Abstract
Among the variety of successful eighteenth century contributions, Lagrange’s first paper on the moon’s libration contains a breakthrough in analytical mechanics. Though it is his very own achievement, Lagrange himself was of course not isolated. Being aware of the results of his predecessors, and being in contact with his scientific contemporaries, he was well prepared for such ground-breaking insight, embedded in the cultural-philosophical surrounding of his time. Behind every named formula and equation there was or is, even in our computer dominated times, always a thinking and feeling human - a fact that we “users”, still conneced to our scientific ancestors, should be well aware of.
The historical background, however, is not only fascinating but also yields real benefits: “As far as I studied the basic contributions of our great masters I got insight and understanding which was far beyond everything which could be extracted from secondary sources” says Wilhelm Ostwand (1855-1932).
The formerly tedious search for these sources has become comfortable with the rise of the internet. The corresponding addresses were added to the reference list in order to inspire further reading.
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References
de Lagrange, J.: Analytische Mechanik, 2nd edn., German by H. Servus. Springer, Berlin (1897)
de Lagrange, J.: Récherches sur la libration de la lune. Oeuvres de Lagrange 6 (1873)
Rühlmann, M.: Vorträge über Geschichte der Technischen Mechanik. Baumgärtners Buchhandlung, Leipzig (1885)
de Varignon, P.: Nouvelle Mécanique ou Statique, vol. 2. Claude Jombert, Paris (1725), http://imgbase-scd-ulp.u-strasbg.fr
de Maupertuis, P.: Loi du repos des corps. Académie Royale des Sciences, Paris (1740), http://www.academie-sciences.fr
Euler, L.: Harmonie entre les principes généraux de repos et de mouvement de M. de Maupertuis. Mémoires de l’Academie des Sciences, Berlin (1751), http://www.math.dartmouth.edu/~euler/
de Lagrange, J.: Essai d’une nouvelle méthode pour déterminer les maxima et les minima des formules intégrales indéfinies. Oeuvres de Lagrange 1, 389 (1873), http://gdz.sub.uni-goettingen.de
P. Stäckel (ed.): Variationsrechnung. Wissenschaftliche Buchgesellschaft, Darmstadt (1976)
de Lagrange, J.: Application de la méthode exposée dans le mémoire précédent a la solution de différents problèmes de dynamique. Oeuvres de Lagrange 1, 419 (1873), http://gdz.sub.uni-goettingen.de
de Lagrange, J.: Correspondance. Oeuvres de Lagrange 14, 146–151, 152–154 (1892), http://gdz.sub.uni-goettingen.de
Fraser, C.: J.L. Lagrange’s Early Contributions to the Principles and Methods of Mechanics. Arch. Hist. Ex. Sci. 28(3), 197–241 (1983)
Heun, K.: Ansätze und allgemeine Methoden der Systemmechanik. Enzykl. Math. Wiss. IV(II), 361 (1913)
Hamel, G.: Theoretische Mechanik, p. 219. Springer, Heidelberg (1949)
Heun, K.: Die Bedeutung des d’Alembertschen Prinzips für starre Systeme und Gelenkmechanismen. Archiv der Math.u.Phys. III(2), 61 (1901)
Helmholtz, H.: Über die Erhaltung der Kraft. G. Reimer, Berlin (1849), Ostwald’s Klassiker, vol. 1. W. Engelmann, Leipzig (1889)
d’Alembert, J.: Traité dynamique, 2nd edn., pp. 252–272. David, Paris (1758), http://fr.wikisource.org
de Lagrange, J.: Théorie de la libration de la lune. Oeuvres de Lagrange 5 (1870)
de Lagrange, J.: Analytische Mechanik, 1st edn. German by F.W.A. Murhard. Vandenhoeck und Ruprecht, Göttingen (1797), http://gdz.sub.uni-goettingen.de
Allgemeine Deutsche Biographie, vol. 23, pp. 62–65. Duncker und Humblot, Leipzig (1886)
Kästner, A.G.: Anfangsgründe der höhern Mechanik, 2nd edn. Vandenhoek und Ruprecht, Göttingen (1793)
Poinsot, L.: Éleméns de statique, p. 476. Bachellier, Paris (1837)
Jacobi, C.G.J.: Vorlesungen über Mechanik, A. Clebsch, ed. G. Reimer, Berlin (1866)
Jacobi, C.G.J.: Vorlesungen über analytische Mechanik Berlin 1847/48. In: Pulte, H. (ed.) Dokumente zur Geschichte der Mathematik, vol. 8. Vieweg, Braunschweig (1996)
Truesdell, C.: Die Entwicklung des Drallsatzes. ZAMM 44(3/4), 149–159 (1964)
Radetsky, P.: The Man who Mastered Motion. Science, 52–60 (May 1986)
Pulte, H.: Jacobi’s Criticism of Lagrange: The Changing Role of Mathematics in the Foundations of Mechanics. Historia Mathematica 25, 154–184 (1998)
Bremer, H.: Über eine Zentralgleichung in der Dynamik. ZAMM 68, 307–311 (1988)
Hamel, G.: Über die virtuellen Verschiebungen in der Mechanik. Math. Annalen 59, 416–434 (1904)
Magnus, K.: Vom Wandel unserer Auffassung zur Technischen Mechanik. THD-Schriftenreihe 28, 125–136 (1986)
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Bremer, H. (2014). Lagrange’s “Récherches sur la libration de la lune”. In: Stein, E. (eds) The History of Theoretical, Material and Computational Mechanics - Mathematics Meets Mechanics and Engineering. Lecture Notes in Applied Mathematics and Mechanics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39905-3_3
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