{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T13:01:50Z","timestamp":1770555710410,"version":"3.49.0"},"reference-count":11,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,16]],"date-time":"2018-04-16T00:00:00Z","timestamp":1523836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym10040111","type":"journal-article","created":{"date-parts":[[2018,4,16]],"date-time":"2018-04-16T12:40:26Z","timestamp":1523882426000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Energy, Christiaan Huygens, and the Wonderful Cycloid\u2014Theory versus Experiment"],"prefix":"10.3390","volume":"10","author":[{"given":"Yuval","family":"Ben-Abu","sequence":"first","affiliation":[{"name":"Department of Physics and Project Unit, Sapir Academic College, Sderot 79165, Israel"},{"name":"Hemdat Hadarom Academic College of Education, Netivot 80200, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ira","family":"Wolfson","sequence":"additional","affiliation":[{"name":"Department of Physics, Ben-Gurion University of the Negev, Beer Sheva Campus 84990, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haim","family":"Eshach","sequence":"additional","affiliation":[{"name":"The Department of Science and Technology Education, Ben-Gurion University of Negev, Beer Sheva Campus 84990, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hezi","family":"Yizhaq","sequence":"additional","affiliation":[{"name":"Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede-Boker Campus 84990, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,16]]},"reference":[{"key":"ref_1","unstructured":"Gindkin, S. (2007). Tale of Mathematics and Physicists, Springer. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ben-Abu, Y., Eshach, H., and Yizhaq, H. (2017). Interweaving the Principle of Least Potential Energy in School and Introductory University Physics Courses. Symmetry, 9.","DOI":"10.3390\/sym9030045"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Yoder, J.G. (1988). Unrolling Time, Cambridge University Press.","DOI":"10.1017\/CBO9780511622441"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"045002","DOI":"10.1088\/1361-6404\/aa6c19","article-title":"Minimum descent time along a set of connected inclined planes","volume":"38","author":"Mungan","year":"2017","journal-title":"Eur. J. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"015009","DOI":"10.1088\/1361-6552\/52\/1\/015009","article-title":"Approaching the Brachistochrone using inclined planes\u2014Striving for shortest or equal travelling times","volume":"52","author":"Theilmann","year":"2016","journal-title":"Phys. Educ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1119\/1.2120388","article-title":"An inexpensive technique to measure coefficient of friction with rolling solides","volume":"43","author":"Caravlho","year":"2005","journal-title":"Phys. Teach."},{"key":"ref_7","unstructured":"Walker, J., Resnick, R., and Halliday, D. (2014). Halliday & Resnick Fundamentals of Physics, John Wiley & Sons, Inc.. [10th ed.]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"065005","DOI":"10.1088\/1361-6552\/aa81f0","article-title":"Downhill cycling symmetry breaking: How the rider foils experiment","volume":"52","author":"Wolfson","year":"2017","journal-title":"Phys. Educ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1088\/0031-9120\/40\/3\/F03","article-title":"Balls on an incline roll, slide and skip","volume":"40","author":"Gluck","year":"2011","journal-title":"Phys. Educ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1080\/00207390902825344","article-title":"Ball launched against an inclined plane\u2014An example of using recurrent sequences in school physics","volume":"40","author":"Benacka","year":"2009","journal-title":"Int. J. Math. Educ. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ben-Abu, Y. (2017). Gate Antiphase of Potassium Channel. Symmetry, 9.","DOI":"10.3390\/sym9080150"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/4\/111\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:50Z","timestamp":1760194850000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/4\/111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,16]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["sym10040111"],"URL":"https:\/\/doi.org\/10.3390\/sym10040111","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,16]]}}}