Revisiting Johann Bernoulli

Ido Braun; Joseph Z. Ben-Asher

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Paper

Revisiting Johann Bernoulli's Method for the Brachistochrone Problem

Topics: Engineering Applications on Intelligent Control Systems and Optimization

In Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics ICINCO - Volume 1, 107-114, 2021

Authors: Ido Braun and Joseph Z. Ben-Asher

Affiliation: Faculty of Aerospace Engineering, Technion, Haifa, 32000, Israel

Keyword(s): Johann Bernoulli, Brachistochrone, Snell’s Law, Fermat's Principle, Minimum Time.

Abstract: This paper reviews Johann Bernoulli's solution to the Brachistochrone problem, using an analogy to the movement of light and Fermat's principle of least time. Bernoulli's method is later used to derive solutions to some generalizations of the Brachistochrone problem. The problems solved using Bernoulli's method are the classical flat gravity Brachistochrone, spherical gravity outside the earth, and spherical gravity inside the earth ('gravity train').

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Paper citation in several formats:

Braun, I. and Ben-Asher, J. (2021). Revisiting Johann Bernoulli's Method for the Brachistochrone Problem. In Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO; ISBN 978-989-758-522-7; ISSN 2184-2809, SciTePress, pages 107-114. DOI: 10.5220/0010503501070114

@conference{icinco21,
author={Ido Braun. and Joseph Z. Ben{-}Asher.},
title={Revisiting Johann Bernoulli's Method for the Brachistochrone Problem},
booktitle={Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO},
year={2021},
pages={107-114},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010503501070114},
isbn={978-989-758-522-7},
issn={2184-2809},
}

TY - CONF

JO - Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO
TI - Revisiting Johann Bernoulli's Method for the Brachistochrone Problem
SN - 978-989-758-522-7
IS - 2184-2809
AU - Braun, I.
AU - Ben-Asher, J.
PY - 2021
SP - 107
EP - 114
DO - 10.5220/0010503501070114
PB - SciTePress