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On the Impossibility of Global Stabilization of the Lagrange Top

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Abstract

It is shown that the problem of the asymptotic stabilization of a given position of the Lagrange top for any control from a sufficiently wide class does not permit the existence of a single uniformly asymptotically stable equilibrium, even with possible impacts of the top against the horizontal plane; i.e., the global stabilization of the system is impossible. In particular, we show that it is impossible to globally stabilize the top by moving its pivot point along the horizontal plane.

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Authors and Affiliations

  1. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, 119991, Russia

    I. Yu. Polekhin

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  1. I. Yu. Polekhin
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Correspondence to I. Yu. Polekhin.

Additional information

Original Russian Text © I.Yu. Polekhin, 2018, published in Prikladnaya Matematika i Mekhanika, 2018, Vol. 82, No. 5, pp. 599–604.

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Polekhin, I.Y. On the Impossibility of Global Stabilization of the Lagrange Top. Mech. Solids 53 (Suppl 2), 71–75 (2018). https://doi.org/10.3103/S002565441805014X

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  • DOI: https://doi.org/10.3103/S002565441805014X

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