Billiard scattering on rough sets: two-dimensional case

TL;DR

This paper introduces a new framework for modeling billiard scattering on rough convex bodies in two dimensions, providing a measure-based characterization that aids in solving resistance minimization problems.

Contribution

It defines rough two-dimensional convex bodies and characterizes the measures describing their billiard scattering, advancing the understanding of resistance optimization.

Findings

Characterization of measures generated by rough bodies.

Framework for solving least resistance problems.

Application to aerodynamic resistance minimization.

Abstract

The notion of a rough two-dimensional (convex) body is introduced, and to each rough body there is assigned a measure on $\TTT^3$ describing billiard scattering on the body. The main result is characterization of the set of measures generated by rough bodies. This result can be used to solve various problems of least aerodynamical resistance.