Dynamics of Nanosatellite Deorbit by Bare Electrodynamic Tether in Low Earth Orbit

Zhong, Rui; Zhu, Zheng H.

doi:10.2514/1.a32336

Cited by 57 publications

(11 citation statements)

References 22 publications

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“…In LEO, the last perturbation is generally orders of magnitude smaller than the others and can be safely ignored in the current study [31]. It is worth pointing out here that the geodetic altitude, instead of geocentric altitude, should be used to calculate the atmospheric and plasma densities (in the following subsection) in order to account for the Earth's oblateness [27].…”

Section: B Environmental Perturbation Forcesmentioning

confidence: 99%

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Zhu

Cain

et al. 2016

Journal of Guidance, Control, and Dynamics

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The paper investigates the elastic, thermal, and electrical coupling effects on the dynamics and libration stability of flexible bare electrodynamic tethers in the end-of-mission satellite deorbit. A high-fidelity model is developed by considering transverse and longitudinal dynamics and libration dynamics of the tether and environmental effects with the latest models for atmospheric and plasma density, as well as Earth gravity and magnetic fields. The long-term orbital and libration dynamics of the tether are analyzed by a nodal position finite element method and symplectic time integration. Orbital motion limited theory is used to model the electron collection by bare electrodynamic tethers, whereas a Fowler-Nordheim equation is used for a Spindt array cathode. The thermal effect and its coupling with the dynamics of electrodynamic tethers are investigated parametrically. It is found that the thermal effect significantly affects the stability of electrodynamic tethers, which must be considered in the stability control. Two practical and effective electrical current on/off control strategies are developed based on the libration energy and libration angles. Although the libration energy control is found to be more stable and efficient than the libration angle control, the latter is more appealing for practical applications due to its simplicity and low computational effort. NomenclatureA t , A s = cross section or stress area of tether and projected drag area of satellite, m 2 B g = vector of Earth magnetic field strength in the global frame, T c m = specific heat of tether material, J · kg · K −1 d = tether diameter, m e E = eccentricity of electrodynamic tether orbital plane H 0 = Hamiltonian of tethered system in equilibrium configuration, J I t = electrical current at electron emitter device, A L, L = total and characteristic length of tether, m L e0 L e = unstretched length (instant length) of tether element, m M yaw , M in , M out = components of electrodynamic torque in system orbital frame, N · m n orb = orbital mean motion, rad · s −1 Q = thermal flux, W · m 2 R e = electrical resistance in tether, Ω R, S, W = unit vector of orbital frame of tethered system T, T 0 = instant and initial temperature, K t = time t, n, b = unit vectors of the local frame of tether element V cc = potential bias at the cathodic end C with respect to the ambient plasma, V X, Y, Z = components of position vector in global geocentric inertial frame, m Z T = impedance of emitter device, Ω α, _ α = pitch angle and pitch angular velocity of virtual tether, rad α p , _ α p = periodic solution of pitch angle, rad; and angular velocity of virtual tether, rad · s −1 α s ∕ε = ratio of absorptivity to emissivity of the tether β, _ β = roll angle, rad; and angular velocity of virtual tether, rad · s −1 θ, θ 0 = north latitude and colatitude, rad λ = east longitude, rad μ g = gravitational constant of Earth, m 3 s −2 ρ a ,ρ t = atmospheric density and material density of tether, kg · m −3 σ = electrical conductivity of tether material, Ω −1...

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Section: B Environmental Perturbation Forcesmentioning

confidence: 99%

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Zhu

Cain

et al. 2016

Journal of Guidance, Control, and Dynamics

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“…The miniaturized EDT is a fundamentally novel paradigm because it is much shorter than a conventional EDT, with total length of about 10-20 m, and the tethered end masses are small, subkilogram spacecraft. In contrast, previously proposed "short-tether" concepts were 100-1000 m in length and had 10-100 kg end masses [29][30][31][32][33].…”

Section: B Miniaturized Edt System Concept Descriptionmentioning

confidence: 99%

Investigating Miniaturized Electrodynamic Tethers for Picosatellites and Femtosatellites

Bell¹,

Gilchrist²,

McTernan³

et al. 2017

Journal of Spacecraft and Rockets

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Section: Introductionmentioning

confidence: 99%

“…It is well known that the high-degree IGRF model can make significant difference in numerical analysis by using 13 degree model. In the study of the dynamics of nanosatellite deorbit by EDT, Zhong and Zhu 18 used 13 degree IGRF2000 model and discussed the error margin of the model. Li et al 19 took 13 degree IGRF2010 model to calculate the Lorentz force acting on the tether elements in the investigation of libration dynamics of EDT considering elastic-thermal-electrical coupling.…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions and stability analysis of electrodynamic tethers for 13 degree international geomagnetic reference field

Yang

Cai

2018

Proceedings of the Institution of Mechanical Engineers, Part G:

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The geomagnetic field plays a crucial role in the operation of the electrodynamic tether system in the space. Using the 13 degree International Geomagnetic Reference Field to model the geomagnetic field, the libration dynamic equation of the system is established. The nonlinear libration dynamic equation of the system is a typical chaotic system. In the dynamic equation, there are four free parameters: the orbital inclination, the orbital eccentricity, the altitude of the perigee and the electrodynamic parameter. After adding dummy control terms into the dynamic system, the extended time delayed autosynchronization control method is employed to calculate the periodic solutions of the dynamic equation. The shapes and amplitudes of the periodic libration motions change with the free parameters regularity. Based on the Floquet theory, the stabilities of the periodic solutions are analyzed. The orbit time during which the initial periodic libration turns to the rotation motion is defined as the failure time. It is used to measure the instability of the periodic solution and validate the results from the Floquet theory. Simulations show that the results from the failure time are consistent with the results from the Floquet theory. For all parameters, the periodic solutions are all unstable. In addition, the relationships between the instabilities of the periodic solutions and the free parameters are obtained.

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Dynamics of Nanosatellite Deorbit by Bare Electrodynamic Tether in Low Earth Orbit

Cited by 57 publications

References 22 publications

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Investigating Miniaturized Electrodynamic Tethers for Picosatellites and Femtosatellites

Periodic solutions and stability analysis of electrodynamic tethers for 13 degree international geomagnetic reference field

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