A sphere rolling on a horizontal rotating plane (Q790630)

The author studies the general case of a heavy homogeneous sphere movement on a rough horizontal surface \(\pi\) rotating around a vertical axis with constant angular velocity \(\Omega\). The sphere moves in a viscous fluid which acts through resistance forces on the sphere surface. The author studies three distinct cases of movement: 1. the case when the viscous friction is neglected obtaining a result known in the literature (the center of the sphere describes a circle); 2. the case of movement in a viscous medium when the center of the sphere describes a contracting spiral towards a fixed point and, 3. the case of movement of the sphere on a rotating plane in the presence of rolling resistance when the center of the sphere describes an expanding spiral with the center at the coordinate origin.