Problem of Minimum Resistance to Translational Motion of Bodies

Newton’s aerodynamic problem consists in minimizing the resistance to the translational motion of a three-dimensional body moving in a homogeneous medium of resting particles. The particles do not interact with each other and reflect off elastically in collisions with the body. This problem has been considered for various classes of admissible bodies. In Newton’s initial setting[40], the class of admissible bodies consisted of convex axisymmetric bodies of fixed length and width, that is, bodies inscribed in a fixed right circular cylinder. The problem was later considered for various classes of (convex and axisymmetric) bodies, for example, for bodies whose front generator has a fixed length (and whose width is also fixed)[32,4], for bodies of fixed volume[5], and so on. A major step forward was made in the 1990s, when unexpected and striking results were obtained for some classes of nonaxisymmetric bodies and, later, for nonconvex bodies[8,11,12,16,17,18,29,30,31]). However, the authors kept the initial assumption that the body must have a fixed length and width, that is, can be inscribed in a fixed right circular cylinder.