Stability of the steady rotations of a satellite with internal damping in a central gravitational field

Amel’kin, N. I.; Kholoshchak, V.V.

doi:10.1016/j.jappmathmech.2017.08.002

Cited by 13 publications

(21 citation statements)

References 4 publications

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“…Based on the Eqs. (36a) -(36d) and the particular solutions (28) and (30), if γ * = 3, q * 1 = ν/2, the unperturbed motion (37) and the Hamiltonian (39) corresponding to the particular solution (28); if γ * = 1, q * 1 = −ν/2, they corresponding to another particular solution (30). According to the Eq.…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…According to the Eqs. (43) and (44), the necessary conditions for the existence of the particular solutions (28) and (30) are given as follows:…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…In a plane of dimensionless parameters α and β, the region that the particular solutions (28) and 30exist is shown as Fig. 3.…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…3. The following is a detailed stability analysis of the particular solutions (28) and (30) in their existing region.…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…The stability analysis of the particular solutions (28) and (30) starts with the investigation of the linearized system…”

Section: Linear Stability Analysismentioning

confidence: 99%

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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.

show abstract

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…According to the Eqs. (43) and (44), the necessary conditions for the existence of the particular solutions (28) and (30) are given as follows:…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…In a plane of dimensionless parameters α and β, the region that the particular solutions (28) and 30exist is shown as Fig. 3.…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…3. The following is a detailed stability analysis of the particular solutions (28) and (30) in their existing region.…”

Section: Particular Solutions and The Equations Of Perturbed Motionmentioning

confidence: 99%

“…The stability analysis of the particular solutions (28) and (30) starts with the investigation of the linearized system…”

Section: Linear Stability Analysismentioning

confidence: 99%

See 3 more Smart Citations

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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On the stability of periodic motions of a two-body system with flexible connection in an elliptical orbit

Xue

Zhao

et al. 2021

Nonlinear Dyn

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Attitude dynamics of a dual-spin nanosatellite with a gravitational damper

Doroshin,

Eremenko

2024

Advances in Space Research

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Stability of the steady rotations of a satellite with internal damping in a central gravitational field

Cited by 13 publications

References 4 publications

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

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

On the stability of periodic motions of a two-body system with flexible connection in an elliptical orbit

Attitude dynamics of a dual-spin nanosatellite with a gravitational damper

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