Rolling of a Chaplygin Ball Over a Fixed Surface of Revolution

ABSTRACT

The problem of a Chaplygin ball rolling over a fixed surface of revolution is considered within the framework of the Coulomb model of dry friction. It is assumed that a real (imperfectly) rough rigid contact in one point is established between the ball and the surface of revolution. This type of contact is characterised by a finite value of the coefficient of sliding friction. The influence of changing the orientation of a rolling Chaplygin ball relative to the inertial reference frame on the instants and positions when the ball begins to slip is examined. Using the linear and angular momentum balance laws, the corresponding Cauchy problem is formulated. The tangential and normal components of the surface of revolution's reaction force that are required to ascertain the Chaplygin ball's sliding position are established by solving the Cauchy problem. By solving a numerical example, the use of the provided method for figuring out the Chaplygin ball's slide position is demonstrated.