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Stability in the Regular Precession of an Asymmetrical Gyroscope in the Critical Case of Fourth-Order Resonance

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Abstract

The motion of a solid around a stationary point in a uniform gravity field is considered. The mass geometry of this body is such that it can perform regular precession around an axis inclined to a vertical (Grioli precession). The problem about the orbital stability of this precession is solved in the critical case of fourth-order resonance, when the terms to a power higher than the fourth with respect to perturbations (including the sixth-power terms) must be taken into account in the expansion of the Hamiltonian function.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics RAS, 117526, Moscow, Russia

    A. P. Markeev

  2. Moscow Aviation Institute (National Research University), 125993, Moscow, Russia

    A. P. Markeev

  3. Moscow Institute of Physics and Technology (State University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    A. P. Markeev

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  1. A. P. Markeev
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Correspondence to A. P. Markeev.

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Translated by E. Glushachenkova

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Markeev, A.P. Stability in the Regular Precession of an Asymmetrical Gyroscope in the Critical Case of Fourth-Order Resonance. Dokl. Phys. 63, 297–301 (2018). https://doi.org/10.1134/S1028335818070078

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  • DOI: https://doi.org/10.1134/S1028335818070078

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