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Small oscillations of the pendulum, Euler’s method, and adequality

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Abstract

Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler’s method with infinitesimal mesh, with well-posedness based on a relation of adequality following Fermat and Leibniz. The result is that the period of infinitesimal oscillations is independent of their amplitude.

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Acknowledgments

We are grateful to Jeremy Schiff for drawing our attention to the Hartman–Grobman theorem, and to Semen Kutateladze and Dalibor Pražák for some helpful suggestions. M. Katz was partially supported by the Israel Science Foundation Grant No. 1517/12.

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Authors and Affiliations

  1. IPPI, Moscow, Russia

    Vladimir Kanovei

  2. MIIT, Moscow, Russia

    Vladimir Kanovei

  3. Department of Mathematics, Bar Ilan University, 52900, Ramat Gan, Israel

    Karin U. Katz, Mikhail G. Katz & Tahl Nowik

Authors
  1. Vladimir Kanovei
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  2. Karin U. Katz
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  3. Mikhail G. Katz
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  4. Tahl Nowik
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Correspondence to Mikhail G. Katz.

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Kanovei, V., Katz, K.U., Katz, M.G. et al. Small oscillations of the pendulum, Euler’s method, and adequality. Quantum Stud.: Math. Found. 3, 231–236 (2016). https://doi.org/10.1007/s40509-016-0074-x

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  • DOI: https://doi.org/10.1007/s40509-016-0074-x

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