Solution of Isochronous Curve Problem

doi:10.13438/j.cnki.jdzk.2020.06.002

Journal of Jishou University(Natural Sciences Edition) ›› 2020, Vol. 41 ›› Issue (6): 5-10.DOI: 10.13438/j.cnki.jdzk.2020.06.002

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Solution of Isochronous Curve Problem

XING Jiasheng,WU Sang

(1. School of Mathematics and System Science, Beihang University, Beijing 100191, China;2. LMIB of the Ministry of Education, Beihang University, Beijing 100191, China)

Online:2020-11-25 Published:2021-02-04

Abstract

Abstract: For the solution of isochronal curves with a given isochronal time function and the formula of time for particle to slide down from a certain height along the smooth curve, the problem is transformed into an integral equation solution problem and Abel transformation is performed for the integral equation. Integral order conversion method is applied to obtian the solution formula, and the solution of the isochronous descent problem is proved out an inverted cycloid.

Key words: isochronal curves problem, integral equation, Abel transformation, cycloid

XING Jiasheng, WU Sang. Solution of Isochronous Curve Problem[J]. Journal of Jishou University(Natural Sciences Edition), 2020, 41(6): 5-10.

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Solution of Isochronous Curve Problem

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