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~$M$.

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CWI
Modelling, Analysis and Simulation [MAS]

Lachand-Robert, T, & Peletier, M.A. (2000). Newton's problem of the body of minimal resistance in the class of convex developable functions. Modelling, Analysis and Simulation [MAS]. CWI.