Andrey Moskvin

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.

The paper deals with the rolling motion of a balanced, dynamically asymmetric ball with a gyrostat on a horizontal rough plane. To investigate the dynamical behavior of the system and find singular solutions, the bifurcation diagram of the momentum map and the bifurcation complex are constructed. The singular solutions are described and their stability is examined. It is shown that the addition of a gyrostat can turn stable singular solutions into unstable ones and vice versa.