Rubber ball on a plane: singular solutions

The paper deals with the rolling motion of a balanced, dynamically asymmetric ball on a plane without sliding and spinning. The problem is natural but was not considered by classicists. Generalizations of the problem are analyzed for the case where gyrostat and force Brun field are added. To investigate the dynamic behavior of the system some peculiar periodic solutions are described and their stability is examined. By integral mapping, bifurcation diagrams and bifurcation complexes are constructed.