Chaplygin's ball with a gyrostat: singular solutions

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.