Alexander Plakhov

Billiards and problems of minimal aerodynamic resistance

A body moves in a homogeneous medium composed of immovable point particles; the particles do not mutually interact, and interact with the body in the absolutely elastic manner. It is required to find the shape of body that would minimize the resistance force of the medium to the body’s motion. This problem was first considered by Newton in the class of axially symmetric convex bodies of fixed length and width. Various modifications of Newton’s problem have been considered since then, usually it was supposed that every particle hits the body at most once.

We consider problems of minimal resistance in various classes of non-convex bodies, where multiple collisions of particles with the body are admissible. The results recently obtained in this area are presented.