Geodesic
Topological monodromy in nonholonomic systems
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 203-227

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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.
Keywords: topological monodromy, integrable systems, nonholonomic systems, Poincaré map, bifurcation analysis, focus-focus singularities. 
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     author = {Alexey V. Bolsinov and Alexander A. Kilin and Alexey O. Kazakov},
     title = {Topological monodromy in nonholonomic systems},
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Alexey V. Bolsinov; Alexander A. Kilin; Alexey O. Kazakov. Topological monodromy in nonholonomic systems. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 203-227. http://geodesic.mathdoc.fr/item/ND_2013_9_2_a1/