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arXiv · 1604.06663

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

Vladimir Kanovei·Karin U. Katz·Mikhail G. Katz·Tahl Nowik
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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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Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik. 2016-04-13. Small oscillations of the pendulum, Euler's method, and adequality. https://doi.org/10.1007/s40509-016-0074-x

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