### The problem of the body of revolution of minimal resistanceThe problem of the body of revolution of minimal resistance

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 Author Plakhov, Alexander ♦ Aleksenko, Alena Source arXiv.org Content type Text File Format PDF Date of Submission 2008-04-24 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Optimization and Control ♦ math Abstract Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of {\it convex} axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class of axially symmetric but {\it generally nonconvex} bodies. The infimum in this problem is not attained. We construct a sequence of bodies minimizing the resistance. This sequence approximates a convex body with smooth front surface, while the surface of approximating bodies becomes more and more complicated. The shape of the resulting convex body and the value of minimal resistance are compared with the corresponding results for Newton's problem and for the problem in the intermediate class of axisymmetric bodies satisfying the {\it single impact} assumption \cite{CL1}. In particular, the minimal resistance in our class is smaller than in Newton's problem; the ratio goes to 1/2 as (length)/(width of the body) $\to 0$, and to 1/4 as (length)/(width) $\to +\infty$. Educational Use Research Learning Resource Type Article