The equilibrium positions of a satellite carrying a three-degree-of-freedom powered gyroscope in a central gravitational field

Amel’kin, N. I.

doi:10.1016/j.jappmathmech.2013.07.008

Cited by 2 publications

(1 citation statement)

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“…During the last few decades, studies on the periodic solutions and the attitude stability of a rigid body in an elliptical orbit mainly discussed simple systems such as dynamically symmetric rigid body and dumbbell satellites etc. Although the stability of the relative equilibrium of a mutibody spacecraft in a circular orbit has been studied extensively [27,28,29,30,31], to the best of authors' knowledge, there are no investigations about the attitude stability of multibody systems in an elliptical orbit at the moment. Therefore, we focus on the attitude stability of a flexible connected two-body system in an elliptical orbit.…”

Section: Introductionmentioning

confidence: 99%

On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

Zhong

Zhao

et al. 2021

Preprint

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This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third and fourth order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coeffcients of the normalized Hamiltonian. Then a nonlinear stability analysis for two periodic solutions is performed in the third and fourth order resonance cases as well as in the nonresonance case.

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