The analytical solution to Newton's aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary

TL;DR

This paper derives an analytical differential equation for the optimal shape of symmetric, developable bodies with minimal aerodynamic resistance in a rarefied medium, using Hessian measures and proving their optimality.

Contribution

It introduces a new differential equation characterizing optimal shapes with symmetry and developability, expanding the analytical understanding of minimal resistance bodies.

Findings

Derived the differential equation for optimal shapes

Synthesized solutions for bodies with minimal resistance

Proved the optimality of the solutions

Abstract

The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare medium. The synthesis of optimal solutions is described. A theorem on the optimality of the obtained solutions is proved.