Email this article Stability in the Regular Precession of an Asymmetrical Gyroscope in the Critical Case of Fourth-Order Resonance
- Authors: Markeev A.P.1,2,3
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Affiliations:
- Ishlinsky Institute for Problems in Mechanics RAS
- Moscow Aviation Institute (National Research University)
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 63, No 7 (2018)
- Pages: 297-301
- Section: Mechanics
- URL: https://journals.rcsi.science/1028-3358/article/view/192377
- DOI: https://doi.org/10.1134/S1028335818070078
- ID: 192377
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Abstract
The motion of a solid around a stationary point in a uniform gravity field is considered. The mass geometry of this body is such that it can perform regular precession around an axis inclined to a vertical (Grioli precession). The problem about the orbital stability of this precession is solved in the critical case of fourth-order resonance, when the terms to a power higher than the fourth with respect to perturbations (including the sixth-power terms) must be taken into account in the expansion of the Hamiltonian function.
About the authors
A. P. Markeev
Ishlinsky Institute for Problems in Mechanics RAS; Moscow Aviation Institute (National Research University); Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: anat-markeev@mail.ru
Russian Federation, Moscow, 117526; Moscow, 125993; Dolgoprudnyi, Moscow oblast, 141700
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