Bifurcation of equilibria for general case of gyrostat satellite on a circular orbit

Santos, Luís F. F. M.; Melício, Rui

doi:10.1016/j.ast.2020.106058

Cited by 8 publications

(10 citation statements)

References 19 publications

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“…In the current paper, a gyrostat satellite with a particular configuration is studied. As mentioned above, a previous study Santos and Melicio, 2020, detected small equilibria regions when the gyrostatic moment of inertia is tangent to the orbital plane. The existence of these regions needs confirmation, as well as subsequent analysis of both the equilibria and stability of this case.…”

Section: Introductionmentioning

confidence: 60%

“…Gutnik et al (2015), Santos (2015) conducted a deep analysis of different equilibria and stability. Santos and Melicio (2020) described the number of equilibria orientations of the general case, when its angular momentum is not aligned with any principal axis of the satellite nor with any orbital coordinate frame. A complete numerical analysis was then performed to understand the evolution of the number of equilibria orientations.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

Morais

Santos

Silva

et al. 2022

Advances in Space Research

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Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

Morais

Santos

Silva

et al. 2022

Advances in Space Research

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“…It can be seen, from the cyclic integral (15), that the projection of the angular velocity of the platform on the symmetry axis ω z is the integration constant of the cyclic integral, which is a constant that depends on the initial conditions. Here, we study the special case of ω z = 0, then the corresponding generalized momentum…”

Section: Equations Of Motionmentioning

confidence: 99%

Effect of gyroscopic moments on the attitude stability of a satellite in an elliptical orbit

Zhao

Zhong

et al. 2023

Preprint

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The gyroscopic moments generated by flywheels or control moment gyroscopes have important applications in spacecraft attitude stability and control. However, most of the current research has focused on the effect of gyroscopic torques on the attitude stability of spacecrafts on circular orbits, with little discussion of the case of elliptical orbits. In this paper, we investigate the stability of a particular cylindrical precession in an elliptical orbit by simplifying the spacecraft to a dynamically symmetric gyrostat consisting of a rotor and a platform. In the case of circular orbits, the system discussed here is autonomous, whereas in the case of elliptical orbits it is a periodic Hamiltonian system. The stability of cylindrical precession has been investigated analytically for the case of circular orbits. In the case of elliptical orbits, Floquet theory was used to numerically obtain the unstable regions and linear stable regions of the cylindrical precession. The nonlinear stability was further investigated in the linear stability region of the cylindrical precession. The results indicated that, in the case of the circular orbit, the cylindrical precession can be stabilized as long as the gyroscopic moment is large enough. However, the system may lose its stability even if the gyroscopic torque is sufficiently large in an elliptical orbit. Moreover, we present the effect of gyroscopic moments on the stability of cylindrical precession in three different elliptical orbits with eccentricities of 0.05, 0.2, and 0.5, using stability diagrams.

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“…e bifurcation diagram [12] for the parameter makes it easy for predicting the type of bifurcation and existence of chaos in system (1). Chaos has a vital role in engineering [13][14][15][16][17], medical [18][19][20], aeronautics [14,21] and fluid dynamics [22][23][24]. Apart from the above cited applications, its great influence can also be found in fractional calculus [25][26][27] and reference therein.…”

Section: Introductionmentioning

confidence: 99%

“…21, λ 12 � − 6.75, λ 13 � 14.17. Equation (41) illustrates that two states will move away from E 1 , while a single state will move inward towards equilibria: E 1 , and such information shows occurrence of the saddle.…”

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confidence: 99%

Existence of Solution and Self‐Exciting Attractor in the Fractional‐Order Gyrostat Dynamical System

2022

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This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional-order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self-exciting attractors and a separatrix in a global domain.

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Bifurcation of equilibria for general case of gyrostat satellite on a circular orbit

Cited by 8 publications

References 19 publications

Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

Effect of gyroscopic moments on the attitude stability of a satellite in an elliptical orbit

Existence of Solution and Self‐Exciting Attractor in the Fractional‐Order Gyrostat Dynamical System

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