KAM dynamics and stabilization of a particle sliding over a periodically driven curve |
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Institution: | 1. Departamento de Matemática y Computación, Universidad del Zulia, Maracaibo, 4001, Venezuela;2. Departamento de Matemática Aplicada, Universidad de Granada, Av. Fuentenueva sn, 18071 Granada, Spain |
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Abstract: | The dynamics of a bead sliding without friction along a periodically pulsating wire is under consideration. If the arc length of the wire is taken as the relevant coordinate, the motion of the bead is described by a periodic newtonian equation. Sufficient conditions are derived assuring that a given equilibrium is of twist type, a property that implies its nonlinear stability as well as a KAM scenario around it. Special attention is paid to the stabilization of unstable equilibria, in parallel with the stabilization of the inverted pendulum. |
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