This article is cited in 2 scientific papers (total in 2 papers)
Topological monodromy in nonholonomic systems
Alexey V. Bolsinovab, Alexander A. Kilinb, Alexey O. Kazakovb
a School of Mathematics, Loughborough University,
United Kingdom, LE11 3TU, Loughborough, Leicestershire
b Institute of Computer Science;
Laboratory of nonlinear analysis and the design of new types of vehicles, Udmurt State University, Izhevsk, Russia
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.
topological monodromy, integrable systems, nonholonomic systems, Poincaré map, bifurcation analysis, focus-focus singularities.
PDF file (1771 kB)
MSC: 37J05, 34C14
Alexey V. Bolsinov, Alexander A. Kilin, Alexey O. Kazakov, “Topological monodromy in nonholonomic systems”, Nelin. Dinam., 9:2 (2013), 203–227
Citation in format AMSBIB
\by Alexey~V.~Bolsinov, Alexander~A.~Kilin, Alexey~O.~Kazakov
\paper Topological monodromy in nonholonomic systems
\jour Nelin. Dinam.
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