Motion of a disk within a sphere

    1998, Volume 3, Number 2, pp.  74-81

    Author(s): Kholmskaya A. G.

    The motion of a round dynamically symmetrical disk within a sphere covered by smooth ice is considered. It is shown that in the absence of a gravity field equations of motion may be reduced to quadratures. Conditions for the stability of stationary motions have been found. Probability of a falling of a disk has been investigated. Regions allowed for the motion in a gravity field and characterizing by the disk orientation and the situation of a trajectory of a contact point on a sphere surface have been built. The conclusion on the non-integrability on the analysis of Poincare sections of a problem on a round dynamically symmetrical disk moving on a smooth sphere surface has been made.
    Citation: Kholmskaya A. G., Motion of a disk within a sphere, Regular and Chaotic Dynamics, 1998, Volume 3, Number 2, pp. 74-81

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