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.
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).
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
\Bibitem{Mar19}
\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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Linking options:
https://www.mathnet.ru/eng/rcd1023
https://www.mathnet.ru/eng/rcd/v24/i5/p502
This publication is cited in the following 2 articles:
Jie Zhao, Xue Zhong, Kaiping Yu, Minqiang Xu, “Effect of gyroscopic moments on the attitude stability of a satellite in an elliptical orbit”, Nonlinear Dyn, 111:16 (2023), 14957
“Anatoly Pavlovich Markeev. On the Occasion of his 80th Birthday”, Rus. J. Nonlin. Dyn., 18:4 (2022), 467–472
Citation in format AMSBIB
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