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The problem of a disc and a ball rolling on a horizontal plane withoutslipping is considered. Differential constrained equations are shown to beintegrated when the trajectory of the point of contact is taken in a form ofthe natural equation, i.e. when the dependence of the curvature of thetrajectory is explicitly expressed in terms of the distance passed by thepoint.

Integration of Constraint Equations in Problems of a Disc and a Ball Rolling on a Horizontal Plane