Small oscillations of the pendulum, Euler's method, and adequality
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik
TL;DR
This paper introduces a novel approach to solving differential equations for small oscillations using Euler's method with infinitesimal steps, establishing that the oscillation period remains constant regardless of amplitude.
Contribution
It proposes a solution concept based on Euler's method with infinitesimal mesh and adequality, connecting historical ideas with modern differential equation analysis.
Findings
The period of infinitesimal oscillations is independent of amplitude.
A new solution framework based on Euler's method with infinitesimals.
Historical concepts of adequality are applied to differential equations.
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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