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

Vladimir Kanovei; Karin U. Katz; Mikhail G. Katz; Tahl Nowik

doi:10.1007/s40509-016-0074-x

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

Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	231-236
Number of pages	6
Journal	Quantum Studies: Mathematics and Foundations
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/s40509-016-0074-x
State	Published - 1 Sep 2016

Keywords

Harmonic motion
Infinitesimal
Pendulum
Small oscillations

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics
Mathematical Physics

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10.1007/s40509-016-0074-x

Cite this

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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{\textquoteright}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.",

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AU - Kanovei, Vladimir

AU - Katz, Karin U.

AU - Katz, Mikhail G.

AU - Nowik, Tahl

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Harmonic motion

KW - Infinitesimal

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KW - Small oscillations

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DO - 10.1007/s40509-016-0074-x

M3 - مقالة

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ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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