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

TL;DR

This paper analytically solves a two-dimensional minimal resistance problem for a body moving in a rarefied medium with symmetric particle velocity distribution, identifying four types of minimizers and providing numerical results for a Gaussian velocity distribution.

Contribution

It introduces an analytical solution to the 2D minimal resistance problem in a medium with positive temperature, revealing four types of minimizers and offering numerical analysis for Gaussian velocity distributions.

Findings

Minimizers are of four distinct types.

Analytical solutions are derived for the problem.

Numerical results are provided for Gaussian velocity distribution.

Abstract

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.