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

Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Pages (from-to)231-236
Number of pages6
JournalQuantum Studies: Mathematics and Foundations
Issue number3
StatePublished - 1 Sep 2016

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2016, Chapman University.


  • Harmonic motion
  • Infinitesimal
  • Pendulum
  • Small oscillations


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