| 等时降线问题的求解 |
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| 引用本文： | 邢家省,吴桑.等时降线问题的求解[J].吉首大学学报(自然科学版),2021,41(6):5-10. |
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| 作者姓名： | 邢家省 吴桑 |
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| 作者单位： | （1.北京航空航天大学数学与系统科学学院，北京 100191；2.数学、信息与行为教育部重点实验室，北京 100191） |
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| 基金项目： | 国家自然科学基金资助项目（11771004）；北京航空航天大学校级重大教改项目（北航培育项目2019-01—2021-12） |
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| 摘 要： | 考虑了给定下降时间函数的下降曲线的求解问题.将质点沿光滑曲线从一定高度下滑所需时间的问题转化为积分方程求解的问题，并对积分方程进行阿贝尔积分变换，再利用积分换序方法给出了求解公式，最后证明了等时降线问题的解是一条倒摆线.
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Solution of Isochronous Curve Problem |
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| XING Jiasheng,WU Sang.Solution of Isochronous Curve Problem[J].Journal of Jishou University(Natural Science Edition),2021,41(6):5-10. |
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| Authors: | XING Jiasheng WU Sang |
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| Institution: | (1. School of Mathematics and System Science, Beihang University, Beijing 100191, China;2. LMIB of the Ministry of Education, Beihang University, Beijing 100191, China) |
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| 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. |
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| Keywords: | isochronal curves problem integral equation Abel transformation cycloid |
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