On a simple formulation of the golf ball paradox

The motion of a ball rolling without slipping on the lateral section inside a fixed vertical cylinder is analysed in the Earth referential frame which is assumed to be Galilean. Equations of motion are rapidly obtained and the golf ball paradox is understood: these equations describe a motion consisting of a vertical harmonic oscillation related to a horizontal one which is characterized by a revolution with a constant angular velocity around the vertical ( or axis cylinder). The analysis in the Earth frame is simpler compared to the analysis made in an artificial rotating frame in which inertial forces such as the Coriolis one must be taken into account.