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On the Stability of the Regular Precession of an Asymmetric Gyroscope at a Second-order Resonance

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Abstract

The motion of a rigid body about a fixed point in a homogeneous gravitational field is investigated. The body is not dynamically symmetric and its center of gravity lies on the perpendicular, raised from the fixed point, to one of the circular sections of an ellipsoid of inertia. A body with such mass geometry may precess regularly about a nonvertical axis (Grioli’s precession). The problem of the orbital stability of this precession is solved for critical cases of second-order resonance, when terms higher than degree four in the series expansion of the Hamiltonian of the perturbed motion should be taken into account.

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Funding

This research was partially supported by the Russian Foundation for Basic Research (project No. 17-01-00123) and was carried out within the framework of the state assignment (registration No. AAAA-A17-117021310382-5) at the Ishlinskii Institute of Mechanics Problems (Russian Academy of Sciences) and at the Moscow Aviation Institute (National Research University).

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  1. Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101-1, Moscow, 119526, Russia

    Anatoly P. Markeev

  2. Moscow Aviation Institute (National Research University), Volokolamskoe shosse 4, Moscow, 125080, Russia

    Anatoly P. Markeev

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  1. Anatoly P. Markeev
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Correspondence to Anatoly P. Markeev.

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The authors declare that they have no conflicts of interest.

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Markeev, A.P. On the Stability of the Regular Precession of an Asymmetric Gyroscope at a Second-order Resonance. Regul. Chaot. Dyn. 24, 502–510 (2019). https://doi.org/10.1134/S1560354719050046

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  • DOI: https://doi.org/10.1134/S1560354719050046

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