Abstract
In his analysis of his new image (Bild) of mechanics Heinrich Hertz (PM 29) distinguished between its physical content and its mathematical form. The physical content was characterized by the assumption that neither force nor potential energy are fundamental quantities of mechanics. When a mechanical system seems to be acted on by forces, it is, according to Hertz, because it is rigidly connected to another system of hidden masses whose fast cyclic motions to a first approximation have the same effect as forces in the traditional Newtonian-Lagrangian image of mechanics. The mathematical form of Hertz’s mechanics was characterized by a geometric structure of configuration space that he called the geometry of systems of points.
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Notes
Bernhard Riemann, Über die Hypothesen welcher der Geometrie zu Grunde liegen’(1854-lecture) in Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematische Classe 13 (1867), pp. 1–20, also in Gesammelte mathematische Werke (Leipzig: Teubner, 1876), pp: 254–269.
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A more comprehensive presentation can be found in Lützen (1995b).
Carl Friedrich Gauss, Disquisitiones generales circa superficies curvas’ in Werke(Göttingen: Königliche Gesellschaft der Wissenschaften, 1873), vol. 4, pp. 217–258, English translation General Investigations of Curved Surfaces (Hewlett: Raven Press, 1965); William Rowan Hamilton, Theory of Systems of Rays’ in Mathematical Papers (London: Cambridge University Press, 1931–67), vol. 1, pp. 1–87.
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For more details see Jesper Lützen Joseph Liouville op.cit.(note 8), pp. 680–686 and 751–755.
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Lützen, J. (1998). Heinrich Hertz and the Geometrisation of Mechanics. In: Baird, D., Hughes, R.I.G., Nordmann, A. (eds) Heinrich Hertz: Classical Physicist, Modern Philosopher. Boston Studies in the Philosophy of Science, vol 198. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8855-3_8
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