Two-Dimensional Problems of Minimal Resistance in a Medium of Positive Temperature

Details Two-Dimensional Problems of Minimal Resistance in a Medium of Positive Temperature Two-Dimensional Problems of Minimal Resistance in a Medium of Positive Temperature

2004-04-09

arxiv.org/abs/math/0404194v1

Proceedings of the 6th Portuguese Conference on Automatic Control - Controlo 2004, Faro, Portugal, June 7-11, 2004, pp. 488-49

Mathematics

Optimization and Control

Accepted to the Proceedings of the Sixth Portuguese Conference on Automatic Control - Controlo 2004, Faro, Portugal, June 7-9,

Scientific paper

We study the Newton-like problem of minimal resistance for a two-dimensional body moving with constant velocity in a homogeneous rarefied medium of moving particles. The distribution of the particles over velocities is centrally symmetric. The problem is solved analytically; the minimizers are shown to be of four different types. Numerical results are obtained for the physically significant case of gaussian circular distribution of velocities, which corresponds to a homogeneous ideal gas of positive temperature.

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