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This article is cited in 13 scientific papers (total in 13 papers)
On the Stability of Resonant Rotation of a Symmetric Satellite in an Elliptical Orbit
Boris S. Bardin, Evgeniya A. Chekina Theoretical Mechanics Department, Faculty of Applied Mathematics and Physics, Moscow Aviation Institute, Volokolamskoe sh. 4, Moscow, 125871 Russia
Abstract:
We deal with the stability problem of resonant rotation of a symmetric rigid body about its center of mass in an elliptical orbit. The resonant rotation is a planar motion such that the body completes one rotation in absolute space during two orbital revolutions of its center of mass. In [1–3] the stability analysis of the above resonant rotation with respect to planar perturbations has been performed in detail.
In this paper we study the stability of the resonant rotation in an extended formulation taking into account both planar and spatial perturbations. By analyzing linearized equations of perturbed motion, we found eccentricity intervals, where the resonant rotation is unstable. Outside of these intervals a nonlinear stability study has been performed and subintervals of formal stability and stability for most initial data have been found. In addition, the instability of the resonant rotation was established at several eccentricity values corresponding to the third and fourth order resonances.
Our study has also shown that in linear approximation the spatial perturbations have no effect on the stability of the resonant rotation, whereas in a nonlinear system they can lead to its instability at some resonant values of the eccentricity.
Keywords:
Hamiltonian system, symplectic map, normal form, resonance, satellite, stability.
Citation:
Boris S. Bardin, Evgeniya A. Chekina, “On the Stability of Resonant Rotation of a Symmetric Satellite in an Elliptical Orbit”, Regul. Chaotic Dyn., 21:4 (2016), 377–389
Linking options:
https://www.mathnet.ru/eng/rcd84 https://www.mathnet.ru/eng/rcd/v21/i4/p377
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Abstract page: | 213 | References: | 31 |
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