Chaplygin's Ball with a Rotor: Non-Degeneracy of Singular Points / A. I. Zhila. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 2. P. 3-12 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 45-54].
A problem of a dynamically balanced asymmetric ball with a rotor rolling over a rough horizontal plane is considered. Earlier, A. Y. Moskvin constructed bifurcation diagrams of the momentum map and bifurcation complexes in order to study the dynamics of the system and to obtain singular solutions. A natural development of this research is a fine Liouville analysis of the system. The first step in this direction is presented in the paper, namely, we verify the non-degeneracy of singularities and describe the Liouville foliation in a neighborhood of singular points of the momentum map.
Key words: Chaplygin ball with a rotor, conformally Hamiltonian systems, singular points of the momentum map, Liouville foliation, Fomenko–Zieschang invariants.