2020
DOI: 10.1088/1361-6404/abaf41
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From the discrete to the continuous brachistochrone: a tale of two proofs

Abstract: In a previous paper (2019 Eur. J. Phys. 40 035005) we showed how to design a discrete brachistochrone with an arbitrary number of segments. We have proved, numerically and graphically, that in the limit of a large number of segments, N ≫ 1, the discrete brachistochrone converges into the continuous brachistochrone, i.e. into a cycloid. Here we show this convergence analytically, in two different ways, based upon the results we obtained from investigating the characteristics of the discrete b… Show more

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Cited by 2 publications
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“…This kind of studies have been of interest, e.g., to accurately model the Tour de France bicycle race [13] or to find a solution to an important practical problem -which tanks empty most rapidly [14]. On the other hand, the results of the present study have some common features with recent innovations in studying a discrete brachistochrone with an arbitrary number of segments [15].…”
Section: Brachistochrone Vs Broken Line Of Chordsmentioning
confidence: 60%
“…This kind of studies have been of interest, e.g., to accurately model the Tour de France bicycle race [13] or to find a solution to an important practical problem -which tanks empty most rapidly [14]. On the other hand, the results of the present study have some common features with recent innovations in studying a discrete brachistochrone with an arbitrary number of segments [15].…”
Section: Brachistochrone Vs Broken Line Of Chordsmentioning
confidence: 60%