Asymptotics of Maxwell time in the plate-ball problem
  The problem on rolling of a sphere on a plane without slipping or twisting is considered. One should roll the sphere from one contact configuration to another so that the length of the curve traced by the contact point in the plane was the shortest possible. Asymptotics of Maxwell time for rolling of the sphere along small amplitude sinusoids is studied. Two-sided estimate for this asymptotics is obtained. 
A. P. Mashtakov, A. Yu. Popov
math.OC