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

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.

Original languageEnglish
Pages (from-to)231-236
Number of pages6
JournalQuantum Studies: Mathematics and Foundations
Volume3
Issue number3
DOIs
StatePublished - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016, Chapman University.

Funding

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.

FundersFunder number
Israel Science Foundation1517/12

    Keywords

    • Harmonic motion
    • Infinitesimal
    • Pendulum
    • Small oscillations

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