English

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

R2 v1 2026-06-22T13:38:37.931Z