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

Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik
2016 Quantum Studies: Mathematics and Foundations  

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2016 pre-print arXiv:1604.06663v1 fatcat:escgm5k3m5gf5ixvcoor2cll7a
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
doi:10.1007/s40509-016-0074-x fatcat:k5dschbekvf2rkfpcaaoiuyory
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Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik. "Small oscillations of the pendulum, Euler's method, and adequality." Quantum Studies: Mathematics and Foundations 3.3 (2016) 231-236