Dynamic behavior analysis of tethered satellite system based on Floquet theory

Zhu, Guangnan; Lu, Kuan; Cao, Qingjie; Huang, Panfeng; Zhang, Kangyu

doi:10.1007/s11071-022-07466-8

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…The other one is to use the multi-scale method to solve nonlinear vibration equations, the differential equations related to amplitude and phase can be obtained. The periodic solution of the system corresponds to the equilibrium point of this equation, and the stability of the original periodic solution can be studied through the stability of this equilibrium point [30]. Using the eigenvalues of the Jacobian matrix to make judgments, when the eigenvalues of the Jacobian matrix of the system are all negative, the system is stable; if the eigenvalues of the system have positive real parts, the system becomes unstable.…”

Section: Stability Of Periodic Solutions and Bifurcation Analysismentioning

confidence: 99%

Nonlinear vibration and amplitude ratio output performance of a resonant micro-gyroscope based on bifurcation detection

Hao,

Li,

Zhang

2024

Phys. Scr.

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In this paper, we design a 3-degree-of-freedom (3-DOF) nonlinear resonant micro-gyroscope, which innovatively utilizes the bifurcation phenomenon of the nonlinear resonant beam as a detection method and uses the amplitude ratio before and after bifurcation as the sensitivity output of the system. The steady-state response of the driving equation is first solved by the complex exponential method. Coriolis force is amplified by the lever mechanism and transmitted to the axial direction of the resonant beam. The dimensions of the resonant beam are designed so that the frequency of Coriolis force is in a 2:1 relationship with the natural frequency of the resonant beam to enhance the parametric excitation effect. Subsequently, Hamilton principle and Galerkin method are used to derive and discretize the dynamical equations of the resonant beam containing axial force, respectively. The multi-scale method is used to perturbation analysis of discrete equations. Finally, the bifurcation characteristics and the amplitude-frequency response with different input angular velocities are studied. The results show that the comprehensive performance of the micro-gyroscope system using backward frequency sweep (BFS) is better than forward frequency sweep (FFS). Furthermore, by using the BFS, the relative sensitivity of the nonlinear resonant micro-gyroscope based on the amplitude ratio variation rises by about 168 times compared with that based on the frequency variation in the linear case. In addition, when considering the input angular velocity with the same magnitude but different directions, the bifurcation frequency of resonant beam is closely related to the direction of the input angular velocity, and the direction of the input angular velocity can be further identified by utilizing this phenomenon.

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Section: Stability Of Periodic Solutions and Bifurcation Analysismentioning

confidence: 99%

Nonlinear vibration and amplitude ratio output performance of a resonant micro-gyroscope based on bifurcation detection

Hao,

Li,

Zhang

2024

Phys. Scr.

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“…The Floquet theory [35] With frame O − XYZ, whose origin is at the Earth's center, the X-axis points in the Vernal Equinox direction, the Z-axis points towards the north pole, and the Y-axis lies in the plane of the equator and completes the right-handed triad. The orbital coordinate system of the target spacecraft, which is denoted as s − xyz, is a relative coordinate system in which s represents the target spacecraft and c denotes the mission spacecraft.…”

Section: Floquet Theorymentioning

confidence: 99%

Application of the Relative Orbit in an On-Orbit Service Mission

Zhang²,

et al. 2023

Electronics

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To achieve an on-orbit service mission, the mission spacecraft must approach the target spacecraft first, which is based on the spacecraft’s relative motion. To enhance the safety and reliability of on-orbit service missions, the relative hovering orbit was proposed and needed to be studied further. A high-precision design method for hovering orbit is presented based on the relative dynamics model of spacecraft in this paper. Firstly, based on the stability analysis of the spacecraft relative dynamics model, a method to determine the initial value of periodic relative motion orbit is explored, and an example is given to verify the validity of the method. Then, through theoretical analysis, the formulae of control acceleration required during the hovering flying mission were put forward for both without considering perturbation and with considering J2 perturbation, and numerical simulations for hovering orbit were made to verify the feasibility of the approaches proposed. Simulation results show that the control acceleration curves are smooth, which indicates that the hovering flying mission is easier to achieve, and the control method based on sliding mode control theory is adopted for hovering control. The relative hovering method proposed can provide references in space on-orbit service missions for practical engineers.

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Dynamics of a Phobos-anchored tether near the L1 libration point

Aslanov

2022

Nonlinear Dyn

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Dynamic behavior analysis of tethered satellite system based on Floquet theory

Cited by 5 publications

References 19 publications

Nonlinear vibration and amplitude ratio output performance of a resonant micro-gyroscope based on bifurcation detection

Nonlinear vibration and amplitude ratio output performance of a resonant micro-gyroscope based on bifurcation detection

Application of the Relative Orbit in an On-Orbit Service Mission

Dynamics of a Phobos-anchored tether near the L1 libration point

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