Newton's problem of the body of minimal resistance in the class of convex developable functions
Newton's problem of the body of minimal resistance in the class of convex developable functions
复制标题
凸可展函数类中最小阻力体的牛顿问题
DOI：
10.1002/1522-2616(200106)226:1
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Peletier
中科院分区：
文献类型：
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作者：
T. L. Robert;M. Peletier
研究了圆盘上凸可展函数类中最大高度为${M>0$ cite{butt}的最小阻力体问题的牛顿泛函的极小化问题。根据cite{lrp 2.我们证明了这类极小元有一个极小集，其形式为一个n边以圆盘为中心的正多边形，数值实验表明自然数ngeq 2是M的非减函数.相应的函数都比具有相同高度~$M$的最优径向对称函数获得更低的泛函值。
We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height ${M>0$ cite{butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite{lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with~$n$ sides centered in the disc, and numerical experiments indicate that the natural number $ngeq2$ is a non-decreasing function of $M$. The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height~$M$.