On realizing nonholonomic constraints by viscous friction forces and celtic stones stability

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Abstract

It is shown that equations of motion of nonholonomic systems can be obtained from the equations of motion of systems freed of nonholonomic constraints subjected to suitably chosen dissipative forces, if in the latter the dissipation coefficient is assumed infinite. It is shown that on fairly general assumptions motions of non-holonomic systems represent limits of motions of corresponding holonomic systems, as the dissipation coefficient approaches infinity. The stability of rotation on a horizontal plane of a heavy asymmetric rigid body (Celtic stone) about the vertical, with allowance for friction, is investigated. The obtained stability conditions are compared with previously published papers about rotation of a body on an absolutely rough horizontal plane around the vertical. © 1982.

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Karapetian, A. V. (1981). On realizing nonholonomic constraints by viscous friction forces and celtic stones stability. Journal of Applied Mathematics and Mechanics, 45(1), 30–36. https://doi.org/10.1016/0021-8928(81)90006-X

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