Small oscillations of the pendulum, Euler's method, and adequality
History and Overview
2017-03-07 v1 Mathematical Physics
Logic
math.MP
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
Keywords
Cite
@article{arxiv.1604.06663,
title = {Small oscillations of the pendulum, Euler's method, and adequality},
author = {Vladimir Kanovei and Karin U. Katz and Mikhail G. Katz and Tahl Nowik},
journal= {arXiv preprint arXiv:1604.06663},
year = {2017}
}
Comments
9 pages, to appear in Quantum Studies: Mathematics and Foundations