 8, p. 186-189Louis, P., Maupertuis, M., (1768) Essai de Cosmologie, , Librairie Philosophique J. Vrin, ParisGuéroult, M., (1934) Dynamique et Métaphysique Leibniziènnes, , Belles Lettres, ParisG.W. Leibniz, Mathematische Schriften, org. por C.I. Gerhardt (Georg Olms, Nova Iorque, 1971), 7 vHankins, T.L., (1967) Journal of the History of Ideas, 28, p. 193Nicolas de Malebranche, De la Recherche de la Vérité (Henry Desbordes, Amsterdam, 1688), Nouvelle Edition Reveue, Corrigée & AugmentteeJean le Rond d'Alembert, Action, in D. Diderot e J.R. d'Alembert (eds), Encyclopédie ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers, par une Societé de Gens de Lettres (Briasson, Paris, 1751-1782), v. 1, p. 119-120, 17+11 vD'Arcy, P., (1753) Histoire de l'Académie Royale des Sciences avec les Mémoires de kathématique et de Physique tirés des Resgistres de cette Academie 531König, S., (1751) Nova Acta Eruditorum, 125, p. 162Radelet-De Grave, P., (1998) LLULL, Revista de la, Sociedad Espanola de Historia de la, Ciensas y las Tecnicas, 21, p. 439Roberto de Andrade Martins e Ana Paula Bispo da Silva, Filosofia Unisinos 8, 146 (2007)Euler, L., (1744) Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Latissimo Sensu Accepti, , Mercum-Michaelem Bousquet & Socios, Lausanne & GenèveEuler, L., (1843) Lettres a une princesse d'Allemagne sur divers sujets de physique et de philosophie, , Charpentier, Paris, Nouvelle Edition, avec une Introduction et des Notes par Émile Saisse