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. Katz
  • Tahl Nowik
Regular Paper

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.

Keywords

Harmonic motion Infinitesimal Pendulum Small oscillations 

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Copyright information

© Chapman University 2016

Authors and Affiliations

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

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