等时降线问题的求解  

Solution of Isochronous Curve Problem

作　　者：邢家省[1,2] 吴桑 XING Jiasheng;WU Sang(School of Mathematics and System Science, Beihang University, Beijing 100191, China;LMIB of the Ministry of Education, Beihang University, Beijing 100191, China)

机构地区：[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

出　　处：《吉首大学学报（自然科学版）》2020年第6期5-10,20,共7页Journal of Jishou University(Natural Sciences Edition)

基　　金：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201901—202112)。

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.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.

关 键 词：等时降线问题 积分方程 阿贝尔积分变换 摆线 

分 类 号：O175.29[理学—数学]