Quickest-descent curve in the problem of rolling of a homogeneous cylinder

The motion of a heavy homogeneous cylinder is considered as rolling without slipping along an unknown curve. A functional in the form of the total time of rolling is found and minimized by solving a variational problem. The algebraic equation of the quickest-descent directrix is derived in parametric form Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 131–138, December 2008.