Integration of Constraint Equations in Problems of a Disc and a Ball   Rolling on a Horizontal Plane
  The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural equation, i.e. when the dependence of the curvature of the trajectory is explicitly expressed in terms of the distance passed by the point. 
Eugeny A. Mityushov
nlin.SI math.DS