Topological analysis of one integrable system related to the rolling of a ball over a sphere

    2012, Vol. 8, No. 5, pp.  957-975

    Author(s): Borisov A. V., Mamaev I. S.

    A new integrable system describing the rolling of a rigid body with a spherical cavity over a spherical base is considered. Previously the authors found the separation of variables for this system at the zero level of a linear (in angular velocity) first integral, whereas in the general case it is not possible to separate the variables. In this paper we show that the foliation into invariant tori in this problem is equivalent to the corresponding foliation in the Clebsch integrable system in rigid body dynamics (for which no real separation of variables has been found either). In particular, a fixed point of focus type is possible for this system, which can serve as a topological obstacle to the real separation of variables.
    Keywords: integrable system, bifurcation diagram, conformally Hamiltonian system, bifurcation, Liouville foliation, critical periodic solution
    Citation: Borisov A. V., Mamaev I. S., Topological analysis of one integrable system related to the rolling of a ball over a sphere, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp.  957-975

    Download File
    PDF, 796.84 Kb

    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License