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Symmetry 2018, 10(4), 111; https://doi.org/10.3390/sym10040111

Energy, Christiaan Huygens, and the Wonderful Cycloid—Theory versus Experiment

1,2,†,* , 3,†
,
4
and
5
1
Department of Physics and Project Unit, Sapir Academic College, Sderot 79165, Israel
2
Hemdat Hadarom Academic College of Education, Netivot 80200, Israel
3
Department of Physics, Ben-Gurion University of the Negev, Beer Sheva Campus 84990, Israel
4
The Department of Science and Technology Education, Ben-Gurion University of Negev, Beer Sheva Campus 84990, Israel
5
Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede-Boker Campus 84990, Israel
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 4 February 2018 / Revised: 14 March 2018 / Accepted: 8 April 2018 / Published: 16 April 2018
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Abstract

The cycloid is one of the most intriguing objects in the classical physics world, at once solving the brachistochrone and isochronous curve problems. Historically, the cycloid shape has been employed to great success in many physical contexts. We discuss one such case, presenting the longitude problem as a pathway into an in-depth discussion of the analytical solution of a point mass motion along a cycloid. The classical solution is presented, and the modifications needed for a rolling ball along a cycloid rail are made. A comparison is then made between the two cases, and we show that the difference in most physical cases between the point mass and the rolling ball is at most ~7%. Next, an experiment is presented in which the isochronous nature of the cycloid path is tested, to different degrees of success. The results are discussed and several possible origins of the discrepancy between the theory and the experimental results are identified. We conclude with a discussion of skidding and slipless rolling. View Full-Text
Keywords: cycloid; brachistochrone; point mass; motion cycloid; brachistochrone; point mass; motion
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ben-Abu, Y.; Wolfson, I.; Eshach, H.; Yizhaq, H. Energy, Christiaan Huygens, and the Wonderful Cycloid—Theory versus Experiment. Symmetry 2018, 10, 111.

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