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The Development of Analytical Mechanics by Euler, Lagrange and Hamilton – From a Student’s Point of View

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The History of Theoretical, Material and Computational Mechanics - Mathematics Meets Mechanics and Engineering

Part of the book series: Lecture Notes in Applied Mathematics and Mechanics ((LAMM,volume 1))

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Abstract

The techniques and methods that were devised during the development of ’Analytical Mechanics’ still feature prominently in many branches of Physics, Engineering Sciences and also in various technical applications. In this paper we give an overview of the historical development of this theory by Leonhard Euler (1707-1783), Joseph-Louis Lagrange (1736-1813) and Sir William Rowan Hamilton (1805-1865). The simple example of the pendulum or more correctly the mathematical pendulum serves to illustrate this development. In the conclusion we present a glimpse of the further development this theory has undergone in modern mathematics and physics and discuss some select use cases.

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References

  1. Newton, I.: Philosophiae naturalis principia mathematica. Jussu Societatis Regiae ac Typis Josephi Streater, Londini (1687)

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  4. Hamilton, W.R.: Philosophical Transactions of the Royal Society, Part II, 247–308 (1834)

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  5. Hamilton, W.R.: Philosophical Transactions of the Royal Society, Part I, 95–144 (1835)

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Author information

Authors and Affiliations

  1. Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstraße 5, D-91058, Erlangen, Germany

    Maximilian Gerstner & Paul Steinmann

  2. Department of Mechanical Engineering, University of Erlangen-Nuremberg, Haberstraße 2, D-91058, Erlangen, Germany

    Patrick R. Schmitt

Authors
  1. Maximilian Gerstner
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  2. Patrick R. Schmitt
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  3. Paul Steinmann
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Editor information

Editors and Affiliations

  1. Institute of Mechanics and Computational Mechanics (IBNM), Gottfried Wilhelm Leibniz Universität Hannover, Hannover, Germany

    Erwin Stein

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Gerstner, M., Schmitt, P.R., Steinmann, P. (2014). The Development of Analytical Mechanics by Euler, Lagrange and Hamilton – From a Student’s Point of View. 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_4

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  • DOI: https://doi.org/10.1007/978-3-642-39905-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39904-6

  • Online ISBN: 978-3-642-39905-3

  • eBook Packages: EngineeringEngineering (R0)

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