  A two-dimensional body moves through a rarefied medium; the collisions of the
medium particles with the body are absolutely elastic. The body performs both
translational and slow rotational motion. It is required to select the body,
from a given class of bodies, such that the average force of resistance of the
medium to its motion is maximal.
  There are presented numerical and analytical results concerning this problem.
In particular, the maximum resistance in the class of bodies contained in a
convex body K is proved to be 1.5 times resistance of K. The maximum is
attained on a sequence of bodies with very complicated boundary. The numerical
study was made for somewhat more restricted classes of bodies. The obtained
values of resistance are slightly lower, but the boundary of obtained bodies is
much simpler, as compared to the analytical solutions.
