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

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 infinit...

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Bibliographic Details
Published in:arXiv.org 2016-04
Main Authors: Kanovei, Vladimir, Katz, Karin U, Katz, Mikhail G, Nowik, Tahl
Format: Article
Language:English
Subjects:
Differential equations
Harmonic motion
Oscillations
Pendulums
Well posed problems
Online Access:Get full text
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Summary: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
ISSN:2331-8422
DOI:10.48550/arxiv.1604.06663