Abstract
We consider the problem on the dynamics of a Celtic stone on a fixed horizontal plane. By analogy with [1], it is assumed that a classical viscous friction force is exerted on the body by the plane. We analytically justify the change in the direction of rotation from positive (in the sense of rotation of the centroidal principal axes of inertia relative to the geometric symmetry axes of the body) to negative under certain constraints on the problem parameters. For an approximate system of equations describing the dynamics of the body, the corresponding initial conditions are determined and approximate expressions for the final angular velocity are given.
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Funding
This work was financially supported by the Russian Foundation for Basic Research, project no. 19-01-00140, and Program no. 7 of Fundamental Scientific Research in Priority Areas Determined by the Presidium of the Russian Academy of Sciences “New developments in promising areas of power engineering, mechanics and robotics.”
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Translated by V. Potapchouck
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Munitsyna, M.A. Celtic Stone Dynamics on a Plane with Viscous Friction. Autom Remote Control 83, 325–331 (2022). https://doi.org/10.1134/S000511792203002X
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DOI: https://doi.org/10.1134/S000511792203002X