Problem on the brachistochronic motion of a heavy disk with dry friction

The plane motion of a heavy dynamically symmetric circular disk (wheel) touching a supporting regular material curve with no more than one disk periphery point at any instant, is considered. At the instantaneous contact point between the disk and the curve the force of the Coulomb (dry) friction acts. The problem on finding the form of a supporting curve that provides the minimal transition time interval for the disk center which starts at a given position A, when the disk is in rest, and finishes at a given terminal position B, is treated. The method of the conditional variational problem with differential inequalities is used to find the necessary conditions satisfied with the desired curve.