Quantum Studies: Mathematics and Foundations

, Volume 3, Issue 3, pp 231–236 | Cite as

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

  • Vladimir Kanovei
  • Karin U. Katz
  • Mikhail G. KatzEmail author
  • Tahl Nowik
Regular Paper


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.


Harmonic motion Infinitesimal Pendulum Small oscillations 



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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Copyright information

© Chapman University 2016

Authors and Affiliations

  • Vladimir Kanovei
    • 1
    • 2
  • Karin U. Katz
    • 3
  • Mikhail G. Katz
    • 3
    Email author
  • Tahl Nowik
    • 3
  1. 1.IPPIMoscowRussia
  2. 2.MIITMoscowRussia
  3. 3.Department of MathematicsBar Ilan UniversityRamat GanIsrael

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