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Regul. Chaotic Dyn., 2019, Volume 24, Issue 5, Pages 502–510 (Mi rcd1023)  

Sergey Chaplygin Memorial Issue

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

Anatoly P. Markeevab

a Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101-1, Moscow, 119526 Russia
b Moscow Aviation Institute (National Research University), Volokolamskoe shosse 4, Moscow, 125080 Russia

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 (Grioliís 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.

Keywords: rigid body, precession, stability

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00123
Ministry of Education and Science of the Russian Federation AAAA-A17-117021310382-5
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).


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

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Bibliographic databases:

MSC: 70E17, 70E50, 70H14
Received: 10.04.2019
Accepted:27.07.2019
Language:

Citation: Anatoly P. Markeev, “On the Stability of the Regular Precession of an Asymmetric Gyroscope at a Second-order Resonance”, Regul. Chaotic Dyn., 24:5 (2019), 502–510

Citation in format AMSBIB
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\by Anatoly P. Markeev
\paper On the Stability of the Regular Precession of an Asymmetric Gyroscope at a Second-order Resonance
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 5
\pages 502--510
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