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
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.
rigid body, precession, stability
|Russian Foundation for Basic Research
|Ministry of Education and Science of the Russian Federation
|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).
MSC: 70E17, 70E50, 70H14
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
\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.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|