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Whittaker’s analytical dynamics: a biography

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Abstract

Originally published in 1904, Whittaker’s A Treatise on the Analytical Dynamics of Particles and Rigid Bodies soon became a classic of the subject and has remained in print for most of these 108 years. In this paper, we follow the book as it develops from a report that Whittaker wrote for the British Society for the Advancement of Science to its influence on Dirac’s version of quantum mechanics in the 1920s and beyond.

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Notes

  1. les orbite planétaires doivent être regardées comme les ellipses dont le dimensions et les position dans l’espace, varient par dégres insensibles.

  2. l’on imagina, pour résoudre ces nouvelles équations, de considerer comme variables les constants arbitraires des intégrales relatives au mouvement elliptique. Il est remarquable que ce procédé, l’un des plus feconds de l’analyse, qui consiste à faire varier des quantités regradées d’abord comme constantes.

  3. Eccentricity, semimajor axis, inclination, longitude of the ascending node, argument of periapsis and mean anomaly at epoch.

  4. relatives à cette même théorie, que je reprends en entier sous un nouveau point de vue.

  5. Ce Mémoire contient une savant analyse qui est comme l’inverse de la mienne, et dont l’objet est d’eviter les éliminations que celle-ci exigeait.

  6. Es ist kein Lehrbuch für den Anfänger, sondern vielmehr ein reichhaltiges Kompendium, in welchem der Verf. mit grosser Sorgfalt und vielem Geschick alles verarbeitet hat, was die Forschung der besten Gelehrten bis in die jüngste Vergangenheit über den Gegenstand zutage gefördert hat.

  7. Es ist kein Lehrbuch für den Anfänger, sondern vielmehr ein reichhaltiges Kompendium, in welchem der Verf. mit großer Sorgfalt und vielem Geschick alles verarbeitet hat, was die Forschung der besten Gelehrten bis in die jüngste Vergangenheit über den Gegenstand zutage gefördert hat.

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  1. Departamento de Ciência da Computação, Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, Rio de Janeiro, RJ, 21945-970, Brazil

    S. C. Coutinho

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Communicated by : Jeremy Gray.

This paper was made possible by the Internet Archive, the Gallica site of the Bibliothèque nationale de France, Project Euclid, the American Mathematical Society and the Jahrbuch Database of the European Mathematical Society, where many of the books and papers we mention can be downloaded at no cost. I would like to thank Antonio Roberto da Silva for his help with the translations from the German, Jeremy Gray for his many suggestions and R. Abraham, H. Bursztyn, J. Koiler, Y. Kosmann-Schwarzbach, S. Sternberg and A. Weinstein for their help in clarifying the history of the geometric approach to mechanics. The work on this paper was partially supported by a grant from the Brazilian National Research Council (CNPq).

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Coutinho, S.C. Whittaker’s analytical dynamics: a biography. Arch. Hist. Exact Sci. 68, 355–407 (2014). https://doi.org/10.1007/s00407-013-0133-1

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