Abstract:
This paper is concerned with the dynamics of a top in the form of a truncated ball
as it moves without slipping and spinning on a horizontal plane about a vertical. Such a system
is described by differential equations with a discontinuous right-hand side. Equations describing
the system dynamics are obtained and a reduction to quadratures is performed. A bifurcation
analysis of the system is made and all possible types of the top’s motion depending on the
system parameters and initial conditions are defined. The system dynamics in absolute space
is examined. It is shown that, except for some special cases, the trajectories of motion are
bounded.
Keywords:
integrable system, system with discontinuity, nonholonomic constraint, bifurcation diagram, absolute dynamics.
The work of A.A. Kilin (Sections 1, 2, and 4) is supported by the RFBR grants 15-08-09093-a and 15-38-20879 mol_a_ved. The work of E.N. Pivovarova (Section 3) is carried out within the framework of the RSF grant no. 15-12-20035.
Citation:
Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317
\Bibitem{KilPiv17}
\by Alexander A. Kilin, Elena N. Pivovarova
\paper The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 3
\pages 298--317
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