Ricci-based chaos analysis for roto-translatory motion of a Kelvin-type gyrostat satellite

Abtahi, Sayyed Mahdi; Sadati, Seyed Hossein; Salarieh, Hassan

doi:10.1177/1464419313504915

Cited by 7 publications

(8 citation statements)

References 22 publications

(44 reference statements)

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“…According to the Hamiltonian in equation (17), È is a cyclic coordinate, as it does not directly appear in the Hamiltonian. The generalized momentum P È relative to the cyclic coordinate is a constant of motion.…”

Section: Reduction Of Hamiltonianmentioning

confidence: 99%

“…Substituting equations (21) to (25) into equations (17) to (20), the reduced Hamiltonian is obtained as…”

Section: Reduction Of Hamiltonianmentioning

confidence: 99%

“…One such method is the Deprit canonical transformation. 16,17 The orbital motion exceedingly affects in the attitude dynamics of the GS, particularly in the augmentation of chaotic vibrations in the spin motion. In this work, the interactions of the orbital motion on its spin dynamics of the GS as a novel approach are illustrated.…”

Section: Introductionmentioning

confidence: 99%

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Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

Abtahi

2019

Proceedings of the Institution of Mechanical Engineers, Part K:

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Interactions of the orbital motion on attitude dynamics of the gyrostat satellite are considered in this paper. The mathematical model is derived using the Hamiltonian method for the spin-orbit motion of the spacecraft followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method is used innovatively to study chaos on the complex Spin-Orbit dynamics of the gyrostat satellite. Also, the numerical methods such as Lyapunov exponent criterion, Poincaré section, trajectories of phase portrait, and the time–history responses can be proved the heteroclinic bifurcation and chaotic vibrations in the highly nonlinear system. Using the results based on the Melnikov integral, the parameters of the spacecraft including the mass and inertia moment of satellite with respect to the altitude of orbit can be designed in order to control the bifurcation with a view to prevention of chaos in the system in the absence of an active control system.

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Section: Reduction Of Hamiltonianmentioning

confidence: 99%

“…Substituting equations (21) to (25) into equations (17) to (20), the reduced Hamiltonian is obtained as…”

Section: Reduction Of Hamiltonianmentioning

confidence: 99%

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Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

Abtahi

2019

Proceedings of the Institution of Mechanical Engineers, Part K:

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“…where the explicit expressions of such coefficients depend on the functional parametric form given to the embedding constraints in Eq. (92). From Eq.…”

Section: E Complexity Reduction Arising From Macrocorrelationsmentioning

confidence: 99%

Theoretical investigations of an information geometric approach to complexity

Ali

Cafaro

2017

Rev. Math. Phys.

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It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. The existence of fundamental links among physical systems, dynamical equations, experimental data and statistical modeling motivate us to present in this article our theoretical modeling scheme which combines information geometry and inductive inference methods to provide a probabilistic description of complex systems in the presence of limited information. Special focus is devoted to describe the role of our entropic information geometric complexity measure. In particular, we provide several illustrative examples wherein our modeling scheme is used to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, limitations, possible improvements, and future investigations are discussed.

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“…All of these analyses specially illustrate the chaotic behavior in comparison with random responses, because the periodic uneven road surface is induced on the vehicle but the numerous frequencies are created in the output responses (Figures 2 to 4). 14,22,23 Chaos control strategy…”

Section: Mathematical Modelmentioning

confidence: 99%

Chaotic study and chaos control in a half-vehicle model with semi-active suspension using discrete optimal Ott–Grebogi–Yorke method

Abtahi

2016

Proceedings of the Institution of Mechanical Engineers, Part K:

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The chaotic dynamics along with the control of chaos in a half-car model with semi-active suspension system is considered in this paper. The time series responses, phase space trajectories, Poincaré sections, and Lyapunov exponent methods are used to analyze the chaotic behavior in the open-loop system. In order to suppress the chaotic responses in the system, a chaos controller is applied based on the development of Ott-Grebogi-Yorke algorithm. In this new control strategy, the Poincaré map of the system is estimated using the support vector machine innovatively. After linearization of the Poincaré map, the optimal discrete-time linear quadratic regulator is designed for the linear map as a main contribution. The discrete optimal Ott-Grebogi-Yorke controller improves the performance of the system along with the rejection of chaos in the responses. This improvement involves the reduction in settling time, control effort, and energy consumption in the suspension system.

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Ricci-based chaos analysis for roto-translatory motion of a Kelvin-type gyrostat satellite

Cited by 7 publications

References 22 publications

Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

Theoretical investigations of an information geometric approach to complexity

Chaotic study and chaos control in a half-vehicle model with semi-active suspension using discrete optimal Ott–Grebogi–Yorke method

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