Application of Lagrangian coherent structures to Coulomb formation on elliptic orbit
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ORIGINAL PAPER
Application of Lagrangian coherent structures to Coulomb formation on elliptic orbit Mingpei Lin . Yaru Zheng . Ming Xu
Received: 29 November 2019 / Accepted: 17 September 2020 Springer Nature B.V. 2020
Abstract Coulomb thrusting presents attractive prospects in many astronautical missions from the standpoint of close-proximity formation flying. In this study, a dynamical model of Coulomb formation and its Hamiltonian is derived on the basis of the Tschauner–Hempel equation. As a nonautonomous system, it is more complicated than the dynamical model based on the Clohessy–Wiltshire equation. The Lagrangian coherent structure (LCS), a useful tool for describing the dynamical behavior of nonautonomous systems, is used to study the Coulomb formation dynamics, design, and reconfiguration. Simulation results show that, in the autonomous case of Coulomb formation, the LCS coincides with the invariant manifolds in the proper Poincare´ section. When it is extended to the nonautonomous case with a smalleccentricity reference orbit, the global morphology of the Coulomb formation dynamics remains almost unchanged. Based on the property that the LCS can act as the transport barrier in dynamical systems, it is used to construct homoclinic and heteroclinic orbits and search for invariant relative orbits and transfer trajectories for formation design and reconfiguration.
M. Lin Y. Zheng M. Xu (&) School of Astronautics, Beihang University, Beijing 100191, China e-mail: [email protected]
Keywords Coulomb formation flying Lagrangian coherent structures Finite-time Lyapunov field Formation reconfiguration
1 Introduction Close-proximity formation flying has many applications in multiple astronautical missions. Marked by fast throttle ability, extremely low propellant consumption, and avoidance of plume impingement issues [1–3], Coulomb thrusting has attracted sustained attention in close-proximity formation maintenance and reconfiguration. The feasibility of active spacecraft potential control [4] has been verified in several space missions, such as SCATHA [5], ATS [6], and CLUSTER [7]. Early investigations into Coulomb formation flying focused on orbital dynamics and control. Felicetti and Palmerini [8] investigated the stability of Coulomb formation by using a sequence of purposely defined Lyapunov functions and developed a specific underactuated control strategy to control selected ‘‘virtual links’’ of the formation. In other research [9], a Lyapunov-based global control strategy was presented and applied to formation construction and maintenance. Subsequently, the charge distribution was optimized to reduce the power requirements and the number of charge switches. Considering the best
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features of the tethered formation and Coulomb formation, Qi and Misra [10] proposed a ‘‘Coulomb tether double-pyramid’’ formation. The analytical charges and tether extensions for stationary formation were determined, and open-loop charge control st
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