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This article is cited in 1 scientific paper (total in 2 paper)
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 (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.
Keywords:
rigid body, precession, stability.
Received: 10.04.2019 Accepted: 27.07.2019
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
Linking options:
https://www.mathnet.ru/eng/rcd1023 https://www.mathnet.ru/eng/rcd/v24/i5/p502
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Abstract page: | 117 | References: | 16 |
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