Small oscillations of the pendulum, Euler's method, and adequality
arXiv:1604.06663 · doi:10.1007/s40509-016-0074-x
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
9 pages, to appear in Quantum Studies: Mathematics and Foundations
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