| 抢渡长江最优路径的讨论 |
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| 引用本文： | 孔敏,姚天行.抢渡长江最优路径的讨论[J].数学的实践与认识,2005,35(7):136-140. |
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| 作者姓名： | 孔敏 姚天行 |
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| 作者单位： | 南京大学效学系,南京,210093 |
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| 摘 要： | 给出了2003年全国大学生数学建模竞赛D题的一种求解方法.运用拉格朗日乘数法与变分法建立了水速变化时最优路径适合的方程.特别针对问题4,当水流速度线性变化时,导出了求解最优解的函数方程.
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| 关 键 词： | 运动偏角 拉格朗日乘数法 变分原理 |
On the Optimal Path of Swimming Race Across the Yangtze River |
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| KONG Min,YAO Tian-xing.On the Optimal Path of Swimming Race Across the Yangtze River[J].Mathematics in Practice and Theory,2005,35(7):136-140. |
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| Authors: | KONG Min YAO Tian-xing |
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| Abstract: | In this article, we present a method for solving the problem D in the CUMCM 2003. By applying Lagrange′s method of multipliers and the variational principle, we establish equations for solving the optimal path fitting for varied speeds of water. For the problem 4, when the speed of water varying with linearity, we educe the functional equations for solving the optimal solutions. |
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| Keywords: | the partial angle of movement Lagrange′s method of multipliers variational principle |
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