Topological monodromy in nonholonomic systems
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An eﬃcient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The ﬁrst of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no diﬀerence between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.